This PDF file contains the front matter associated with SPIE Proceedings Volume 8717, including the Title Page, Copyright Information, Table of Contents, and the Conference Committee listing.

MIMO radar utilizes the transmission and reflection of multiple independent waveforms to construct an image approximating a target scene. Compressed sensing (CS) techniques such as total variation (TV) minimization and greedy algorithms can permit accurate reconstructions of the target scenes from undersampled data. The success of these CS techniques is largely dependent on the structure of the measurement matrix. A discretized inverse scattering model is used to examine the imaging problem, and in this context the measurement matrix consists of array parameters regarding the geometry of the transmitting and receiving arrays, signal type, and sampling rate. We derive some conditions on these parameters that guarantee the success of these CS reconstruction algorithms. The effect of scene sparsity on reconstruction accuracy is also addressed. Numerical simulations illustrate the success of reconstruction when the array and sampling conditions are satisfied, and we also illustrate erroneous reconstructions when the conditions are not satisfied.

We consider a compressive video acquisition system where frame blocks are sensed independently. Varying block sparsity is exploited in the form of individual per-block open-loop sampling rate allocation with minimal system overhead. At the decoder, video frames are reconstructed via sliding-window inter-frame total variation minimization. Experimental results demonstrate that such rate-adaptive compressive video acquisition improves noticeably the rate-distortion performance of the video stream over fixed-rate acquisition approaches.

We overview two optical compressive motion detection technique we have developed. First technique detects changes in a sequence of frames reconstructed from a compressive imager that captures optically Radon projections. The second technique uses a specially designed optical motion detector. Compressive motion tracking with compression ratio of 2-3 orders of magnitude is achieved.

Compressive sensing (CS) theory has drawn great interest and led to new imaging techniques in many different fields. In recent years, the FAU/HBOI OVOL has conducted extensive research to study the CS based active electro-optical imaging system in the scattering medium such as the underwater environment. The unique features of such system in comparison with the traditional underwater electro-optical imaging system are discussed. Building upon the knowledge from the previous work on a frame based CS underwater laser imager concept, more advantageous for hover-capable platforms such as the Hovering Autonomous Underwater Vehicle (HAUV), a compressive line sensing underwater imaging (CLSUI) system that is more compatible with the conventional underwater platforms where images are formed in whiskbroom fashion, is proposed in this paper. Simulation results are discussed.

Obtaining high frame rates is a challenge with compressive sensing (CS) systems that gather measurements in a sequential manner, such as the single-pixel CS camera. One strategy for increasing the frame rate is to divide the FOV into smaller areas that are sampled and reconstructed in parallel. Following this strategy, InView has developed a multi-aperture CS camera using an 8×4 array of photodiodes that essentially act as 32 individual simultaneously operating single-pixel cameras. Images reconstructed from each of the photodiode measurements are stitched together to form the full FOV. To account for crosstalk between the sub-apertures, novel modulation patterns have been developed to allow neighboring sub-apertures to share energy. Regions of overlap not only account for crosstalk energy that would otherwise be reconstructed as noise, but they also allow for tolerance in the alignment of the DMD to the lenslet array. Currently, the multi-aperture camera is built into a computational imaging workstation configuration useful for research and development purposes. In this configuration, modulation patterns are generated in a CPU and sent to the DMD via PCI express, which allows the operator to develop and change the patterns used in the data acquisition step. The sensor data is collected and then streamed to the workstation via an Ethernet or USB connection for the reconstruction step. Depending on the amount of data taken and the amount of overlap between sub-apertures, frame rates of 2–5 frames per second can be achieved. In a stand-alone camera platform, currently in development, pattern generation and reconstruction will be implemented on-board.

We look at the design of projective measurements for compressive imaging based upon image priors and device constraints. If one assumes that image patches from natural imagery can be modeled as a low rank manifold, we develop an optimality criterion for a measurement matrix based upon separating the canonical elements of the manifold prior. We then describe a stochastic search algorithm for finding the optimal measurements under device constraints based upon a subspace mismatch algorithm. The algorithm is then tested on a prototype compressive imaging device designed to collect an 8x4 array of projective measurements simultaneously. This work is based upon work supported by DARPA and the SPAWAR System Center Pacific under Contract No. N66001-11-C-4092. The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government.

A modified robust two-dimensional compressive sensing algorithm for reconstruction of sparse time-frequency representation (TFR) is proposed. The ambiguity function domain is assumed to be the domain of observations. The two-dimensional Fourier bases are used to linearly relate the observations to the sparse TFR, in lieu of the Wigner distribution. We assume that a set of available samples in the ambiguity domain is heavily corrupted by an impulsive type of noise. Consequently, the problem of sparse TFR reconstruction cannot be tackled using standard compressive sensing optimization algorithms. We introduce a two-dimensional L-statistics based modification into the transform domain representation. It provides suitable initial conditions that will produce efficient convergence of the reconstruction algorithm. This approach applies sorting and weighting operations to discard an expected amount of samples corrupted by noise. The remaining samples serve as observations used in sparse reconstruction of the time-frequency signal representation. The efficiency of the proposed approach is demonstrated on numerical examples that comprise both cases of monocomponent and multicomponent signals.

An important outcome of radar signal processing is the detection of the presence or absence of target reflections at each pixel location in a radar image. In this paper, we propose a technique based on extreme value theory for characterizing target detection in the context of compressive sensing. In order to accurately characterize target detection in radar systems, we need to relate detection thresholds and probabilities of false alarm. However, when convex optimization algorithms are used for compressive radar imaging, the recovered signal may have unknown and arbitrary probability distributions. In such cases, we resort to Monte Carlo simulations to construct empirical distributions. Computationally, this approach is impractical for computing thresholds for low probabilities of false alarm. We propose to circumvent this problem by using results from extreme-value theory.

A new pseudorandom coded aperture design framework for multi-frame Coded Aperture Snapshot Spectral Imaging (CASSI) system is presented. Our previous work determines a matrix system model for multi-frame CASSI which is used to design sets of spectrally selective coded apertures. Then, the required number of CASSI measurements is dictated by the desired profile of spectral bands. This work aims at optimizing the set of selective coded apertures such that the number of FPA CASSI measurements is reduced to a desired number of shots, regardless of the targeted spectral profile. A set of pseudorandom weights are determined such that the rank of the matrix representing the ensemble of weighted spectrally selective coded apertures is optimized. Simulations show higher quality of spectral image reconstruction than those attained by systems using random coded aperture sets.

The emerging field of Compressive Sensing (CS) provides a new way to capture data by shifting the heaviest burden of data collection from the sensor to the computer on the user-end. This new means of sensing requires fewer measurements for a given amount of information than traditional sensors. We investigate the efficacy of CS for capturing HyperSpectral Imagery (HSI) remotely. We also introduce a new family of algorithms for constructing HSI from CS measurements with Split Bregman Iteration [Goldstein and Osher,2009]. These algorithms combine spatial Total Variation (TV) with smoothing in the spectral dimension. We examine models for three different CS sensors: the Coded Aperture Snapshot Spectral Imager-Single Disperser (CASSI-SD) [Wagadarikar et al.,2008] and Dual Disperser (CASSI-DD) [Gehm et al.,2007] cameras, and a hypothetical random sensing model closer to CS theory, but not necessarily implementable with existing technology. We simulate the capture of remotely sensed images by applying the sensor forward models to well-known HSI scenes - an AVIRIS image of Cuprite, Nevada and the HYMAP Urban image. To measure accuracy of the CS models, we compare the scenes constructed with our new algorithm to the original AVIRIS and HYMAP cubes. The results demonstrate the possibility of accurately sensing HSI remotely with significantly fewer measurements than standard hyperspectral cameras.

Coded Aperture Snapshot Spectral Imaging system (CASSI) captures spectral information of a scene using a reduced amount of focal plane array (FPA) projections. These projections are highly structured and localized such that each measurement contains information of a small portion of the data cube. Compressed sensing reconstruction algorithms are then used to recover the underlying 3-dimensional (3D) scene. The computational burden to recover a hyperspectral scene in CASSI is overwhelming for some applications such that reconstructions can take hours in desktop architectures. This paper presents a new method to reconstruct a hyperspectral signal from its compressive measurements using several overlapped block reconstructions. This approach exploits the structure of the CASSI sensing matrix to separately reconstruct overlapped regions of the 3D scene. The resultant reconstructions are then assembled to obtain the full recovered data cube. Typically, block-processing causes undesired artifacts in the recovered signal. Vertical and horizontal overlaps between adjacent blocks are then used to avoid these artifacts and increase the quality of reconstructed images. The reconstruction time and the quality of the reconstructed images are calculated as a function of the block-size and the amount of overlapped regions. Simulations show that the quality of the reconstructions is increased up to 6 dB and the reconstruction time is reduced up to 4 times when using block-based reconstruction instead of full data cube recovery at once. The proposed method is suitable for multi-processor architectures in which each core recovers one block at a time.

Compressive hyperspectral imaging is based on the fact that hyperspectral data is highly redundant. However, there is no symmetry between the compressibility of the spatial and spectral domains, and that should be taken into account for optimal compressive hyperspectral imaging system design. Here we present a study of the influence of the ratio between the compression in the spatial and spectral domains on the performance of a 3D separable compressive hyperspectral imaging method we recently developed.

In this paper, a distributed compressive sensing (CS) model is proposed to recover missing data samples along the temporal frequency domain for through-the-wall radar imaging (TWRI). Existing CS-based approaches recover the signal from each antenna independently, without considering the correlations among measurements. The proposed approach, on the other hand, exploits the structure or correlation in the signals received across the array aperture by using a hierarchical Bayesian model to learn a shared prior for the joint reconstruction of the high-resolution radar profiles. A backprojection method is then applied to form the radar image. Experimental results on real TWRI data show that the proposed approach produces better radar images using fewer measurements compared to existing CS-based TWRI methods.

Compressive sensing (CS) based multi-input multi-output (MIMO) radar systems that explore the sparsity of targets in the target space enable either the same localization performance as traditional methods but with significantly fewer measurements, or significantly improved performance with the same number of measurements. However, the enabling assumption, i.e., the target sparsity, diminishes in the presence of clutter, since clutters is highly correlated with the desire target echoes. This paper proposes an approach to suppress clutter in the context of CS MIMO radars. Assuming that the clutter covariance is known, Capon beamforming is applied at the fusion center on compressively obtained data, which are forwarded by the receive antennas. Subsequently, the target is estimated using CS theory, by exploiting the sparsity of the beamformed signals.

In this paper, we address sparsity-based imaging of building interior structures for through-the-wall radar imaging and urban sensing applications. The proposed approach utilizes information about common building construction practices to form an appropriate sparse representation of the building layout. With a ground based SAR system, and considering that interior walls are either parallel or perpendicular to the exterior walls, the antenna at each position would receive reflections from the walls parallel to the radar's scan direction as well as from the corners between two meeting walls. We propose a two-step approach for wall detection and localization. In the first step, a dictionary of possible wall locations is used to recover the positions of both interior and exterior walls that are parallel to the scan direction. A follow-on step uses a dictionary of possible corner reflectors to locate wall-wall junctions along the detected wall segments, thereby determining the true wall extents and detecting walls perpendicular to the scan direction. The utility of the proposed approach is demonstrated using simulated data.

In this paper, radar detection via compressive sensing is explored. Compressive sensing is a new theory of sampling which allows the reconstruction of a sparse signal by sampling at a much lower rate than the Nyquist rate. By using this technique in radar, the use of matched filter can be eliminated and high rate sampling can be replaced with low rate sampling. In this paper, compressive sensing is analyzed by applying varying factors such as noise and different measurement matrices. Different reconstruction algorithms are compared by generating ROC curves to determine their detection performance. We conduct simulations for a 64-length signal with 3 targets to determine the effectiveness of each algorithm in varying SNR. We also propose a simplified version of Orthogonal Matching Pursuit (OMP). Through numerous simulations, we find that a simplified version of Orthogonal Matching Pursuit (OMP), can give better results than the original OMP in noisy environments when sparsity is highly over estimated, but does not work as well for low noise environments.

Ultra-wideband (UWB) technology has been widely utilized in radar system because of the advantage of the ability of high spatial resolution and object-distinction capability. A major challenge in UWB signal processing is the requirement for very high sampling rate under Shannon-Nyquist sampling theorem which exceeds the current ADC capacity. Recently, new approaches based on the Finite Rate of Innovation (FRI) allow significant reduction in the sampling rate. A system for sampling UWB radar echo signal at an ultra-low sampling rate and the estimation of time-delays is presented in the paper. An ultra-low rate sampling scheme based on FRI is applied, which often results in sparse parameter extraction for UWB radar signal detection. The parameters such as time-delays are estimated using the framework of compressed sensing based on total-variation norm minimization. With this system, the UWB radar signal can be accurately reconstructed and detected with overwhelming probability at the rate much lower than Nyquist rate. The simulation results show that the proposed method is effective for sampling and detecting UWB radar signal at an ultra-low sampling rate.

Detection and estimation of wideband radio frequency signals are major functions of persistent surveillance systems and rely heavily on high sampling rates dictated by the Nyquist-Shannon sampling theorem. In this paper we address the problem of detecting wideband signals in the presence of AWGN and interference with a fraction of the measurements produced by traditional sampling protocols. Our approach uses learned dictionaries in order to work with less restriction on the class of signals to be analyzed and Compressive Sensing (CS) to reduce the number of samples required to process said signals. We apply the K-SVD technique to design a dictionary, reconstruct using a recently developed signal-centric reconstruction algorithm (SSCoSaMP), then use maximum likelihood estimation to detect and estimate the carrier frequencies of wideband RF signals while assuming no prior knowledge of the frequency location. This solution relaxes the assumption that signals are sparse in a fixed/predetermined orthonormal basis and reduces the number of measurements required to detect wideband signals all while having comparable error performance to traditional detection schemes. Simulations of frequency hopping signals corrupted by additive noise and chirp interference are presented. Other experimental results are included to illustrate the flexibility of learned dictionaries whereby the roles of the chirps and the sinusoids are reversed.

Robust signal analysis based on the L-statistic was introduced for signals disturbed with high additive impulse noise. The basic idea is that a certain, usually large number of arbitrary positioned signal samples is declared as heavily corrupted by noise. Then, these samples are removed. Thus, they can be considered as absent or unavailable. Hence, the L-statistics significantly reduces the number of available signal samples. Moreover these samples are randomly distributed, so an efficient analysis of such signals invokes the compressive sensing reconstruction algorithms. Also, it will be shown that the variance of noise, produced by missing samples, can be used as powerful tool for signal reconstruction. Additionally, in order to provide separation of stationary and nonstationary signals the L-statistic is combined with compressive sensing algorithms. The theoretical considerations are verified by various examples, where discrete forms of the Fourier transform and short-time Fourier transform are used to demonstrate the effective integration of the two techniques.

In this paper, compressive detection strategies for FHSS signals are introduced. Rapid switching of the carrier frequency among many channels using a pseudorandom sequence makes detection of FHSS signals challenging. The conventional approach to detect these signals is to rapidly scan small segments of the spectrum sequentially. However, such a scanner has the inherent risk of never overlapping with the transmitted signal depending on factors such as rate of hopping and scanning. In this paper, we propose compressive detection strategies that sample the full spectrum in a compressive manner. Theory and simulations are presented to illustrate the benefits of the proposed framework.

The potential of compressive sensing (CS) has spurred great interest in the research community and is a fast growing area of research. However, research translating CS theory into practical hardware and demonstrating clear and significant benefits with this hardware over current, conventional imaging techniques has been limited. This article helps researchers to find those niche applications where the CS approach provide substantial gain over conventional approaches by articulating guidelines for finding these niche CS applications. Furthermore, in this paper we utilized these guidelines to find one such new application for CS; sea skimming missile detection. As a proof of concept, it is demonstrated that a simplified CS missile detection architecture and algorithm provides comparable results to the conventional imaging approach but using a smaller FPA.