This PDF file contains the front matter associated with SPIE Proceedings Volume 9109, including the Title Page, Copyright information, Table of Contents, Invited Panel Discussion, and Conference Committee listing.

Passive radar systems, which utilize broadcast and navigation signals as sources of opportunity, have attracted significant interests in recent years due to their low cost, covertness, and the availability of different illuminator sources. In this paper, we propose a novel method for synthetic aperture imaging in multi-static passive radar systems based on a group sparse Bayesian learning technique. In particular, the problem of imaging sparse targets is formulated as a group sparse signal reconstruction problem, which is solved using a complex multi- task Bayesian compressive sensing (CMT-BCS) method to achieve a high resolution. The proposed approach significantly improves the imaging resolution beyond the range resolution. Compared to the other group sparse signal reconstruction methods, such as the block orthogonal matching pursuit (BOMP) and group Lasso, the CMT-BCS provides significant performance improvement for the reconstruction of sparse targets in the redundant dictionary with high coherence. Simulations results demonstrate the superior performance of the proposed approach.

Compressive laser ranging (CLR) is a method that exploits the sparsity available in the range domain using compressive sensing methods to directly obtain range domain information. Conventional ranging methods are marred by requirements of high bandwidth analog detection which includes severe SNR fall off with bandwidth in analog-to-digital conversion (ADC). Compressive laser ranging solves this problem by obtaining sub-centimeter resolution while using low bandwidth detection. High rate digital pulse pattern generators and off the shelf photonic devices are used to modulate the transmitted and received light from a superluminescent diode. CLR detection is demonstrated using low bandwidth, high dynamic range detectors along with photon counting techniques. The use of an incoherent source eliminates speckle issues and enables simplified CLR methods to get multi-target range profiles with 1-3cm resolution. Using compressive sensing methods CLR allows direct range measurements in the sub-Nyquist regime while reducing system resources, in particular the need for high bandwidth ADC.

Dual-frequency radars offer the benefit of reduced complexity, fast computation time, and real-time target tracking in through-the-wall and urban sensing applications. Compared to single-frequency (Doppler) radar, the use of an additional frequency increases the maximum unambiguous range of dual-frequency radars to acceptable values for indoor target range estimation. Conventional dual-frequency technique uses phase comparison of the transmitted and received continuous-wave signals to provide an estimate of the target range. The case of multiple moving targets is handled by separating the different Doppler signatures prior to phase estimation. However, the dual-frequency approach for range estimation can be compromised due to the presence of noise and multipath. In this paper, we investigate a sparsity-based ranging approach as an alternative to the phase difference based technique for dual-frequency radar measurements. Supporting results based on computer simulations are provided that illustrate the advantages of the sparsity-based ranging technique over the conventional method.

Compressive noise radar imaging involves the inversion of a linear system using l1-based sparsity constraints. This linear system is characterized by the circulant system matrix generated by the transmit waveform. The imaging problem is solved using convex optimization. The characterization of imaging performance in the presence of additive noise and other random perturbations remains an important open problem. Computational studies designed to be generalizable suggest that uncertainties related to multiplicative noise adversely affect detection performance. Multiplicative noise occurs when the recorded transmit waveform is an inaccurate version of the actual transmitted signal. The actual transmit signal leaving the antenna is treated as the signal. If the recorded version is considered as a noisy version of this signal, then, generalizable numerical experiments show that the signal to noise ratio of the recorded signal should be greater than about 35 dB for accurate signal recovery.

Through-the-wall radar (TWR) systems are indispensable for situational awareness in a wide range of civilian and military applications. Multi-input multi-output (MIMO) TWR provides high spatial resolution for improved target detection in indoor environments. When combined with compressive sensing (CS), MIMO TWR enables good performance with a reduced number of samples, which, in turn, reduces the data acquisition time. Most of the existing MIMO TWR systems, either conventional or CS based, employ time-multiplexed transmitters. In this paper, we present a CS-MIMO TWR approach for the indoor environment under multipath propagation, in which the transmit antennas simultaneously emit different waveforms, thus allowing for further reduction of acquisition time as compared to time-multiplexed transmissions. Supporting simulation results are provided.

Analog sparse signals resulting from biomedical and sensing network applications are typically non–stationary with frequency–varying spectra. By ignoring that the maximum frequency of their spectra is changing, uniform sampling of sparse signals collects unnecessary samples in quiescent segments of the signal. A more appropriate sampling approach would be signal–dependent. Moreover, in many of these applications power consumption and analog processing are issues of great importance that need to be considered. In this paper we present a signal dependent non–uniform sampler that uses a Modified Asynchronous Sigma Delta Modulator which consumes low–power and can be processed using analog procedures. Using Prolate Spheroidal Wave Functions (PSWF) interpolation of the original signal is performed, thus giving an asynchronous analog to digital and digital to analog conversion. Stable solutions are obtained by using modulated PSWFs functions. The advantage of the adapted asynchronous sampler is that range of frequencies of the sparse signal is taken into account avoiding aliasing. Moreover, it requires saving only the zero–crossing times of the non–uniform samples, or their differences, and the reconstruction can be done using their quantized values and a PSWF–based interpolation. The range of frequencies analyzed can be changed and the sampler can be implemented as a bank of filters for unknown range of frequencies. The performance of the proposed algorithm is illustrated with an electroencephalogram (EEG) signal.

Multi-window spectrograms offer higher energy concentration in contrast to the traditional single-window spec- trograms. However, these quadratic time-frequency distributions were not introduced to deal with randomly undersampled signals. This paper applies sparse reconstruction techniques to provide time-frequency represen- tations of nonstationary signals using the Hermite functions as multiple windows, under randomly sampled or missing data. The multi-window sparse reconstruction approach improves energy concentration by utilizing the common local sparse frequency support property across the different employed windows.

In this paper, Compressive Sensing (CS) methods for Direct Sequence Spread Spectrum (DSSS) signals are introduced. DSSS signals are formed by modulating the original signal by a Pseudo-Noise sequence. This modulation spreads the spectra over a large bandwidth and makes interception of DSSS signals challenging. Interception of DSSS signals using traditional methods require Analog-to-Digital Converters sampling at very high rates to capture the full bandwidth. In this work, we propose CS methods that can intercept DSSS signals from compressive measurements. The proposed methods are evaluated with DSSS signals generated using Maximum-length Sequences and Binary Phase-Shift-Keying modulation at varying signal-to-noise and compression ratios.

Missing samples in the time domain introduce noise-like artifacts in the ambiguity domain due to their de facto zero values assumed by the bilinear transform. These artifacts clutter the dual domain of the time-frequency signal representation and obscures the time-frequency signature of single and multicomponent signals. In order to suppress the artifacts influence, we formulate a problem based on the sparsity aware kernel. The proposed kernel design is more robust to the artifacts caused by the missing samples.

Computer Algebra Software, especially Maple and its Image Tools package, is used to develop image compression using the Weibull distribution, Wavelet transform application and Singular Value Decomposition (SVD). For prototyping of the image compression process, Maple packages, Linear Algebra, Array Tools and Discrete Transform are used simultaneously with Image Tools image processing package. The image compression process implies the realization of matrix computing with high dimension matrices, and Maple software develops those operations easily and efficiently. Some image compression experiments are done, and the matrix dimension for minimum information needed to store an image is shown clearly, also the matrix dimension of redundant information. Implementation of algorithms for image compression in other computer algebra systems such as Mathematica and Maxima is proposed as future investigation path. Also it is proposed the use of curvelet transform as a tool for image compression,

We present a compressive spectral polarization imager driven by a rotating prism and a colored detector with a micropolarizer array. The prism which shears the scene along one spatial axis according to its wavelength components is successively rotated to different angles as measurement shots are taken. With 0°, 45°, 90°, 135° linear micropolarizers randomly distributed, the micropolarizer array is matched to the detector thus the the first three Stokes parameters of the scene are compressively sensed. The four dimensional (4D) data cube is thus projected onto the two dimensional (2D) FPA. Multiple snapshots are obtained for scenes with detailed spatial and spectral content. The 4D spectral-polarization data cube is reconstructed from the 2D measurements via nonlinear optimization with sparsity constraints. Polarization state planes (degree of linear polarization and angle of polarization) for each spectral slice of the hypercube are presented.

Digital holography, as any other coherent imaging modalities, is subject to speckle noise. Speckles may degrade significantly the image quality, therefore many optical and digital techniques were developed to suppress the speckles. In this paper we present a comparison between six digital speckle filtering techniques used for digital holography.

An experimental investigation of super-resolution imaging from measurements of projections onto a random basis is presented. In particular, a laboratory imaging system was constructed following an architecture that has become familiar from the theory of compressive sensing. The system uses a digital micromirror array located at an intermediate image plane to introduce binary matrices that represent members of a basis set. The system model was developed from experimentally acquired calibration data which characterizes the system output corresponding to each individual mirror in the array. Images are reconstructed at a resolution limited by that of the micromirror array using the split Bregman approach to total-variation regularized optimization. System performance is evaluated qualitatively as a function of the size of the basis set, or equivalently, the number of snapshots applied in the reconstruction.

Compressive Sensing (CS) is a novel scheme, in which a signal that is sparse in a known transform domain can be reconstructed using fewer samples. The signal reconstruction techniques are computationally intensive and have sluggish performance, which make them impractical for real-time processing applications . The paper presents novel architectures for Orthogonal Matching Pursuit algorithm, one of the popular CS reconstruction algorithms. We show the implementation results of proposed architectures on FPGA, ASIC and on a custom many-core platform. For FPGA and ASIC implementation, a novel thresholding method is used to reduce the processing time for the optimization problem by at least 25%. Whereas, for the custom many-core platform, efficient parallelization techniques are applied, to reconstruct signals with variant signal lengths of N and sparsity of m. The algorithm is divided into three kernels. Each kernel is parallelized to reduce execution time, whereas efficient reuse of the matrix operators allows us to reduce area. Matrix operations are efficiently paralellized by taking advantage of blocked algorithms. For demonstration purpose, all architectures reconstruct a 256-length signal with maximum sparsity of 8 using 64 measurements. Implementation on Xilinx Virtex-5 FPGA, requires 27.14 μs to reconstruct the signal using basic OMP. Whereas, with thresholding method it requires 18 μs. ASIC implementation reconstructs the signal in 13 μs. However, our custom many-core, operating at 1.18 GHz, takes 18.28 μs to complete. Our results show that compared to the previous published work of the same algorithm and matrix size, proposed architectures for FPGA and ASIC implementations perform 1.3x and 1.8x respectively faster. Also, the proposed many-core implementation performs 3000x faster than the CPU and 2000x faster than the GPU.

Conventional subspace-based signal direction-of-arrival estimation methods rely on the familiar L₂-norm-derived principal components (singular vectors) of the observed sensor-array data matrix. In this paper, for the first time in the literature, we find the L₁-norm maximum projection components of the observed data and search in their subspace for signal presence. We demonstrate that L₁-subspace direction-of-arrival estimation exhibits (i) similar performance to L₂ (usual singular-value/eigen-vector decomposition) direction-of-arrival estimation under normal nominal-data system operation and (ii) significant resistance to sporadic/occasional directional jamming and/or faulty measurements.

We propose and demonstrate a novel a compressive sensing swept source optical coherence tomography (SSOCT) system that enables high speed images to be taken while maintaining the high resolution offered from a large bandwidth sweep. Conventional SSOCT systems sweep the optical frequency of a laser ω(t) to determine the depth of the reflectors at a given lateral location. A scatterer located at delay τ appears as a sinusoid cos (ω(t)τ ) at the photodetector. The finite optical chirp rate and the speed of analog to digital and digital to analog converters limit the acquisition rate of an axial scan. The proposed acquisition modality enables much faster image acquisition rates by interrogating the beat signal at randomly selected optical frequencies while preserving resolution and depth of field. The system utilizes a randomly accessible laser, a modulated grating Y-branch laser, to sample the interference pattern from a scene at randomly selected optical frequencies over an optical bandwidth of 5 THz , corresponding to a resolution of 30 μm in air. The depth profile is then reconstructed using an l₁ minimization algorithm with a LASSO constraint. Signal-dependent noise sources, shot noise and phase noise, are analyzed and taken into consideration during the recovery. Redundant dictionaries are used to improve the reconstruction of the depth profile. A compression by a factor of 10 for sparse targets up to a depth of 15 mm in noisy environments is shown.

Swallowing accelerometry is a promising tool for non-invasive assessment of swallowing difficulties. A recent contribution showed that swallowing accelerometry signals for healthy swallows and swallows indicating laryn- geal penetration or tracheal aspiration have different time-frequency structures, which may be problematic for compressive sensing schemes based on time-frequency dictionaries. In this paper, we examined the effects of dif- ferent swallows on the accuracy of a compressive sensing scheme based on modulated discrete prolate spheroidal sequences. We utilized tri-axial swallowing accelerometry signals recorded from four patients during routinely schedule videofluoroscopy exams. In particular, we considered 77 swallows approximately equally distributed between healthy swallows and swallows presenting with some penetration/aspiration. Our results indicated that the swallow type does not affect the accuracy of a considered compressive sensing scheme. Also, the results con- firmed previous findings that each individual axis contributes different information. Our findings are important for further developments of a device which is to be used for long-term monitoring of swallowing difficulties.

Dynamic contrast enhanced MRI requires high spatial resolution for morphological information and high temporal resolution for contrast pharmacokinetics. The current techniques usually have to compromise the spatial information for the required temporal resolution. This paper presents a novel method that effectively integrates sparse sampling, parallel imaging, partial separable (PS) model, and sparsity constraints for highly accelerated DCE-MRI. Phased array coils were used to continuously acquire data from a stack of variable-density spiral trajectory with a golden angle. In reconstruction, the sparsity constraints, the coil sensitivities, spatial and temporal bases of the PS model are jointly estimated through alternating optimization. Experimental results from in vivo DCE liver imaging data show that the proposed method is able to achieve high spatial and temporal resolutions at the same time.

GPU computing of medical imaging applications adds an extra layer of acceleration after mathematical algorithms are used to reduce computation times. Our work improves the performance of the multiple-input multiple-output ultrasonic tomography algorithm, by using target sparseness and GPUs with CUDA. The main goal was to determine how GPUs can be best used to accelerate sparsity-aware algorithms for ultrasonic tomography applications. We present smart kernels to compute portions of the algorithm that exploit GPU resources such as shared memory and computing units that can be applied to other applications. Using our accelerated algorithm, we analyze different sparsity constraints setups and evaluate how GPU ultrasonic tomography with target sparseness behaves against the same algorithm that does not incorporate prior knowledge of target sparseness.

Lamb waves are utilized extensively for structural health monitoring of thin structures, such as plates and shells. Normal practice involves fixing a network of piezoelectric transducers to the structural plate member for generating and receiving Lamb waves. Using the transducers in pitch-catch pairs, the scattered signals from defects in the plate can be recorded. In this paper, we propose an l₁-norm minimization approach for localizing defects in thin plates, which inverts a multimodal Lamb wave based model through exploitation of the sparseness of the defects. We consider both symmetric and anti-symmetric fundamental propagating Lamb modes. We construct model-based dictionaries for each mode, taking into account the associated dispersion and attenuation through the medium. Reconstruction of the area being interrogated is then performed jointly across the two modes using the group sparsity constraint. Performance validation of the proposed defect localization scheme is provided using simulated data for an aluminum plate.

In certain imaging applications, conventional lens technology is constrained by the lack of materials which can effectively focus the radiation within reasonable weight and volume. One solution is to use coded apertures –opaque plates perforated with multiple pinhole-like openings. If the openings are arranged in an appropriate pattern, the images can be decoded, and a clear image computed. Recently, computational imaging and the search for means of producing programmable software-defined optics have revived interest in coded apertures. The former state-of-the-art masks, MURAs (Modified Uniformly Redundant Arrays) are effective for compact objects against uniform backgrounds, but have substantial drawbacks for extended scenes: 1) MURAs present an inherently ill-posed inversion problem that is unmanageable for large images, and 2) they are susceptible to diffraction: a diffracted MURA is no longer a MURA. This paper presents a new class of coded apertures, Separable Doubly-Toeplitz masks, which are efficiently decodable, even for very large images –orders of magnitude faster than MURAs, and which remain decodable when diffracted. We implemented the masks using programmable spatial-lightmodulators. Imaging experiments confirmed the effectiveness of Separable Doubly-Toeplitz masks - images collected in natural light of extended outdoor scenes are rendered clearly.

The recently introduced compressed sensing (CS) framework enables low complexity video acquisition via sub- Nyquist rate sampling. In practice, the resulting CS samples are quantized and indexed by finitely many bits (bit-depth) for transmission. In applications where the bit-budget for video transmission is constrained, rate- distortion optimization (RDO) is essential for quality video reconstruction. In this work, we develop a double-level RDO scheme for compressive video sampling, where frame-level RDO is performed by adaptively allocating the fixed bit-budget per frame to each video block based on block-sparsity, and block-level RDO is performed by modelling the block reconstruction peak-signal-to-noise ratio (PSNR) as a quadratic function of quantization bit-depth. The optimal bit-depth and the number of CS samples are then obtained by setting the first derivative of the function to zero. In the experimental studies the model parameters are initialized with a small set of training data, which are then updated with local information in the model testing stage. Simulation results presented herein show that the proposed double-level RDO significantly enhances the reconstruction quality for a bit-budget constrained CS video transmission system.

We look at the design of projective measurements based upon image priors. 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. Any sparse image reconstruction algorithm has improved performance using the developed measurement matrix over using random projections. We implement a 2-way clustering then K-means algorithm to separate the estimated image space into low dimensional clusters for image reconstruction via a minimum mean square error estimator. Some insights into the empirical estimation of the image patch manifold are developed and several results are presented.

The compressive sensing imaging technique, based on the realization of random measurement via active or passive devices (e.g., DMD), has attracted more and more attention. For imaging target of interest within large uniform scene (e.g., ships in the sea), high-resolution image was usually reconstructed and then used to detect targets, however the process is time-consuming, and moreover only part of the image consists of the targets of interest. In this paper, the stepwise multi-resolution fast target detection and imaging method through the combination of different numbers of DMD mirrors was explored. Low resolution image for larger area target searching and successively higher resolution image for smaller area containing the targets were reconstructed. Also, non-imaging fast target detection was realized based on the detector energy intensity, which includes the steps of rough target positioning by successively opening DMD blocks and accurate target positioning by adjusting the rough areas via intelligent search algorithm. Simulation experiments were carried out to compare the proposed method with traditional method. The result shows the area of the ships are accurately positioned without reconstructing the image by the proposed method and the multi-level scale imaging for suspect areas is realized. Compared with traditional target detection method from the reconstructed image, the proposed method not only highly enhances the measuring and reconstruction efficiency but also improves the positioning accuracy, which would be more significant for large area scene.

Recently, Compressive Sensing (CS) has been successfully applied to multiple branches of science. However, most CS methods require sequential capture of a large number of random data projections, which is not advantageous to LIDAR systems, wherein reduction of 3D data sampling is desirable. In this paper, we introduce a new method called Resampling Compressive Sensing (RCS) that can be applied to a single capture of a LIDAR point cloud to reconstruct a 3- dimensional representation of the scene with a significant reduction in the required amount of data. Examples of 50 to 80% reduction in point count are shown for sample point cloud data. The proposed new CS method leads to a new data collection paradigm that is general and different from traditional CS sensing such as the single-pixel camera architecture.

Originally proposed in SPIE DSS’13, the compressive line sensing (CLS) imaging system adopts the paradigm of independently sensing each line and jointly reconstructing a group of lines. Such system achieves “resource compression” and is still compatible with the conventional push-broom operation mode. This paper attempts to extend the CLS concept, originally developed to effectively acquire scene intensity images in a scattering medium, to 3D scene reconstruction through the adoption of a temporal-spatial measurement matrix. The sensing model is discussed. Simulation results are presented as part of this work.