We propose a novel application of the sparse and low-rank (SLR) decomposition method to decode cognitive states for concept activity measured using fMRI BOLD. Current decoding methods attempt to reduce the dimensionality of fMRI BOLD signals to increase classification rate, but do not address the separable issues of multiple noise sources and complexity in the underlying data. Our feature transformation method extends SLR to separate task activity from the resting state and extract concept specific cognitive state. We show a significant increase in single trial decoding of concepts from fMRI BOLD using SLR to extract task specific cognitive state.
We propose a method to image a complex scene with spotlight synthetic aperture radar (SAR) despite the presence of multiple moving targets. Many recent methods use sparsity-based reconstruction coupled with phase error corrections of moving targets to reconstruct stationary scenes. However, these methods rely on the assumption that the scene itself is sparse and thus unfortunately cannot handle realistic SAR scenarios with complex backgrounds consisting of more than just a few point targets. Our method makes use of sparse and low-rank (SLR) matrix decomposition, an efficient method for decomposing a low-rank matrix and sparse matrix from their sum. For detecting the moving targets and reconstructing the stationary background, SLR uses a convex optimization model that penalizes the nuclear norm of the low rank background structure and the L1 norm of the sparse moving targets. We propose an L1-norm regularization reconstruction method to form the input data matrix, which is grossly corrupted by the moving targets. Each column of the input matrix is a reconstructed SAR image with measurements from a small number of azimuth angles. The use of the L1-norm regularization and a sparse transform permits us to reconstruct the scene with significantly fewer measurements so that moving targets are approximately stationary. We demonstrate our SLR-based approach using simulations adapted from the GOTCHA Volumetric SAR data set. These simulations show that SLR can accurately image multiple moving targets with different individual motions in complex scenes where methods that assume a sparse scene would fail.
In this paper we introduce two novel methods for application of `1-minimization. In the first method, sparse and low-rank decomposition and compressive sensing-based retrieval are combined and applied to a low power surveillance model. The method exploits the ability of sparse and low-rank decompositions to extract significant and stationary features and the ability of compressive sensing approaches to reduce the number of measurements necessary. In the second method, a contiguity prior is added to compressive sensing methods on images and a numerical approach is proposed to solve this novel problem. Results are displayed in which the contiguity constrained method is applied to the low power surveillance model.
We describe a foveated compressive sensing approach for image analysis applications that utilizes knowledge of the task to be performed to reduce the number of required measurements compared to conventional Nyquist sampling and compressive sensing based approaches. Our Compressive Optical Foveated Architecture (COFA) adapts the dictionary and compressive measurements to structure and sparsity in the signal, task, and scene by reducing measurement and dictionary mutual coherence and increasing sparsity using principles of actionable information and foveated compressive sensing. Actionable information is used to extract task-relevant regions of interest (ROIs) from a low-resolution scene analysis by eliminating the effects of nuisances for occlusion and anomalous motion detection. From the extracted ROIs, preferential measurements are taken using foveation as part of the compressive sensing adaptation process. The task-specific measurement matrix is optimized by using a novel saliency-weighted coherence minimization with respect to the learned signal dictionary. This incorporates the relative usage of the atoms in the dictionary. Therefore, the measurement matrix is not random, as in conventional compressive sensing, but is based on the dictionary structure and atom distributions. We utilize a patch-based method to learn the signal priors. A treestructured dictionary of image patches using KSVD is learned which can sparsely represent any given image patch with the tree-structure. We have implemented COFA in an end-to-end simulation of a vehicle fingerprinting task for aerial surveillance using foveated compressive measurements adapted to hierarchical ROIs consisting of background, roads, and vehicles. Our results show 113x reduction in measurements over conventional sensing and 28x reduction over compressive sensing using random measurements.
With the advent of a new sampling theory in recent years, compressed sensing (CS), it is possible to reconstruct signals
from measurements far below the Nyquist rate. The CS theory assumes that signals are sparse and that measurement
matrices satisfy certain conditions. Even though there have been many promising results, unfortunately there still exists a
gap between the theory and actual real world applications. This is because of the fundamental problem that the CS
formulation is discrete. We propose a sampling and reconstructing method for frequency-sparse signals that addresses
this issue. The signals in our scenario are supported in a continuous sparsifying domain rather than discrete. This work
focuses on a typical case in which the unknowns are frequencies and amplitudes. However, directly looking for the
unknowns that best fit the measurements in the least-squares sense is a non-convex optimization problem, because
sinusoids are oscillatory. Our approach extends the utility of CS to simplify this problem to a locally convex problem,
hence making the solutions tractable. Direct measurements are taken from non-uniform time-samples, which is an
extension of the CS problem with a subsampled Fourier matrix. The proposed reconstruction algorithm iteratively
approximates the solutions using CS and then accurately solves for the frequencies with Newton's method and for the
amplitudes with linear least squares solutions. Our simulations show success in accurate reconstruction of signals with
arbitrary frequencies and significantly outperform current spectral compressed sensing methods in terms of
reconstruction fidelity for both noise-free and noisy cases.
An aerial multiple camera tracking paradigm needs to not only spot unknown targets and track them, but also needs to
know how to handle target reacquisition as well as target handoff to other cameras in the operating theater. Here we
discuss such a system which is designed to spot unknown targets, track them, segment the useful features and then create
a signature fingerprint for the object so that it can be reacquired or handed off to another camera. The tracking system
spots unknown objects by subtracting background motion from observed motion allowing it to find targets in motion,
even if the camera platform itself is moving. The area of motion is then matched to segmented regions returned by the
EDISON mean shift segmentation tool. Whole segments which have common motion and which are contiguous to each
other are grouped into a master object. Once master objects are formed, we have a tight bound on which to extract
features for the purpose of forming a fingerprint. This is done using color and simple entropy features. These can be
placed into a myriad of different fingerprints. To keep data transmission and storage size low for camera handoff of
targets, we try several different simple techniques. These include Histogram, Spatiogram and Single Gaussian Model.
These are tested by simulating a very large number of target losses in six videos over an interval of 1000 frames each
from the DARPA VIVID video set. Since the fingerprints are very simple, they are not expected to be valid for long
periods of time. As such, we test the shelf life of fingerprints. This is how long a fingerprint is good for when stored
away between target appearances. Shelf life gives us a second metric of goodness and tells us if a fingerprint method
has better accuracy over longer periods. In videos which contain multiple vehicle occlusions and vehicles of highly
similar appearance we obtain a reacquisition rate for automobiles of over 80% using the simple single Gaussian model
compared with the null hypothesis of <20%. Additionally, the performance for fingerprints stays well above the null
hypothesis for as much as 800 frames. Thus, a simple and highly compact single Gaussian model is useful for target
reacquisition. Since the model is agnostic to view point and object size, it is expected to perform as well on a test of
target handoff. Since some of the performance degradation is due to problems with the initial target acquisition and
tracking, the simple Gaussian model may perform even better with an improved initial acquisition technique. Also, since
the model makes no assumption about the object to be tracked, it should be possible to use it to fingerprint a multitude of
objects, not just cars. Further accuracy may be obtained by creating manifolds of objects from multiple samples.
A recently proposed approach for compressed sensing, or compressive sampling, with deterministic measurement
matrices made of chirps is applied to images that possess varying degrees of sparsity in their wavelet representations.
The "fast reconstruction" algorithm enabled by this deterministic sampling scheme as developed by
Applebaum et al.  produces accurate results, but its speed is hampered when the degree of sparsity is not
sufficiently high. This paper proposes an efficient reconstruction algorithm that utilizes discrete chirp-Fourier
transform (DCFT) and updated linear least squares solutions and is suitable for medical images, which have
good sparsity properties. Several experiments show the proposed algorithm is effective in both reconstruction
fidelity and speed.