2.2.1.

Autoencoder

An AE is an NN that is used for unsupervised learning of efficient codings (from unlabeled data). The AE’s codings often reveal useful features from unsupervised data. One of the first AE applications was dimensionality reduction, which is required in many RS applications. One advantage of using an AE with RS data is that the data do not need to be labeled. In an AE, reducing the size of the adjacent layers forces the AE to learn a compact representation of the data. The AE maps the input through an encoder function $f$ to generate an internal (latent) representation, or code, $h$. The AE also has a decoder function, $g$ that maps $h$ to the output $\widehat{\mathbf{x}}$. Let an input vector to an AE be $\mathbf{x}\in {\mathbb{R}}^d$. In a simple one hidden layer case, the function $h=f(\mathbf{x})=g(\mathbf{Wx}+\mathbf{b})$, where $\mathbf{W}$ is the learned weight matrix and $\mathbf{b}$ is a bias vector. A decoder then maps the latent representation to a reconstruction or approximation of the input via ${\mathbf{x}}^{\prime }=f^{\prime }({\mathbf{W}}^{\prime }\mathbf{x}+{\mathbf{b}}^{\prime })$, where ${\mathbf{W}}^{\prime }$ and ${\mathbf{b}}^{\prime }$ are the decoding weight and bias, respectively. Usually, the encoding and decoding weight matrices are tied (shared), so that ${\mathbf{W}}^{\prime }={\mathbf{W}}^T$, where $T$ is the matrix transpose operator.

In general, the AE is constrained, either through its architecture, or through a sparsity constraint (or both), to learn a useful mapping (but not the trivial identity mapping). A loss function $\mathcal{L}$ measures how close the AE can reconstruct the output: $\mathcal{L}$ is a function of $\mathbf{x}$ and $\widehat{\mathbf{x}}=f^{\prime }[f(\mathbf{x})]$. For example, a commonly used loss function is the mean squared error, which penalizes the approximated output from being different from the input, $\mathcal{L}(x,x^{\prime })={\Vert \mathbf{x}-{\mathbf{x}}^{\prime }\Vert }^2$.

A regularization function $\mathrm{\Omega }(h)$ can also be added to the loss function to force a more sparse solution. The regularization function can involve penalty terms for model complexity, model prior information, penalizing based on derivatives, or penalties based on some other criteria such as supervised classification results (reference Sec. 14.2 of Ref. 23). Regularization is typically used with a deep encoder, not a shallow one. Regularization encourages the AE to have other properties than just reconstructing the input, such as making the representation sparse, robust to noise, or constraining derivatives in the representation. Arpit et al.²⁴ show that denoising and contractive AEs that also contain activations such as sigmoid or rectified linear units (ReLUs), which are commonly found in many AEs, satisfy conditions sufficient to encourage sparsity. A common practice is to add a weighted regularizing term to the optimization function, such as the $l_1$ norm, ${\Vert \mathbf{h}\Vert }_1=\sum _{m=1}^K|h[i]|$, where $K$ is the dimensionality of $\mathbf{h}$ and $\lambda$ is a term which controls how much effect the regularization has on the optimization process. This optimization can be solved using alternating optimization over $\mathbf{W}$ and $\mathbf{h}$.

A denoising autoencoder (DAE) is an AE designed to remove noise from a signal or an image. Chen et al.²⁵ developed an efficient DAE, which marginalizes the noise and has a computationally efficient closed-form solution. To provide robustness, the system is trained using additive Gaussian noise or binary masking noise (force some percentage of inputs to zero). Many RS applications use an AE for denoising. Figure 1(a) shows an example of an AE. The diabolo shape results in dimensionality reduction.

Fig. 1

Block diagrams of DL architectures: (a) AE, (b) CNN, (c) DBN, and (d) RNN.

2.2.2.

Convolutional neural network

A CNN is a network that is loosely inspired by the human visual cortex. A typical CNN consists of multiple layers of operations such as convolution, pooling, nonlinear activation functions, and normalization, to name a few. The first part of the CNN is typically the so-called feature extractor and the latter portion of the CNN is usually a multilayer perceptron (MLP), which assigns class labels or computes probabilities of a given class being present in the input.

CNNs have dominated many perceptual tasks. Following Ujjwalkarn,²⁶ the image recognition community has shown keen interest in CNNs. Starting in the 1990s, LeNet was developed by LeCun et al.,²⁷ and was designed for reading zip codes. It generated great interest in the image processing community. In 2012, Krizhevsky et al.²⁸ introduced AlexNet, a deep CNN. It won the ImageNet Large Scale Visual Recognition Challenge (ILSVRC) in 2012 by a significant margin. In 2013, Zeiler and Fergus²² created ZFNet, which was AlexNet with tweaked parameters and won ILSVRC. Szegedy et al.²⁹ won ILSVRC with GoogLeNet in 2014, which used a much smaller number of parameters (4 million) than AlexNet (60 million). In 2015, ResNets were developed by He et al.,³⁰ which allowed CNNs to have very deep networks. In 2016, Huang et al.³¹ published DenseNet, where each layer is directly connected to every other layer in a feedforward fashion. This architecture also eliminates the vanishing-gradient problem, allowing very deep networks. The aforementioned examples are only a few examples of CNNs.

Most layers in the CNN have parameters to estimate, e.g., the convolution filter parameters, or the scales and shifts in batch normalization. For example, a CNN that analyzes grayscale imagery employs two-dimensional (2-D) convolution filters, whereas a CNN that uses red–green–blue (RGB) imagery uses three-dimensional (3-D) filters. In general, it is easy, in theory, to support any $N$-dimensional signal, such as an HSI, as it really only affects the dimensionality of the first layers of filters. Through training, these filters learn to extract hierarchical features directly from the data, versus traditional machine learning approaches, that use “hand-crafted” features. Figure 1(b) shows an example CNN for HSI processing. Note that there are two convolution and pooling layers, followed by two fully connected (FC) layers.

The number of convolution filters and the filter sizes, the pooling sizes and strides, and all other layer operators and associated parameters need to be learned. In general, it has been demonstrated that the lower layers of a CNN typically learn basic features, and as one traverses the depths of the network, the features become more complex and are built up hierarchically. The FC layers are usually near the end of the CNN network, and allow complex nonlinear functions to be learned from the hierarchical outputs of the previous layers. These final layers typically output class labels, estimates of the posterior probabilities of the class label, or some other quantities such as softmax normalized values. Convolution layers perform filtering, e.g., enhancement, denoising, detection, etc., on the outputs of the previous layers. Consider convolution on a single grayscale image using a $m\times m$ mask. If the input data have dimensions of $K\times K$, then the convolution output will be $(K-m+1)\times (K-m+1)$, assuming a stride of one and no padding. Often, CNNs start with smaller mask sizes such as $3\times 3$ or $5\times 5$ and may have different sizes per layer. More information on convolution can be found in Secs. 9.1 and 9.2 of Ref. 23.

Most CNNs then apply a nonlinear activation function $\sigma$ to the linear convolution result. Early CNNs used functions such as the hyperbolic tangent (tanh) or sigmoid function, but researchers later discovered that using a ReLU produced good results and was far more computationally efficient. Using the nonlinear function gives the CNN convolution layers highly expressive power. In most CNNs, there are ReLUs or parametric ReLUs (PReLUs) following the convolution layers. Given the input $x$, the ReLU computes the output as $\mathrm{ReLU}(\mathbf{x})=\max (0,\mathbf{x})$. ReLU units are often used after an affine transformation of the data, such as $\mathrm{ReLU}(\mathbf{x})=\max (0,{\mathbf{w}}^T\mathbf{x}+\mathbf{b})$, where $\mathbf{w}$ is a weight vector, $\mathbf{0}$ is the all zero vector, and $\mathbf{b}$ is a bias vector. For reference refer Sec. 6.3 of Goodfellow et al.²³ for more information.

For RGB imagery, 3-D convolution is used. Likewise, for $N$-dimensional data, a $N$-dimensional convolution is used. Padding can also be applied to keep information around the edge pixels in the input. Zero padding is a common practice in image processing. Another parameter for the convolution masks is the stride, or how many units are shifted in each direction between applications of the convolution mask. For a stride of one, the convolution mask shifts over one unit in each direction. A smaller stride produces larger results because more outputs are produced.

Data can be reduced by pooling, and a commonly used approach is max pooling. Consider an input with a max pooling layer with a $2\times 2$ pooling mask and a stride of two. Figure 2 shows an example input and output. In this instance, the first output is the max of $\{\mathrm{3,2},\mathrm{7,5}\}$, which is 7. The other outputs are computed in a similar manner. The max pooling layer keeps the strongest responses but destroys information on where these responses occurred in the earlier layers. Some other pooling options are average and $l_2$ norm pooling, which is the square root of the sum of squares of the inputs. More information on pooling can be found in Sec. 9.3 of Ref. 23.

Fig. 2

CNN max pooling example with $2\times 2$ pooling and stride of two.

A legitimate question is what hyperparameters to choose? Unfortunately, there is no easy answer to date, just rules of thumb and knowing from the literature what has worked for other researchers. Often experimentation and knowledge of the problem at hand are required. Some good tips can be found in Sec. 11 of Goodfellow et al.²³

For those unfamiliar with CNNs, some good beginner tutorial and explanations can be found in Refs. 32 and 33. For those who want to use TensorFlow, helpful tutorials can be found in Ref. 32. Furthermore, a useful beginning guide to convolutional arithmetic for CNNs is Ref. 34.

2.2.3.

Deep belief network and deep Boltzmann machine

A deep belief network (DBN) is a type (generative) of probabilistic graphical model (PGM), the marriage of probability and graph theory. Specifically, a DBN is a “deep” (large) directed acyclic graph (DAG). A deep Boltzmann machine (DBM), on the other hand, is a similar graph, but is undirected. Thus in a DBM, data can flow both ways, and training can be bottom-up or top-down. A number of well-known algorithms exist for exact and approximate inference [infer the states of unobserved (hidden) variables] and learning (learn the interactions between variables) in PGMs. A DBN can also be thought of as a type of deep NN. In Ref. 35, Hinton showed that a DBN can be viewed and trained (in a greedy manner) as a stack of simple unsupervised networks, namely restricted Boltzmann machines (RBMs), or generative AEs. To date, CNNs have demonstrated better performance on various benchmark CV data sets. However, in theory DBNs are arguably superior. CNNs possess generally a lot more “constraints.” The DBN versus CNN topic is likely subject to change as better algorithms are proposed for DBN learning. Figure 1(c) depicts a DBN, which is made up of RBM layers and a visible layer.

Consider a DBM with $D$ visible and $P$ hidden units. The DBM energy function is $E(\mathbf{v},\mathbf{h};\theta )=-\frac{1}{2}{\mathbf{v}}^T\mathbf{L}\mathbf{v}-\frac{1}{2}{\mathbf{h}}^T\mathbf{J}\mathbf{h}-{\mathbf{v}}^T\mathbf{W}\mathbf{h}$, where the visible units are represented by a binary vector $\mathbf{v}\in {\{\mathrm{0,1}\}}^D$, the hidden units are represented by a binary vector $\mathbf{h}\in {\{\mathrm{0,1}\}}^P$, and the DBM network parameters are in $\theta =\{\mathbf{L},\mathbf{J},\mathbf{W}\}$, and $\mathbf{J}$ and $\mathbf{L}$ have zero diagonals.³⁶ The conditional probabilities based on the visible and hidden input states can be evaluated via

2.2.4.

Recurrent neural network

The RNN is a network where connections form directed cycles. The RNN is primarily used for analyzing nonstationary processes such as speech and time-series analysis. The RNN has memory, so the RNN has persistence, which the AE and CNN do not possess. An RNN can be unrolled and analyzed as a series of interconnected networks that process time-series data. A major breakthrough for RNNs was the seminal work of Hochreiter and Schmidhuber,³⁷ the long short-term memory (LSTM) unit, which allows information to be written to a cell, output from the cell, and stored in the cell. The LSTM allows information to flow and helps counteract the vanishing/exploding gradient problems in very deep networks. Figure 1(d) shows an RNN and its unfolded version. Unlike a traditional NN, the RNN shares the network parameters $(\mathbf{U},\mathbf{V},\mathbf{W})$ across all steps, which makes the number of parameters to learn much smaller. In RS, RNNs have been mainly used to generate semantic image descriptions.

From Fig. 1(d), and following Ref. 38, we let ${\mathbf{x}}_t$ be the input to the RNN at time $t$ and ${\mathbf{s}}_t$ is the hidden state at time $t$ (e.g., the memory of the network). The hidden state is a function of the current input and the immediate past hidden state, e.g., a simple Ellman and Jordan network, $s_t=f({\mathbf{Us}}_t+{\mathbf{Ws}}_{t-1}+\mathbf{b})$, where the function $f$ is usually an activation function such as tanh or a ReLU, $\mathbf{U}$ and $\mathbf{V}$ are matrices containing the network parameters, and $\mathbf{b}$ is the vector bias term. A common practice is to set the initial memory state $s_0$ to the zero vector. The output of our simple RNN, ${\mathbf{o}}_t$, is calculated as ${\mathbf{o}}_t=\mathrm{softmax}({\mathbf{Vs}}_t)$, where $\mathbf{W}$ is a matrix containing the output parameters. The network parameters $\mathbf{U}$, $\mathbf{V}$, $\mathbf{W}$, and $\mathbf{b}$ must be learned by the network. Some good tutorials on RNNs are provided in Refs. 3839.40.–41.

2.2.5.

Deconvolutional neural network

CNNs are often used for tasks, such as classification. However, a wealth of questions exists beyond classification, e.g., what are our filters really learning, how diverse are our filters, how transferable are these filters, what filters are the most active in a given (set of) image(s), where is a filter active at in a (set of) image(s), or more holistically, where in the image is our object(s) of interest (soft or hard segmentation)? In general, we want tools to help us (maybe visually) understand the networks we are working with for purposes such as “explainable AI” and/or network tuning. To this end, researchers have recently begun to explore topics such as deconvolutional CNNs.^21,22,42,43 The idea is to more-or-less “reverse” the flow of information. In most works, authors use the concept of “unpooling”—the inverse of pooling. Unpooling makes use of switch variables, which help us keep track of and place activation in layer $l$ back to its original pooled location in layer $l-1$. Unpooling results in an enlarged, be it sparse, activation map that is then fed to some other operations.

Noh et al.⁴³ adapted the visual geometry group (VGG) 16-layer CNN into a deep deconvolutional network. First, they took the already trained VGG network (trained on non-RS RGB imagery) and they removed the classification layer. Next, they constructed a mirrored CNN using unpooling versus pooling—thus, the data are expanding versus shrinking in a standard pooled CNN. The first half of the network is a standard CNN and the second half is performing deconvolution. The network is then trained and it was ultimately used for semantic image segmentation.

In a different approach,^21,22 Zeiler and Fergus put forth a deconvolution CNN approach, DeconvNet, which should really be called transpose convolution, for visualizing and understanding CNNs. The crux of their approach is to use the CNN “as is.” Their idea is to use the filters that were learned by the CNN to help us (visually) understand how it is working. The mathematics is relatively straight forward. First, one applies unpooling. Next, a ReLU function is applied. Last, transpose filtering (using the filter learned by the CNN) is applied. For a given image, let ${\mathbf{M}}_{\mathbf{i}}$ be the $i$’th feature map at layer $l$. Furthermore, let $r({\widehat{\mathbf{M}}}_{\mathbf{i}})$ be the unpooled result (${\widehat{\mathbf{M}}}_{\mathbf{i}}$) that has had ReLU ($r$) applied to it. Last, let ${\mathbf{F}}_{\mathbf{k}}$ be the filter that we wish to deconvolve with. The operation, technically transpose filtering, is $r({\widehat{\mathbf{M}}}_{\mathbf{i}})*{\mathbf{F}}_{\mathbf{k}}$, where * is the convolution operator. Zeiler used this idea to accomplish the following. First, he randomly picked filters in different layers and he identified the top nine activations (and thus images) across a validation data set. He took the location in the image (so the patch grows in size as we go deeper in the network) and he extracted its corresponding subimage so we could see what the filters are firing on. He also plotted the transpose convolution filter result. This was an interesting visual odyssey and exploration of what hierarchical features the network was learning. However, Zeiler also used his approach to observe that some filters were dwarfed in response to others and if one normalizes filters then the behavior is less prevalent and the CNNs train (converge) faster.

In summary, interesting non-—but clearly related—RS CNN deconvolution research has been put forth to date. However, there is no systematic way yet to select and/or train the network. Furthermore, as the authors remark, their approaches respond to “parts” (the responses of what filters were learned). However, if the goal is segmentation, we may not ensure a desirable result. For example, if the CNN learns to cue off of wheels and decals on the vehicles, this will not help us to segment the entire car. Furthermore, when there are multiple instances of an object in a scene, it is not yet clear how one can associate which evidence with which instance. Regardless, this is an area of interest to the RS community.

2.3.1.

Graphical processing units

GPUs are hardware devices that are optimized for fast parallel processing. GPUs enable DL by offloading computations from the computer’s main processor (which is basically optimized for serial tasks) and efficiently performing the matrix-based computations at the heart of many DL algorithms. The DL community can leverage the personal computer gaming industry, which demands relatively inexpensive and powerful GPUs. A major driver of the research interest in CNNs is the ImageNet contest, which has over 1 million training images and 1000 classes.⁴⁴ DNNs are inherently parallel, use matrix operations, and use a large number of floating point operations per second. GPUs are a match because they have the same characteristics.⁴⁵ GPU speedups have been measured from 8.5 to 9⁴⁵ and even higher depending on the GPU and the code being optimized. The CNN convolution, pooling, and activation calculation operations are readily portable to GPUs.

2.3.2.

DL NN expressiveness

Cybenko⁴⁶ proved that MLPs are universal function approximators. Specifically, Cybenko showed that a feedforward network with a single hidden layer containing a finite number of neurons can approximate continuous functions on compact subsets of ${\mathfrak{R}}^n$, with respect to relatively minimalistic assumptions regarding the activation function. However, Cybenko’s proof is an existence theorem, meaning it tells us a solution exists, but it does not tell us how to design or learn such a network. The point is, NNs have an intriguing mathematical foundation that makes them attractive with respect to machine learning. Furthermore, in a theoretical work, Telgarsky⁴⁷ has shown that for NN with ReLU (1) functions with few oscillations poorly approximate functions with many oscillations and (2) functions computed by NN with few (many) layers have few (many) oscillations. Basically, a deep network allows decision functions with high oscillations. This gives evidence to show why DL performs well in classification tasks, and that shallower networks have limitations with highly oscillatory functions. Sharir and Shashua⁴⁸ showed that having overlapping local receptive fields (RFs) and more broadly denser connectivity gives an exponential increase in the expressive capacity of the NN. Liang and Srikant⁴⁹ showed that shallow networks require exponentially more neurons than a deep network to achieve the level of accuracy for function approximation.

2.3.3.

Training a DL system

Training a DL system is not a trivial task, because: (1) many DL systems have thousands or millions of parameters, (2) RS data are limited and may not have labeled instances readily available, (3) RS data, especially hyperspectral data, are a very large data cube and many successful DL algorithms are tuned for small RGB image patches, (4) RS data gathered via light detection and ranging (LiDAR) have insufficient DL literature (data are point clouds and not images), and (5) the best architecture is usually unknown a priori which means a gridded search (which can be very time consuming) or random methods such as those discussed in Ref. 50 are required for optimization. Chapter 8 of Ref. 23 discusses optimization techniques for training DL models. A thorough discussion of these techniques is beyond the scope of this paper; however, we list some common methods typically used to train DL systems.

Goodfellow et al.²³ in Sec. 8.5.4 point out that there is no current consensus on the best training/optimization algorithm. For the interested reader, the survey paper of Schaul et al.⁵¹ provides results for many optimization algorithms over a large variety of tasks. CNNs are typically trained using stochastic gradient descent (SGD), SGD with momentum,⁵² AdaGrad,⁵³ RMSProp,⁵⁴ and ADAM.⁵⁵ For details on the pros and cons of these algorithms, refer to Secs. 8.3 and 8.5 of Ref. 23. There are also second-order methods, and these are discussed in Sec. 8.6 of Ref. 23. A good history of DL is provided in Ref. 56, and training is discussed in Sec. 5.24. Further discussions in this paper can be found in open questions 7 (Sec. 4.7), 8 (Sec. 4.8), and 9 (Sec. 4.9).

AEs can be trained with optimization algorithms similar to a CNN. Some special AEs, such as the marginalized DAE in Ref. 25, have closed-form solutions. DBNs can be trained using greed-layer wise training, as shown in Hinton et al.⁵⁷ and Bengio et al.⁵⁸ and Salakhutdinov and Hinton⁵⁹ developed an improved pretraining method for DBNs and DBMs, by doubling or halving the weights (see the paper for more details).

Computation comparisons are complex and highly dependent on factors such as the training architecture, computer system (and GPUs), the way the architectures get data onto and off of the GPUs, the particular settings of the optimization algorithm (e.g., the mini-batch size), the learning rate, etc., and, of course, on the data itself. It is very difficult to know a priori what the complexities will be. This question is currently unanswered in current DL knowledge.

The survey paper by Shi et al.⁶⁰ investigates tools performance to help users of common DL tools (see Sec. 2.3.5) such as Caffe and TensorFlow to understand these tools’ speed, capabilities, and limitations. They discovered that GPUs are critical to speeding up DL algorithms, whereas multicore systems do not scale linearly after about 8 cores. The GTX1080 (and now 1080Ti) GPUs performed the best among the GPUs they tested.

RNNs can be difficult to train due to the exploding gradient problem.⁶¹ To overcome this issue, Pascanu et al.⁶² developed a gradient-clipping strategy to more effectively train RNNs. Martens and Sutskever⁶³ developed a Hessian-free with dampening scheme RNN optimization and tested it on very challenging data sets.

Last, the survey paper of Deng² discusses DL architectures and gives many references for training DL systems. The survey paper of Bengio et al.⁶⁴ on unsupervised FL also discusses various learning and optimization strategies.

2.3.4.

Big data

Every day, approximately 350 million images are uploaded to Facebook,⁴⁵ Wal-Mart collects approximately 2.5 petabytes of data per day,⁴⁵ and National Aeronautics and Space Administration (NASA) is actively streaming 1.73 gigabytes of spacecraft borne observation data for active missions alone.⁶⁵ IBM reports that 2.5 quintillion bytes of data are now generated every data, which means that “90% of the data in the world today has been created in the last two years alone.”⁶⁶ The point is that an unprecedented amount of (varying quality) data exists due to technologies such as RS, smartphones, and inexpensive data storage. In times past, researchers used tens to hundreds, maybe thousands of data training samples, but nothing on the order of magnitude as today. In areas such as CV, high data volume and variety are at the heart of advancements in performance, meaning reported results are a reflection of advances in data and machine learning.

To date, a number of approaches have been explored relative to large-scale deep networks (e.g., hundreds of layers) and big data (e.g., high volume of data). For example, Raina et al.⁶⁷ put forth central processing unit (CPU) and GPU ideas to accelerate DBNs and sparse coding. They reported a 5- to 15-fold speed-up for networks with 100 million plus parameters versus previous works that used only a few million parameters at best. On the other hand, CNNs typically use back propagation and they can be implemented either by pulling or pushing.⁶⁸ Furthermore, ideas such as circular buffers⁶⁹ and multi-GPU-based CNN architectures, e.g., Krizhevsky et al.,²⁸ have been put forth. Outside of hardware speedups, operators such as ReLUs have been shown to run several times faster than other common nonlinear functions. Deng et al.⁷⁰ put forth a deep stacking network (DSN) that consists of specialized NNs (called modules), each of which has a single hidden layer. Hutchinson et al.⁷¹ put forth Tensor-DSN as an efficient and parallel extension of DSNs for CPU clusters. Furthermore, DistBelief is a library for distributed training and learning of deep networks with large models (billions of parameters) and massive sized data sets.⁷² DistBelief makes use of machine clusters to manage the data and parallelism via methods such as multithreading, message passing, synchronization, and machine-to-machine communication. DistBelief uses different optimization methods, namely SGD and Sandblaster.⁷² Last, but not least, there are network architectures such as highway networks, residual networks, and dense nets.^30,7374.75.^–76 For example, highway networks are based on LSTM recurrent networks and they allow for the efficient training of deep networks with hundreds of layers based on gradient descent.⁷³74.^–75

Najafabadi et al.⁷⁷ discuss some aspects of DL in big data analysis and challenges associated with these efforts, including nonstationary data, high-dimensional data, and large-scale models. The survey paper of Chen and Len⁷⁸ also discusses challenges associated with big data and DL, including high volumes, variety, and velocity of data. The survey paper of Landset et al.⁷⁹ discusses open-source tools for ML with big data in Hadoop ecosystem.

2.3.5.

Tools

Tools are also a large factor in DL research and development. Wan et al.⁸⁰ observed that DL is at the intersection of NNs, graphical modeling, optimization, pattern recognition, and signal processing, which means there is a fairly high background level required for this area. Good DL tools allow researchers and students to try some basic architectures and create new ones more efficiently.

Table 1 lists some popular DL toolkits and links to the code. Herein, we review some of the DL tools, and the tool analysis below is based on our experiences with these tools. We thank our graduate students for providing detailed feedback on these tools.

Table 1

Some popular DL tools.

AlexNet²⁸ was a revolutionary paper that reintroduced the world to the results that DL can offer. AlexNet uses ReLU because it is several times faster to evaluate than the hyperbolic tangent. AlexNet revealed the importance of preprocessing by incorporating some data augmentation techniques and was able to combat overfitting using max pooling and dropout layers.

Caffe⁸¹ was the first widely used DL toolkit. Caffe is C++ based and can be compiled on various devices, and offers command line, Python, and MATLAB interfaces. There are many useful examples provided. The cons of Caffe are that is relatively hard to install, due to lack of documentation and not being developed by an organized company. For those interested in something other than image processing (e.g., image classification, image segmentation) it is not really suitable for other areas, such as audio signal processing.

TensorFlow⁸² is arguably the most popular DL tool available. Its pros are that TensorFlow (1) is relatively easy to install both with CPU and GPU version on Ubuntu (The GPU version needs CUDA and cuDNN to be installed ahead of time, which is a little complicated); (2) has most of the state-of-the-art models implemented, and while some original implementations are not implemented in TensorFlow, it is relatively easy to find a reimplementation in TensorFlow; (3) has very good documentation and regular updates; (4) supports both Python and C++ interfaces; and (5) is relatively easy to expand to other areas besides image processing, as long as you understand the tensor processing. One con of TensorFlow is that it is really restricted to Linux applications, as the windows version is barely usable.

MatConvNet⁸³ is a convenient tool, with unique abstract implementations for those very comfortable with using MATLAB. It offers many popular trained CNNs, and the data sets used to train them. It is fairly easy to install. Once the GPU setup is ready (installation of drivers + CUDA support), training with the GPU is very simple. It also offers windows support. The cons are (1) there is a substantially smaller online community compared to TensorFlow and Caffe, (2) code documentation is not very detailed and in general does not have good online tutorials besides the manual. Lack of getting started help besides a very simple example, and (3) GPU setup can be quite tedious. For windows, visual studio is required, due to restrictions on MATLAB and its mex setup, as well as Nvidia drivers and CUDA support. On Linux, one has much more freedom but must be willing to adapt to manual installations of Nvidia drivers, CUDA support, and more.

3.1.1.

Hyperspectral image

HSI data classification is of major importance to RS applications, so many of the DL results we reviewed were on HSI classification. HSI processing has many challenges, including high data dimensionality and usually low numbers of training samples. Chen et al.³³¹ propose an DBN-based HSI classification framework. The input data are converted to a one-dimensional (1-D) vector and processed via a DBN with three RBM layers, and the class labels are output from a two-layer logistic regression NN. A spatial classifier using principal component analysis (PCA) on the spectral dimension followed by 1-D flattening of a 3-D box, a three-level DBN, and two-level logistic regression classifier. A third architecture uses combinations of the 1-D spectrum and the spatial classifier architecture. He et al.¹⁷⁰ developed a DBN for HSI classification that does not require SGD training. Nonlinear layers in the DBN allow for the nonlinear nature of HSI data and a logistic regression classifier is used to classify the outputs of the DBN layers. A parametric depth study showed depth of nine layers produced the best results of depths from 1 to 15, and after a depth of nine, no improvement resulted by adding more layers.

Some of the HSI DL approaches use both spectral and spatial information. Ma et al.¹⁸⁷ created an HSI spatial updated deep AE, which integrates spatial information. Small training sets are mitigated by a collaborative, representation-based classifier and salt-and-pepper noise is mitigated by a graph-cut-based spatial regularization. Their method is more efficient than comparable kernel-based methods, and the collaborative representation-based classification makes their system relatively robust to small training sets. Yang et al.¹⁹⁹ use a two-channel CNN to jointly learn spectral and spatial features. Transfer learning is used when the number of training samples is limited, where low-level and midlevel features are transferred from other scenes. The network has a spectral CNN and spatial CNN, and the results are combined in three FC layers. A softmax classifier produces the final class labels. Pan et al.¹⁹³ proposed the so-called rolling guidance filter and vertex component analysis network (R-VCANet), which also attempts to solve the common problem of lack of HSI training data. The network combines spectral and spatial information. The rolling guidance filter is an edge-preserving filter used to remove noise and small details from imagery. The VCANet is a combination of vertex component analysis,³³² which is used to extract pure endmembers, and PCANet.³³³ A parameter analysis of the number of training samples, rolling times, and the number and size of the convolution kernels is discussed. The system performs well even when the training ratio is only 4%. Lee and Kwon¹⁷⁷ designed a contextual deep fully convolutional DL network with 14 layers that jointly exploit spatial and HSI spectral features. Variable size convolutional features are used to create a spectral–spatial feature map. A feature of the architecture is the initial layers use both $[3\times 3\times B]$ convolutional masks to learn spatial features, and $[1\times 1\times B]$ for spectral features, where $B$ is the number of spectral bands. The system is trained with a very small number of training samples (200/class).

3.1.2.

3-D

In 3-D analysis, there are several interesting DL approaches. Chen et al.³³⁴ used a 3-D CNN-based feature extraction model with regularization to extract effective spectral–spatial features from HSI. $L_2$ regularization and dropout are used to help prevent overfitting. In addition, a virtual-enhanced method imputes training samples. Three different CNN architectures are examined: (1) a 1-D using only spectral information, consisting of convolution, pooling, convolution, pooling, stacking, and logistic regression; (2) a 2-D CNN with spatial features, with 2-D convolution, pooling, 2-D convolution, pooling, stacking, and logistic regression; (3) 3-D convolution (2-D for spatial and third dimension is spectral); the organization is same as 2-D case except with 3-D convolution. The 3-D CNN achieves near-perfect classification on the data sets.

Chen et al.²⁰⁹ proposed an innovative 3-D CNN to extract the spectral–spatial features of HSI data, a deep 2-D CNN to extract the elevation features of LiDAR data, and then an FC DNN to fuse the 2-D and 3-D CNN outputs. The HSI data are processed via two layers of 3-D convolution followed by pooling. The LiDAR elevation data are processed via two layers of 2-D convolution followed by pooling. The results are stacked and processed by an FC layer followed by a logistic regression layer.

Cheng et al.²⁴³ developed a rotation-invariant CNN (RICNN), which is trained by optimizing an objective function with a regularization constraint that explicitly enforces the training feature representations before and after rotating to be mapped close to each other. New training samples are imputed by rotating the original samples by $k$ rotation angles. The system is based on AlexNet,²⁸ which has five convolutional layers followed by three FC layers. The AlexNet architecture is modified by adding a rotation-invariant layer that used the output of AlexNet’s FC7 layer, and replacing the 1000-way softmax classification layer with a $(C+1)$-layer softmax classifier layer. AlexNet is pretrained, then fine-tuned using the small number of HSI training samples. Haque et al.¹²⁸ developed an attention-based human body detector that leverages four-dimensional (4-D) spatiotemporal signatures and detects humans in the dark (depth images with no RGB content). Their DL system extracts voxels then encodes data using a CNN, followed by an LSTM. An action network gives the class label and a location network selects the next glimpse location. The process repeats at the next time step.

3.1.3.

Traffic sign recognition

In the area of traffic sign recognition, a nice result came from Ciresan et al.,¹³⁸ who created a biologically plausible DNN that is based on the feline visual cortex. The network is composed of multiple columns of DNNs, coded for parallel GPU speedup. The output of the columns is averaged. It outperforms humans by a factor of two in traffic sign recognition.

3.1.4.

Satellite imagery

In the area of satellite imagery analysis, Zhang et al.²⁰⁴ proposed a gradient-boosting random convolutional network (GBRCN) to classify very high-resolution (VHR) satellite imagery. In GBRCN, a sum of functions (called boosts) is optimized. A modified multiclass softmax function is used for optimization, making the optimization task easier. SGD is used for optimization. Proposed future work was to use a variant of this method on HSI. Zhong et al.²⁰⁸ use efficient small CNN kernels and a deep architecture to learn hierarchical spatial relationships in satellite imagery. A softmax classifier output class labels based on the CNN DL outputs. The CPU handles preprocessing (data splitting and normalization), while the GPU performs convolution, ReLU and pooling operations, and the CPU handles dropout and softmax classification. Networks with one to three convolution layers are analyzed, with RFs from $10\times 10$ to $1000\times 1000$. SGD is used for optimization. A hyperparameter analysis of the learning rate, momentum, training-to-test ratio, and number of kernels in the first convolutional layer was also performed.

3.1.5.

SAR

In the area of SAR processing, De and Bhattacharya³⁰⁵ used DL to classify urban areas, even when rotated. Rotated urban target exhibits different scattering mechanisms, and the network learns the $\alpha$ and $\gamma$ parameters from the HH, VV, and HV bands (H, horizontal; V, vertical polarization). Bentes et al.¹⁴³ use a constant false alarm rate (CFAR) processor on SAR data followed by $N$ AEs. The final layer associates the learned features with class labels. Geng et al.¹⁶⁸ used an eight-layer network with a convolutional layer to extract texture features from SAR imagery, a scale transformation layer to aggregate neighbor features, four-stacked AE (SAE) layers for feature optimization and classification, and a two-layer postprocessor. Gray-level co-occurrence matrix and Gabor features are also extracted, and average pooling is used in layer two to mitigate noise.

4.1.1.

Open question #1a: how can DL systems work well with limited data sets?

There are two main issues with most current RS data sets. Table 4 provides a summary of the more common open-source data sets for the DL papers using HSI data. Many of these papers used custom data sets, and these are not reported. Table 4 shows that the most commonly used data sets were Indian Pines, Pavia University, Pavia City Center, and Salinas.

Table 4

HSI Data set usage.

A detailed online table (too large to put in this paper) is provided, which lists each paper cited in Table 2. For each paper, a summary of the contributions is given, the data sets used are listed, and the papers are categorized in areas (e.g., HSI/MSI, SAR, 3-D, etc.). The interested reader can find this table at  http://cs-chan.com/source/FADL/Online_Paper_Summary_Table.pdf. In addition, a second online table lists details about data sets from the papers we reviewed. It is located at  http://cs-chan.com/source/FADL/Online_Dataset_Summary_Table.pdf

Although these are all good data sets, the accuracies from many of the DL papers are nearly saturated. This is shown clearly in Table 5. Table 5 shows results for the HSI DL papers against the commonly used data sets Indian Pines, Kennedy Space Center, Pavia City Center, Pavia University, Salinas, and the Washington DC Mall. First, overall accuracy (OA) results from different papers must be taken with a grain of salt, since (1) the number of training samples per class can differ for each paper, (2) the number of testing samples can also differ, (3) classes with few relative training samples can even have 0% OA, and if there is a large number of test samples of the other classes, the final overall accuracies can still be high. Nevertheless, it is clear from examination of the table that the Indian Pines, Pavia City Center, Pavia University, and Salinas data sets are basically saturated.

Table 5

HSI OA results in percent.

Note: Results higher than 99% are in bold.

Note: IP, Indian Pines, KSC, Kennedy Space Center, PaCC, Pavia City Center, Pau, Pavia University, Sal, Salinas, and DCM, Washington DC Mall.

In general, it is good to compare new methods with commonly used data sets, new and challenging data sets are required. Cheng et al.^1,361 point out that many existing RS data sets lack image variation, diversity, and have a small number of classes, and some data sets are also saturating with accuracy. They created a large-scale benchmark data set, “NWPU-RESISC45,” which attempts to address all of these issues, and made it available to the RS community. The RS community can also benefit from a common practice in the CV community: publishing both data sets and algorithms online, allowing for more comparisons. A typical RS paper may only test their algorithm on two or three images and against only a few other methods. In the CV community, papers usually compare against a large amount of other methods and with many data sets, which may provide more insight about the proposed solution and how it compares with previous work.

An extensive table of all the data sets used in the papers reviewed for this survey paper is made available online, because it is too large to include in this paper. The table is available at  http://cs-chan.com/source/FADL/Online_Paper_Summary_Table.pdf. The table lists the data set name, briefly describes the data sets, provides a URL (if one is available), and a reference. Hopefully, this table will assist researchers who are looking for publicly available data sets.

4.1.2.

Open question #1b: how can DL systems work well with limited training data?

The second issue is that most RS data have a very small amount of training data available. Ironically, in the CV community, DL has an insatiable hunger for larger and larger data sets (millions or tens of millions of training images), while in the RS field, there is also a large amount of imagery; however, there is usually only a small amount with labeled training samples. RS training data are expensive, error-prone, and usually require some expert interpretation, which is typically expensive (in terms of time, effort involved, and money) and often requires large amounts of field work and many hours or days postprocessing the data. Many DL systems, especially those with large numbers of parameters, require large amounts of training data, or else they can easily overtrain and not generalize well. This problem has also plagued other shallow systems as well, such as SVMs.

Approaches used to mitigate small training samples are (1) transfer learning, where one trains on other imagery to obtain low- to midlevel features which can still be used, or on other images from the same sensor—transfer learning is discussed in Sec. 4.6; (2) data augmentation, including affine transformations, rotations, small patch removal, etc.; (3) using ancillary data, such as data from other sensor modalities [e.g., LiDAR, digital elevation models (DEMs), etc.]; and (4) unsupervised training, where training labels are not required, e.g., AEs and SAEs. SAEs that have a diabolo shape will force the AE network to learn a low-dimensional representation.

Ma et al.¹⁸⁷ used a DAE and employed a collaborative representation-based classification, where each test sample can be linearly represented by the training samples in the same class with the minimum residual. In classification, features of each sample are approximated with a linear combination of features of all training sample within each class, and the label can be derived according to the class that best approximates the test features. Interested readers are referred to Refs. 46–48 in Ref. 187 for more information on collaborative representation. Tao et al.³⁶⁴ used a stacked sparse AE (SSAE) that was shown to be very generalizable and performed well in cases when there were limited training samples. Ghamisi et al.²²⁴ use Darwinian particle swarm optimization in conjunction with CNNs to select an optimal band set for classifying HSI data. By reducing the input dimensionality, fewer training samples are required. Yang et al.¹⁹⁹ used dual CNNs and transfer learning to improve performance. In this method, the lower and middle layers can be trained on other scenes and train the top layers on the limited training samples. Ma et al.¹⁸⁸ imposed a relative distance prior on the SAE DL network to deal with training instabilities. This approach extends the SAE by adding the new distance prior term and corresponding SGD optimization. LeCun³⁶⁵ reviews a number of unsupervised learning algorithms using AEs, which can possibly aid when training data are minimal. Pal³⁶⁶ reviews kernel methods in RS and argues that SVMs are a good choice when there are a small number of training samples. Petersson et al.³⁵² suggest using SAEs to handle small training samples in HSI processing.

4.2.1.

Open question #2a: how can DL improve model-based RS?

Many RS applications depend on models (e.g., a model of crop output given rain, fertilizer and soil nitrogen content, and time of year), many of which are very complicated and often highly nonlinear. Model outputs can be very inaccurate if the models do not adequately capture the true input data and properly handle the intricate interrelationships among input variables.

Abdel-Rahman and Ahmed³⁶⁷ pointed out that more accurate estimation of nitrogen content and water availability can aid biophysical parameter estimation for improving plant yield models. Ali et al.³⁶⁸ examine biomass estimation, which is a nonlinear and highly complex problem. The retrieval problem is ill-posed, and the electromagnetic response is the complex result of many contributions. The data pixels are usually mixed, making this a hard problem. ANNs and support vector regression have shown good results. They anticipate that DL models can provide good results. Both Adam et al.³⁶⁹ and Ozesmi and Bauer³⁷⁰ agree that there is need for improvement in wetland vegetation mapping. Wetland species are hard to detect and identify compared to terrestrial plants. Hyperspectral sensing with narrow bandwidths in frequency can aid. Pixel unmixing is important since canopy spectra are similar and combine with underlying hydrologic regime and atmospheric vapor. Vegetation spectra highly correlated among species, making separation difficult. Dorigo et al.³⁷¹ analyzed inversion-based models for plant analysis, which is inherently an ill-posed and hard task. They found that using artificial neural network (ANN) inversion techniques have shown good results. DL may be able to help improve results. Canopy reflections are governed by large number of canopy elements interacting and by external factors. Since DL networks can learn very complex nonlinear systems, it seems like there is much room for improvement in applying DL models. DBNs or other DL systems seem like a natural fit for these types of problems.

Kuenzer et al.³⁷² and Wang et al.³⁷³ assess biodiversity modeling. Biodiversity occurs at all levels from molecular to individual animals, to ecosystem, and to global. This requires a large variety of sensors and analysis at multiple scales. However, a main challenge is low temporal resolution. There needs to be a focus beyond just pixel-level processing and using spatial patterns and objects. DL systems have been shown to learn hierarchical features, with smaller scale features learned at the beginning of the network, and more complex and abstract features learned in the deeper portions.

4.2.2.

Open question #2b: what tools and techniques are required to “understand” how the DL works?

It is also worth mentioning that many of these applications involve biological and scientific end-users, who will definitely want to understand how the DL systems work. For instance, modeling some biological processes using a linear model is easily understood—both the mathematical model and the statistics resulting from estimating the model parameters are well understood by scientists and biologists. However, a DL system can be so large and complex as to defy analysis. We note that this is not specific to RS, but a general problem in the broader DL community.

The DL system is seen by many researchers, especially scientists and RS end-users, as a black box that is hard to understand what is happening “under the hood.” Egmont-Petersen et al.³⁴⁸ and Fassnacht et al.³⁷⁴ both state that disadvantages of NNs are understanding what they are actually doing, which can be difficult to understand. In many RS applications, just making a decision is not enough; people need to understand how reliable the decision is and how the system arrived at that decision. Ali et al.³⁶⁸ also echo this view in their review paper on improving biomass estimation. Visualization tools, which show the convolutional filters, learning rates, and tools with deconvolution capabilities to localize the convolutional firings, are all helpful.^22,375376.377.^–378 Visualization of what the DL is actually learning is an open area of research. Tools and techniques capable of visualizing what the network is learning and measures of how robust the network is (estimating how well it may generalize) would be of great benefit to the RS community (and the general DL community).

4.3.1.

Open question #3: what happens when DL meets big data?

As already discussed in Sec. 2.3.4, a number of mathematics, algorithms, and hardware have been put forth to date relative to large-scale DL networks and DL in big data. However, this challenge is not close to being solved. Most approaches to date have focused on big data challenges in RGB or RGBD data for tasks, such as face and object detection or speech. With respect to RS, we have many of the same problems as CV, but there are unique challenges related to different sensors and data. First, we can break big data into its different so-called “parts,” e.g., volume, variety, and velocity. With respect to DBNs, CNNs, AEs, etc., we are primarily concerned with creating new robust and distributed mathematics, algorithms, and hardware that can ingest massive streams of large, missing, noisy data from different sources, such as sensors, humans, and machines. This means being able to combine image stills, video, audio, text, etc., with symbolic and semantic variations. Furthermore, we require real-time evaluation and possibly online learning. As big data in DL are large topic, we restrict our focus herein to factors that are unique to RS.

The first factor that we focus on is high spatial and more-so spectral dimensionality. Traditional DLs operate on relatively small grayscale or RGB imagery. However, SAR imagery has challenges due to noise, and MSI and HSI can have from four to hundreds to possibly thousands of channels. As Arel et al.¹²⁰ pointed out, a very difficult question is how well DL architectures scale with dimensionality. To date, preliminary research has tried to combat dimensionality by applying dimensionality reduction or feature selection prior to DL, e.g., Benediktsson et al.³⁷⁹ reference a different band selection, grouping, feature extraction, and subspace identification in HSI RS.

Ironically, most RS areas suffer from a lack of training data. Whereas they may have massive amounts of temporal and spatial data, there may not be the seasonal variations, times of day, object variation (e.g., plants, crops, etc.), and other factors that ultimately lead to sufficient variety needed to train a DL model. For example, most online hyperspectral data sets have little-to-no variety and it is questionable about what they are, and really can at that, learn. In stark contrast, most DL systems in CV use very large training sets, e.g., millions or billions of faces in different illuminations, poses, inner class variations, etc. Unless the RS DL applies a method such as transfer learning, DL in RS often has very limited training data. For example, Ma et al.¹⁸⁸ tried to address this challenge by developing a new prior to deal with the instability of parameter estimation for HSI classification with small training samples. The SAE is modified by adding the relative distance prior in the fine-tuning process to cluster the samples with the same label and separate the ones with different labels. Instead of minimizing classification error, this network enforces intraclass compactness and attempts to increase interclass discrepancy.

Part of this open question is also an open question in the DL community in general, that is, what is the best training method? There is currently no consensus, and many times people use whatever method is easy to use based on their DL software. Packages, such as TensorFlow, offer many different methods, so the user can try them and experiment. Significantly different results can be found running the same algorithms with different data on different machines (especially machines with GPUs versus machines with no GPUs, etc.).

4.4.1.

Open question #4a: how can DL work with nontraditional data sources?

Nontraditional data sources, such a Twitter and YouTube, offer data that can be useful to RS. Analyzing these types of data will probably never replace traditional RS methods, but usually offer benefits to augment RS data, or provide quality real-time data before RS methods, which usually take longer to execute.

Fohringer et al.³⁸⁰ used information extracted from social media photos to enhance RS data for flood assessments. They found one major challenge was filtering posts to a manageable amount of relevant ones to further assess. The data from Twitter and Flickr proved useful for flood depth estimation prior to RS-based methods, which typically take 24 to 28 h. Frias-Martinez and Frias-Martinez³⁸¹ take advantage of large amounts of geolocated content in social media by analyzing tweets as a complimentary source of data for urban land-use planning. Data from Manhattan (New York), London (UK), and Madrid (Spain) were analyzed using a self-organizing map³⁸² followed by a Voronoi tessellation. Middleton et al.³⁸³ match geolocated tweets and created real-time crisis maps via statistical analysis, which are compared to the National Geospatial Agency postevent impact assessments. A major issue is that only about 1% of tweets contain geolocation data. These tweets usually follow a pattern of a small number of first-hand reports and many retweets and comments. High-precision results were obtained. Singh³⁸⁴ aggregates user’s social interest about any particular theme from any particular location into so-called “social pixels,” which are amenable to media processing techniques (e.g., segmentation and convolution), which allow semantic information to be derived. They also developed a declarative operator set to allow queries to visualize, characterize, and analyze social media data. Their approach would be a promising front-end to any social media analysis system. In the survey paper of Sui and Goodchild,³⁸⁵ the convergence of geographic information system (GIS) and social media is examined. They observed that GIS has moved from software helping a user at a desk to a means of communicating earth surface data to the masses (e.g., OpenStreetMap, Google Maps, etc.).

In all of the aforementioned methods, DL can play a significant role of parsing data, analyzing data, and estimating results from the data. It seems that social media is not going away, and data from social media can often be used to augment RS data in many applications. Thus, the question is what work awaits the researcher in the area of using DL to combine nontraditional data sources with RS?

4.4.2.

Open question #4b: how does DL ingest heterogeneous data?

Fusion can take place at numerous so-called “levels,” including signal, feature, algorithm, and decision. For example, signal in–signal out (SISO) is where multiple signals are used to produce a signal out. For $\mathfrak{R}$-valued signal data, a common example is the trivial concatenation of their underlying vectorial data, i.e., $X=\{{\widehat{x}}_1,\dots ,{\widehat{x}}_N\}$ becomes $[{\widehat{x}}_1{\widehat{x}}_2\dots {\widehat{x}}_N]$ of length $|{\widehat{x}}_1|+\dots +|{\widehat{x}}_N|$. Feature in–feature out (FIFO), which is often related to if not the same as SISO, is where multiple features are combined, e.g., an HOG and an LBP, and the result is a new feature. One example is multiple kernel learning (MKL), e.g., $\ell \text{-}p$ norm genetic algorithm MKL (GAMKLp).³⁸⁶ Typically, the input is $N$ $\mathfrak{R}$-valued Cartesian spaces, and the result is a Cartesian space. Most often, one engages in MKL to search for space in which pattern obeys some property, e.g., they are nicely linearly separable and a machine learning tool, such as a SVM, can be employed. On the other hand, decision in–decision out (DIDO), e.g., the Choquet integral (ChI), is often used for the fusion of input from decision makers, e.g., human experts, algorithms, classifiers, etc.³⁸⁷ Technically speaking, a CNN is typically a signal in–decision out (SIDO) or feature in–decision out (FIDO) system. Internally, the FL part of the CNN is an SIFO or FIFO and the classifier is an FIDO. To date, most DL approaches have “fused” via (1) concatenation of $\mathfrak{R}$-valued input data (SISO or FIFO) relative to a single DL, (2) each source has its own DL, minus classification, that is later combined into a single DL, or (3) multiple DLs are used, one for each source, and their results are once again concatenated and subjected to the classifier (either an MLP, SVM, or other classifier).

Herein, we highlight the challenges of syntactic and semantic fusion. Most DL approaches to date syntactically have addressed how $N$ things, which are typically homogeneous mathematically, can be ingested by a DL. However, the more difficult challenge is semantically how should these sources be combined, e.g., what is a proper architecture, what is learned (can we understand it), and why should we trust the solution? This is of particular importance to numerous challenges in RS that require a physically meaningful/grounded solution, e.g., model-based approaches. The most typical example of fusion in RS is the combining of data from two (or more) sensors. Whereas there may be semantic variation but little-to-no semantic variation, e.g., both are possibly $\mathfrak{R}$-valued vector data, the reality is most sensors record objective evidence about our universe. However, if human information (e.g., linguistic or text) is involved or algorithmic outputs (e.g., binary decisions, labels/symbols, probabilities, etc.), fusion becomes increasingly more difficult syntactically and semantically. Many theoretical (mathematical and philosophical) investigations, which are beyond the scope of this work, have concerned themselves with how to meaningfully combine objective versus subjective information, qualitative versus quantitative information, and mixed uncertainty information (e.g., beliefs, evidence, probabilities, etc.). It is a naive and dangerous belief that one can simply just “cram” data/information into a DL and get a meaningful result. How is fusion occurring? Where is it occurring? Fusion is further compounded if one is using uncertain information, e.g., probabilistic, possibilities, or other interval or distribution-based input. The point is, heterogeneous, be it mathematical representation, associated uncertainty, etc., is a real and serious challenge. If the DL community wishes to fuse multiple inputs or sources (humans, sensors, and algorithms), then DL must theoretically rise to the occasion to ensure that the proposed DL architectures be able to answer the question of what is the DL system really learning, and is it meaningful?

Two preliminary examples of DL works employing multisensor fusion include fusion of (1) HSI with LiDAR³⁸⁸ (two sensors yielding objective data) and (2) text with imagery or video³⁸⁹ (thus high-level human information sensor data). The point is, the question remains, how can/does DL fuse data/information arising from one or more sources?

4.5.1.

DL Open question #5: what architectural extensions will DL systems require in order to tackle complicated RS problems?

Current DL architectures, components (e.g., convolution), and optimization techniques may not be adequate to solve complex RS problems. In many cases, researchers have developed network architectures, new layer structures with their associated SGD or BP equations for training, or new combinations of multiple DL networks. This problem is also an open issue in the broader CV community. This question is at the heart of DL research. Other questions related to the open issues are:

We examine several general areas where DL systems have evolved to handle RS data: (i) multisensor processing, (ii) using multiple DL systems, (iii) rotation and displacement-invariant DL systems, (iv) new DL architectures, (v) SAR, (vi) ocean and atmospheric processing, (vii) 3-D processing, (viii) spectral–spatial processing, and (ix) multitemporal analysis. Furthermore, we examine some specific RS applications noted in several RS survey papers as areas that DL can benefit: (a) oil spill detection, (b) pedestrian detection, (c) urban structure detection, (d) pixel unmixing, and (e) road extraction. This is by no means an exhaustive list, but meant to highlight some of the important areas.

4.6.1.

Open question #6: how can DL in RS successfully use transfer learning?

In general, we note that transfer learning is also an open question in DL in general, not just in DL related to RS. Section 4.9 discusses transfer learning in the broader contact of the entire field of DL, which this section discusses transfer learning in an RS context.

According to Tuia et al.³⁹⁹ and Pan and Yang,⁴⁰⁰ transfer learning seeks to learn from one area to another in one of the four ways: instance-transfer, feature-representation transfer, parameter transfer, and relational-knowledge transfer. Typically in RS, when changing sensors or changing to a different part of a large image or other imagery collected at different times, the transfer fails. RS systems need to be robust, but many do not necessarily require near-perfect knowledge. Transfer among HSI images where the number and types of endmembers are different has very few studies. Ghazi et al.²⁵⁵ suggest that two options for transfer learning are to (1) use pretrained network and learn new features in the imagery to be analyzed or (2) fine-tune the weights of the pretrained network using the imagery to be analyzed. The choice depends on the size and similarity of the training and testing data sets. There are many open questions about transfer learning in HSI RS:

Although in general these open questions remain, we do note that the following papers have successfully used transfer learning in RS applications: Yang et al.¹⁹⁹ trained on other RS imagery and transferred low- to midlevel features to other imagery. Othman et al.²³⁵ used transfer learning by training on the ILSVRC-12 challenge data set, which has 1.2 million $224\times 224$ RGB images belonging to 1000 classes. The trained system was applied to the UC Merced Land Use⁴⁰¹ and Banja-Luka⁴⁰² data sets. Iftene et al.¹⁷³ applied a pretrained CaffeNet and GoogLeNet models on the ImageNet data set, and then applying the results to the VHR imagery denoted the WHU-RS data set.^403,404 Xie et al.³¹⁰ trained a CNN on nighttime imagery and used it in a poverty mapping. Ghazi et al.²⁵⁵ and Lee et al.⁴⁰⁵ used a pretrained networks AlexNet, GoogLeNet, and VGGNet on the LifeCLEF 2015 plant task data set⁴⁰⁶ and MalayaKew data set⁴⁰⁷ for plant identification. Alexandre²⁴⁰ used four independent CNNs, one for each channel of RGBD, instead of using a single CNN receiving the four input channels. The four independent CNNs are then trained in a sequence using the weights of a trained CNN as starting point to train the other CNNs that will process the remaining channels. Ding et al.⁴⁰⁸ used transfer learning for automatic target recognition from midwave infrared (MWIR) to longwave IR (LWIR). Li et al.¹⁴¹ used transfer learning by using pixel-pairs based on reference data with labeled sampled using Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) hyperspectral data.

4.7.1.

DL open question #7: what new developments will allow researchers to better understand DL systems theoretically?

The CV and NN image processing communities understand BP and SGD, but until recently, researchers struggled to train deep networks. One issue has been identified as vanishing or exploding gradients.^61,409 Using normalized initialization and normalization layers can help alleviate this problem. Using special architectures, such as deep residual learning³⁰ or highway networks⁷⁶ feed data into the deeper layers, thus allowing very deep networks to be trained. FCNs³³⁷ have achieved success in pixel-based semantic segmentation tasks and are another alternative to going deep. Sokolic et al.⁴¹⁰ determined that the spectral norm of the NN’s Jacobian matrix in the neighborhood of the training samples must be bounded in order for the network to generalize well. All of these methods deal with a central problem in training very deep NNs. The gradients must not vanish, explode, or become too uncorrelated, or else learning is severely hindered.

The DL field needs practical (and theoretical) methods to go deep, and ways to train efficiently with good generalization capabilities. Many DL RS systems will probably require new components, and these networks with the new components need to be analyzed to see if the methods above (or new methods not yet invented) will enable efficient and robust network training. Egmont-Petersen et al.³⁴⁸ point out that DL training is sensitive to the initial training samples, and it is a well-known problem in SGD and BP of potentially reaching a local minimum solution but not being at the global minimum. In the past, seminal papers, such as Hinton et al.’s,⁵⁷ that allow efficient training of the network have allowed researchers to break past a previously difficult barrier.

4.8.1.

DL open question #8: how to best handle high entry barriers to DL?

Most DL papers assume that the reader is familiar with DL concepts, e.g., BP, SGD, etc. This is in reality a steep learning curve that takes a long time to master. Good tutorials and online training can aid students and practitioners who are willing to learn. Implementing BP or SGD on a large DL system is a difficult task, and simple errors can be hard to determine. Furthermore, BP can fail in large networks, so alternate architectures, such as highway nets, may be required.

Many DL systems have a large number of parameters to learn and often require large amounts of training data. Computers with GPUs and GPU-capable DL programs can greatly benefit by offloading computations onto the GPUs. However, multi-GPU systems are expensive, and students often use laptops that cannot be equipped with a GPU. Some DL systems run under Microsoft Windows, while others run under variants of Linux (e.g., Ubuntu or Red Hat). Furthermore, DL systems are programmed in a variety of languages, including MATLAB^®, C, C++, Lua, and Python. Thus, practitioners and researchers have a potentially steep learning curve to create custom DL solutions.

Finally, a large variety of data types in RS, including RGB imagery, RGBD imagery, MSI, HSI, SAR, LiDAR, stereo imagery, tweets, and GPS data, all of which may require different architectures of DL systems. Often, many of the tasks in the RS community require components that are not part of a standard DL library tool. A good understanding of DL systems and programming is required to integrate these components into off-the-shelf DL systems.

One of the authors provides a set of MatConvNet DL example codes and codes for fusion on his website. Interested readers are referred to  http://derektanderson.com/FuzzyLibrary/.

4.9.1.

Open question #9: how to train and optimize the DL system?

Training a DL system can be difficult. Large systems can have millions of parameters. There are many methods that DL researchers use to effectively train systems. These methods are discussed as follows.