This PDF file contains the front matter associated with SPIE Proceedings Volume 8365, including the Title Page, Copyright information, Table of Contents, and the Conference Committee listing.

Traditional compression involves sampling a signal at the Nyquist rate, then reducing the signal to its essential components via some transformation. By taking advantage of any sparsity inherent in the signal, compressed sensing attempts to reduce the necessary sampling rate by combining these two steps. Currently, compressive sampling operators are based on random draws of Bernoulli or Gaussian distributed random processes. While this ensures that the conditions necessary for noise-free signal reconstruction (incoherence and RIP) are fulfilled, such operators can have poor SNR performance in their measurements. SNR degradation can lead to poor reconstruction despite using operators with good incoherence and RIP. Due to the effects of incoherence-related signal loss, SNR will degrade by M/K compared to the SNR of the fully sampled signal (where M is the dimensionality of the measurement operator and K is the dimensionality of the representation space). We model an RF compressive receiver where the sampling operator acts on noise as well as signal. The signal is modeled as a bandlimited pulse parameterized by random complex amplitude and time of arrival. Hence, the received signal is random with known prior distribution. This allows us to represent the signal via Karhunen-Loeve expansion and so investigate the SNR loss in terms of a random vector that exists in the deterministic KL basis. We are then able to show the SNR trade-off that exists between sampling operators based on random matrices and operators matched to the K-dimensional basis.

A rich body of literature has emerged during the last decade that seeks to exploit the sparsity of a signal for a reduction in the number of measurements required for various inference tasks. Much of the initial work in this direction has been for the case when the measurements correspond to a projection of the signal of interest onto the column space of (sub)Gaussian and subsampled Fourier matrices. The physics in a number of applications, however, dictates the use of "structured" matrices for measurement purposes. This has led to a recent push in the direction of structured measurement (or sensing) matrices for inference of sparse signals. This paper complements some of the recent work in this direction by studying the geometry of Toeplitz-block sensing matrices. Such matrices are bound to arise in any system that can be modeled as a linear, time-invariant (LTI) system with multiple inputs and single output. The reported results therefore should be of particular benefit to researchers interested in exploiting sparsity in LTI systems with multiple inputs.

We suggest and explore a parallelism between linear block code parity check matrices and binary zero/one measurement matrices for compressed sensing. The resulting family of deterministic compressive samplers renders itself to the development of eective and ecient recovery algorithms for sparse signals that are not ℓ₁-based. Experimental results that we include herein demonstrate the utility of the presented developments.

We present several improvements to published algorithms for sparse image modeling with the goal of improving processing of imagery of small watercraft in littoral environments. The first improvement is to the K-SVD algorithm for training over-complete dictionaries, which are used in sparse representations. It is shown that the training converges significantly faster by incorporating multiple dictionary (i.e., codebook) update stages in each training iteration. The paper also provides several useful and practical lessons learned from our experience with sparse representations. Results of three applications of sparse representation are presented and compared to the state-of-the-art methods; image compression, image denoising, and super-resolution.

The Code Aperture Snapshot Spectral Imaging system (CASSI) senses the spectral information of a scene using the underlying concepts of compressive sensing (CS). The random projections in CASSI are localized such that each measurement contains spectral information only from a small spatial region of the data cube. The goal of this paper is to translate high-resolution hyperspectral scenes into compressed signals measured by a low-resolution detector. Spatial super-resolution is attained as an inverse problem from a set of low-resolution coded measurements. The proposed system not only offers significant savings in size, weight and power, but also in cost as low resolution detectors can be used. The proposed system can be efficiently exploited in the IR region where the cost of detectors increases rapidly with resolution. The simulations of the proposed system show an improvement of up to 4 dB in PSNR. Results also show that the PSNR of the reconstructed data cubes approach the PSNR of the reconstructed data cubes attained with high-resolution detectors, at the cost of using additional measurements.

We present an architecture for rapid spectral classification in spectral imaging applications. By making use of knowledge gained in prior measurements, our spectral imaging system is able to design adaptive feature-specific measurement kernels that selectively attend to the portions of a spectrum that contain useful classification information. With measurement kernels designed using a probabilistically-weighted version of principal component analysis, simulations predict an orders-of-magnitude reduction in classification error rates. We report on our latest simulation results, as well as an experimental prototype currently under construction.

Focal plane arrays with associated electronics and cooling are a substantial portion of the cost, complexity, size, weight, and power requirements of Long-Wave IR (LWIR) imagers. Hyperspectral LWIR imagers add significant data volume burden as they collect a high-resolution spectrum at each pixel. We report here on a LWIR Hyperspectral Sensor that applies Compressive Sensing (CS) in order to achieve benefits in these areas. The sensor applies single-pixel detection technology demonstrated by Rice University. The single-pixel approach uses a Digital Micro-mirror Device (DMD) to reflect and multiplex the light from a random assortment of pixels onto the detector. This is repeated for a number of measurements much less than the total number of scene pixels. We have extended this architecture to hyperspectral LWIR sensing by inserting a Fabry-Perot spectrometer in the optical path. This compressive hyperspectral imager collects all three dimensions on a single detection element, greatly reducing the size, weight and power requirements of the system relative to traditional approaches, while also reducing data volume. The CS architecture also supports innovative adaptive approaches to sensing, as the DMD device allows control over the selection of spatial scene pixels to be multiplexed on the detector. We are applying this advantage to the detection of plume gases, by adaptively locating and concentrating target energy. A key challenge in this system is the diffraction loss produce by the DMD in the LWIR. We report the results of testing DMD operation in the LWIR, as well as system spatial and spectral performance.

Compressive Sensing (CS) is an emerging data acquisition scheme with the potential to reduce the number of measurements required by the Nyquist sampling theorem to acquire sparse signals. We recently used the interbeat correlation to find the common support between jointly sparse adjacent heartbeats. In this paper, we fully exploit this correlation to find the magnitude, in addition to the support of the significant coefficients in the sparse domain. The approach used for this purpose is based on sparse Bayesian learning algorithms due to its superior performance compared to other reconstruction algorithms and the fact that being a probabilistic approach facilitates the incorporation of correlation information. The reconstruction includes, in the first place, the detection of the R peaks and the length normalization of ECG cycles to take advantage of the quasi-periodic structure. Since the common support reduces as the number of heartbeats increases, we propose the use of a sliding window where the support maintains approximately constant across cycles. The sparse Bayesian algorithm adaptively learns and exploits the high correlation between the heartbeats in the constructed window. Experimental results show that the proposed method reduces significantly the number of measurements required to achieve good reconstruction quality, validating the potential of using correlation information in compressed sensing-based ECG compression.

Compressive sensing (CS) is an emerging signal processing paradigm that enables sub-Nyquist sampling of sparse signals. Extensive previous work has exploited the sparse representation of ECG signals in compression applications. In this paper, we propose the use of wavelet domain dependencies to further reduce the number of samples in compressive sensing-based ECG compression while decreasing the computational complexity. R wave events manifest themselves as chains of large coefficients propagating across scales to form a connected subtree of the wavelet coefficient tree. We show that the incorporation of this connectedness as additional prior information into a modified version of the CoSaMP algorithm can significantly reduce the required number of samples to achieve good quality in the reconstruction. This approach also allows more control over the ECG signal reconstruction, in particular, the QRS complex, which is typically distorted when prior information is not included in the recovery. The compression algorithm was tested upon records selected from the MIT-BIH arrhythmia database. Simulation results show that the proposed algorithm leads to high compression ratios associated with low distortion levels relative to state-of-the-art compression algorithms.

High resolution sensors are required for recognition purposes. Low resolution sensors, however, are still widely used. Software can be used to increase the resolution of such sensors. One way of increasing the resolution of the images produced is using multi-frame super resolution algorithms. Limitation of these methods are that the reconstruction only works if multiple frames are available furthermore these algorithms decreases the temporal resolution. In this paper we use a sparse representation of an overcomplete dictionary to significantly increase the resolution of a single low resolution image. This allows for a higher resolution gain and no loss in temporal resolution. We demonstrate this technique to improve the resolution of number plates images obtained from a near infrared roadside camera.

We present an approach for classifying chart images with sparse coding. Three chart categories are considered: bar charts, pie charts and line graphs. We introduce the Laplacian of Gaussian (LoG) to smooth noise in the image and detect candidate regions of interest. Noting that charts typically contain both text and graphics, we identify text and graphic regions and learn informative features from them. Each image is then represented by a feature vector, which can be used to learn a sparse representation via the dictionary learning algorithm for classification. We evaluate the proposed systematic approach by a set of charts drawn from the internet. The encouraging results certifies the proposed method.

Sparse representation based classification (SRC) has achieved state-of-the-art results on face recognition. It is hence desired to extend its power to a broader range of classification tasks in pattern recognition. SRC first encodes a query sample as a linear combination of a few atoms from a predefined dictionary. It then identifies the label by evaluating which class results in the minimum reconstruction error. The effectiveness of SRC is limited by an important assumption that data points from different classes are not distributed along the same radius direction. Otherwise, this approach will lose their discrimination ability, even though data from different classes are actually well-separated in terms of Euclidean distance. This assumption is reasonable for face recognition as images of the same subject under different intensity levels are still considered to be of same-class. However, the assumption is not always satisfied when dealing with many other real-world data, e.g., the Iris dataset, where classes are stratified along the radius direction. In this paper, we propose a new coding strategy, called Nearest- Farthest Neighbors based SRC (NF-SRC), to effectively overcome the limitation within SRC. The dictionary is composed of both the Nearest Neighbors and the Farthest Neighbors. While the Nearest Neighbors are used to narrow the selection of candidate samples, the Farthest Neighbors are employed to make the dictionary more redundant. NF-SRC encodes each query signal in a greedy way similar to OMP. The proposed approach is evaluated over extensive experiments. The encouraging results demonstrate the feasibility of the proposed method.

We have designed and built a working automatic progressive sampling imaging system based on the vector sensor concept, which utilizes a unique sampling scheme of Radon projections. This sampling scheme makes it possible to progressively add information resulting in tradeoff between compression and the quality of reconstruction. The uniqueness of our sampling is that in any moment of the acquisition process the reconstruction can produce a reasonable version of the image. The advantage of the gradual addition of the samples is seen when the sparsity rate of the object is unknown, and thus the number of needed measurements. We have developed the iterative algorithm OSO (Ordered Sets Optimization) which employs our sampling scheme for creation of nearly uniform distributed sets of samples, which allows the reconstruction of Mega-Pixel images. We present the good quality reconstruction from compressed data ratios of 1:20.

In this paper we propose a method to acquire compressed measurements for efficient video reconstruction using a single pixel camera. The method is suitable for implementation using a single pixel detector along with digital micromirror device (DMD) or other forms of spatial light modulators (SLMs). Normal implementations of single pixel cameras are able to compress the spatial dimensions but the fact that it needs to make measurements in a sequential manner before the scene changes makes it inefficient for video imaging. In this paper we discuss a measurement scheme that exploits sparsity along the time axis. After acquiring all measurements required for the first frame, measurements are only acquired from the areas which change in subsequent frames. Segmentation of the first frame is performed and change detection is performed on each segmented area. Compressed measurements are only made for changing segments. We show the reconstruction results for a few test sequences commonly used for performance analysis.

We consider a coded aperture imaging system which collects far fewer measurements than the underlying resolution of the scene we wish to exploit. Our sensing model considers an imaging system which subsamples pixels intensities with a Spatial Light Modulator (SLM) device. We present a general approach that can be applied to compressively sensed measurements gathered with respect to our sensing model, in order to improve reconstruction quality beyond a general reconstruction algorithm. The approach exploits capturing overlapping subsequent frames in a panning camera scene or capturing novel compressively sensed measurements of the static camera scene by utilizing dynamic aperture codes. We also consider the effects of projective distortions from various camera positions of subsequent frames within our approach. The result is a decrease in the effective compression rate of the system and therefore a significantly improved compressively sensed reconstruction. Results are presented for various reconstruction algorithms on natural, man-made, and mixed scenery of panning camera scenery as well as static camera scenery.

We consider a video acquisition system where motion imagery is captured only by direct compressive sampling (CS) without any other form of intelligent encoding/processing. In this context, the burden of quality video sequence reconstruction falls solely on the decoder/player side. We describe a video CS decoding method that implicitly incorporates motion estimation via sliding-window sparsity-aware recovery from locally estimated Karhunen-Loeve bases. Experiments presented herein illustrate and support these developments.

The framework of computing Higher Order Cyclostationary Statistics (HOCS) from an incoming signal has proven useful in a variety of applications over the past half century, from Automatic Modulation Recognition (AMR) to Time Dierence of Arrival (TDOA) estimation. Much more recently, a theory known as Compressive Sensing (CS) has emerged that enables the ecient acquisition of high-bandwidth (but sparse) signals via nonuni- form low-rate sampling protocols. While most work in CS has focused on reconstructing the high-bandwidth signals from nonuniform low-rate samples, in this work, we consider the task of inferring the modulation of a communications signal directly in the compressed domain, without requiring signal reconstruction. We show that the HOCS features used for AMR are compressible in the Fourier domain, and hence, that AMR of various linearly modulated signals is possible by estimating the same HOCS features from nonuniform compressive sam- ples. We provide analytical support for the accurate approximation of HOCS features from nonuniform samples and derive practical rules for classication of modulation type using these samples based on simulated data.

Tracking the shallow water acoustic channel in real time poses an open challenge towards improving the data rate in high-speed underwater communications. Multipath arrivals due to reflection from the moving ocean surface and the sea bottom, along with surface wave focusing events, lead to a rapidly fluctuating complex-valued channel impulse response and associated Delay-Doppler spread function that follow heavy-tailed distributions. The sparse channel or Delay-Doppler spread function components are difficult to track in real time using popular sparse sensing techniques due to the coherent and dynamic nature of the optimization problem as well as the timevarying and potentially non-stationary sparseness of the underlying support. We build on related work using non-convex optimization to track the shallow water acoustic channel in real time at high precision and tracking speed to develop strategies to estimate the non-stationary sparseness of the underlying support. Specifically, we employ non-convex manifold navigational techniques to estimate the support sparseness to balance the weighting between the L1 norm of the tracked coefficients and the L2 norm of the estimation error. We explore the efficacy of our methods against experimental field data collected at 200 meters range, 15 meters depth and varying wind conditions.

Underwater acoustic channels have rich selectivity in time, frequency, space and Doppler. These channel features need to be properly modeled and captured for eective channel equalization and data communication. However, estimation of high-dimensional acoustic channels entails heavy implementation costs, in terms of computational load, processing time and the number of data samples required for eective equalization. Compressed sensing oers a new paradigm for sparse channel estimation by collecting a small number of samples via random pro- jections. Each random projection captures and (equally) weights in all components in the search space, without relying on any structural knowledge of the search space. On the other hand, some physics-based waveguide knowledge can be available for underwater acoustic channels, which can constrain both the number of arrivals and the range of their angles of arrival at a receiver based on the source-receiver geometry and water column, surface, and bottom properties. A structure-based projection approach is hence motivated for data sampling and channel reconstruction. Balancing between structured versus random projections, this paper develops new compressed sensing algorithms under partial structural knowledge that is obtained from a geometric model of the propagation channels. Simulations conrm the benets of partially-structured random projections in terms of both improved recovery performance and reduced sampling costs.

In this paper, compressive sensing strategies for interception of Frequency-Hopping Spread Spectrum (FHSS) signals are introduced. Rapid switching of the carrier among many frequency channels using a pseudorandom sequence (unknown to the eavesdropper) makes FHSS signals dicult to intercept. The conventional approach to intercept FHSS signals necessitates capturing of all frequency channels and, thus, requires the Analog-to-Digital Converters (ADCs) to sample at very high rates. Using the fact that the FHSS signals have sparse instanta- neous spectra, we propose compressive sensing strategies for their interception. The proposed techniques are validated using Gaussian Frequency-Shift Keying (GFSK) modulated FHSS signals as dened by the Bluetooth specication.

Compressive sensing (CS) techniques have shown promise for subsurface imaging applications using wideband sensors such as stepped-frequency ground-penetrating radars (GPR). Excellent images can be computed using the CS techniques. However, the problem size is severely limited for 3-dimensional imaging problems which seem to require an explicit representation matrix that involves six dimensions. This paper shows how the underlying propagation model leads to a block-Toeplitz structure in two of the dimensions which can be exploited to reduce both the storage and computational complexity. The reduction by three orders of magnitude in computational resources for the CS problem will make 3-dimensional imaging applications feasible.

In this paper, we consider moving target detection and localization inside enclosed structures for through-the-wall radar imaging and urban sensing applications. We exploit the fact that the through-the-wall scene is sparse in the Doppler domain, on account of the presence of a few moving targets in an otherwise stationary background. The sparsity property is used to achieve efficient joint range-crossrange-Doppler estimation of moving targets inside buildings using compressive sensing. We establish an appropriate signal model that permits formulation of linear modeling with sensing matrices, so as to achieve scene reconstruction via sparse regularization. Supporting simulation results show that a sizable reduction in the data volume is achieved using the proposed approach without a degradation in system performance.

In multi-input multi-output (MIMO) radar systems, the sparsity of targets in the target space can be exploited by compressive sensing (CS) techniques to achieve either the same localization performance as traditional methods but with significantly fewer measurements, or significantly improved performance with the same number of measurements. This paper proposes a power allocation scheme for widely separated CSbased MIMO radar. In particular, the allocation scheme minimizes the correlation between the target returns from different search cells, or equivalently, the correlation between the columns of the sensing matrix. The proposed power allocation scheme is shown to improve the detection performance as compared to a uniform power allocation approach.

In this paper, we propose a sample selection method for compressive multiple-input multiple-output (MIMO) ultra-wideband (UWB) noise radar imaging. The proposed sample selection is based on comparing norm values of the transmitted sequences, and selects the largest M samples among N candidates per antenna. Moreover, we propose an adaptive weight allocation which improves normalized mean-square error (NMSE) by maximizing the mutual information between target echoes and the transmitted signals. Further, this weighting scheme is applicable to both sample selection schemes, a conventional random sampling and the proposed selection. Simulations show that the proposed selection method can improve the multiple target detection probability and NMSE. Moreover, the proposed weight allocation scheme is applicable to those selection methods and obtains spatial diversity and signal-to-noise ratio (SNR) gains.

Compressive sensing makes it possible to recover sparse target scenes from under-sampled measurements when uncorrelated random-noise waveforms are used as probing signals. The mathematical theory behind this assertion is based on the fact that Toeplitz and circulant random matrices generated from independent identically distributed (i.i.d) Gaussian random sequences satisfy the restricted isometry property. In real systems, waveforms have smooth, non-ideal autocorrelation functions, thereby degrading the performance of compressive sensing algorithms. In this paper, we extend the existing theory to incorporate such non-idealities into the analysis of compressive recovery. The presence of extended scatterers also causes distortions due to the correlation between different cells of the target scene. Extended targets make the target scene more dense, causing random transmit waveforms to be sub-optimal for recovery. We propose to incorporate extended targets by considering them to be sparsely representable in redundant dictionaries. We demonstrate that a low complexity algorithm to optimize the transmit waveform leads to improved performance.

In this paper, we apply the idea of partial sparsity to scene reconstruction associated with through-the-wall radar imaging of stationary targets. Partially sparse recovery considers the case when it is known a priori that the scene being imaged consists of two parts, one of which is sparse and the other is expected to be dense. More specifically, we consider the scene reconstruction problem involving a few stationary targets of interest when the building layout is assumed known. This implies that the support of the dense part of the image corresponding to the exterior and interior walls is known a priori. This knowledge may be available either through building blueprints or from prior surveillance operations. Using experimental data collected in a laboratory environment, we demonstrate the effectiveness of the partially sparse reconstruction of stationary through-the-wall scenes.

According to the feature of strong correlation of remote sensing image, a target recognition method based on Constrained Independent Component Analysis (CICA) via Compressed Sensing is put forward to realize the goal of remote sensing image recognition. By using abundance nonnegative restriction and the abundance sum-to-one constraint, an Adaptive Abundance Modeling (AAM) algorithm is proposed to ensure the reliability of the objective function. Then the CS feature space classifier based on Constrained Independent Component Analysis of sparse signal is established, so as to achieve recognition quickly. Experimental results show that the proposed algorithm can obtain more accurate results as high as 90%, and improve the timeliness effectively.

Image denoising is a fundamental image processing step for improving the overall quality of images. It is more important for remote sensing images because they require significantly higher visual quality than others. Conventional denoising methods, however, tend to over-suppress high-frequency details. To overcome this problem, we present a novel compressive sensing (CS)-based noise removing algorithm using adaptive multiple samplings and reconstruction error control. We first decompose an input noisy image into flat and edge regions, and then generate 8x8 block-based measurement matrices with Gaussian probability distributions. The measurement matrix is applied to the first three levels of wavelet transform coefficients of the input image for compressive sampling. The orthogonal matching pursuit (OMP) is applied to reconstruct each block. In the reconstruction process, we use different error threshold values according to both the decomposed region and the level of the wavelet transform based on the fast that the first level wavelet coefficients in the edge region have the lowest error threshold, whereas the third level wavelet coefficients in the flat region have the highest error threshold. By applying adaptive threshold value, we can reconstruct the image without noise. Experimental results demonstrate that the proposed method removes noise better than existing state-ofthe- art methods in the sense of both objective (PSNR/MSSIM) and subjective measures. We also implement the proposed denoising algorithm for remote sensing images with by minimizing the computational load.