A general echo model is derived for the synthetic aperture radar (SAR) imaging with high resolution based on the scalar form of Maxwell's equations. After the consideration of the general echo model in frequency domain, a compressive sensing (CS) matrix is constructed from random partial Fourier matrices for processing the range CS SAR imaging. Simulations validate the orthogonality of the proposed CS matrix and the CS SAR imaging based on the general echo model.
In this paper, we consider moving target localization in urban environments using a multiplicity of dual-frequency radars. Dual-frequency radars offer the benefit of reduced complexity and fast computation time, thereby permitting real-time indoor target localization and tracking. The multiple radar units are deployed in a distributed system configuration, which provides robustness against target obscuration. We develop the dual-frequency signal model for the distributed radar system under phase errors and employ a joint sparse scene reconstruction and phase error correction technique to provide accurate target location and velocity estimates. Simulation results are provided that validate the performance of the proposed scheme under both full and reduced data volumes.
Passive Bistatic Radar (PBR) systems use illuminators of opportunity, such as FM, TV, and DAB broadcasts. The most common illuminator of opportunity used in PBR systems is the FM radio stations. Single FM channel based PBR systems do not have high range resolution and may turn out to be noisy. In order to enhance the range resolution of the PBR systems algorithms using several FM channels at the same time are proposed. In standard methods, consecutive FM channels are translated to baseband as is and fed to the matched filter to compute the range-Doppler map. Multichannel FM based PBR systems have better range resolution than single channel systems. However superious sidelobe peaks occur as a side effect. In this article, we linearly predict the surveillance signal using the modulated and delayed reference signal components. We vary the modulation frequency and the delay to cover the entire range-Doppler plane. Whenever there is a target at a specific range value and Doppler value the prediction error is minimized. The cost function of the linear prediction equation has three components. The first term is the real-part of the ordinary least squares term, the second-term is the imaginary part of the least squares and the third component is the l2-norm of the prediction coefficients. Separate minimization of real and imaginary parts reduces the side lobes and decrease the noise level of the range-Doppler map. The third term enforces the sparse solution on the least squares problem. We experimentally observed that this approach is better than both the standard least squares and other sparse least squares approaches in terms of side lobes. Extensive simulation examples will be presented in the final form of the paper.
This paper addresses the problem of scene reconstruction in conjunction with wall-clutter mitigation for com- pressed multi-view through-the-wall radar imaging (TWRI). We consider the problem where the scene behind- the-wall is illuminated from different vantage points using a different set of frequencies at each antenna. First, a joint Bayesian sparse recovery model is employed to estimate the antenna signal coefficients simultaneously, by exploiting the sparsity and inter-signal correlations among antenna signals. Then, a subspace-projection technique is applied to suppress the signal coefficients related to the wall returns. Furthermore, a multi-task linear model is developed to relate the target coefficients to the image of the scene. The composite image is reconstructed using a joint Bayesian sparse framework, taking into account the inter-view dependencies. Experimental results are presented which demonstrate the effectiveness of the proposed approach for multi-view imaging of indoor scenes using a reduced set of measurements at each view.
We simulate and study various computational techniques for image reconstruction applied to a multiplexed Mid-wave-IR Imager. The imager consists of two arms where one is dedicated to high resolution imaging using a lower resolution Focal Plane Array and the other is a single measurement Multispectral imager which uses dispersive optics. We exploit the compressibility of images to estimate a high resolution image and its corresponding lower resolution multispectral data cube using standard computational techniques.
Hyperspectral imagery involves capturing and processing a tremendous amount of data, which sets severe system resource requirements. This has motivated the application of compressive sensing for different spectroscopic and spectroscopic imager systems. Several new compressive hyperspectral architectures have been designed to stretch the common limitations of classical systems. However, the application of the compressive sensing framework involves design of system architectures that differ significantly from the conventional ones. Since compressive sensing differs essentially from conventional sensing, it cannot be implemented for hyperspectral imaging by simply modifying one of the components of a conventional hyperspectral system, rather it requires a complete new design. In this work we present a comparison between four compressive hyperspectral architectures to conventional architectures. The compressive hyperspectral sensing compared are: Coded Aperture Snapshot Spectral Imaging (CASSI), Compressive HS Imaging by Separable Spatial And Spectral Operators (CHISSS), (Liquid-crystal Compressive spectral Imager) LiCSI and (Spectral Single-Pixel) SSP systems. Those methods are compared to conventional spatial/spectral scanning hyperspectral such as pushbroom, whiskbroom and color filter techniques. A fundamental comparison between these architectures is presented in terms of optical system volume and radiometric efficiency.
We present a compressive spectral polarization imager based on a prism which is rotated to different angles as the measurement shots are taken, and a colored detector with a micropolarizer array. The prism shears the scene along one spatial axis according to its wavelength components. The scene is then projected to different locations on the detector as measurement shots are taken. Composed of 0°, 45°, 90°, 135° linear micropolarizers, the pixels of the micropolarizer array matched to that of the colored detector, thus 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. Designed patterns for the micropolarizer and the colored detector are applied so as to improve the reconstruction problem. The 4D spectral-polarization data cube is reconstructed from the 2D measurements via nonlinear optimization with sparsity constraints. Computer simulations are performed and the performance of designed patterns is compared with random patterns.
This paper reports an overview of recent results in compressive imaging and detection using a single-pixel camera. These applications use a digital micromirror device to spatially modulate the light from an observed scene using binary sensing patterns. The patterns are obtained from a special Hadamard matrix that contains blocks of rows of which each has a common local signature pattern. The blocks partition the Hadamard spectrum, thus permitting analysis of the scene in terms of these local signature patterns. In contrast, Hadamard patterns are typically described in terms of their sequency, which is a global property of each individual row. The proposed local-signature, row-block point of view can be beneficial since it permits us to adaptively select the best blocks with which to sense the signal/scene of interest, or to select the best blocks based on a priori information. As a result, in imaging applications more fine-scale detail can be extracted from the scene, and in detection applications fewer false positives can result. Note, this signature row-block partitioning is a general mathematical technique that can be applied to the Kronecker product of any two matrices, of any size. For example, in our imaging application, we extend this idea to a Hadamard matrix that is not a power of two, yet whose block-signatures possess the familiar Sylvester-Walsh power-of-two sequency patterns.
We consider the problem of foreground and background extraction from compressed-sensed (CS) surveillance video. We propose, for the first time in the literature, a principal component analysis (PCA) approach that computes the low-rank subspace of the background scene directly in the CS domain. Rather than computing the conventional L2-norm-based principal components, which are simply the dominant left singular vectors of the CS measurement matrix, we compute the principal components under an L1-norm maximization criterion. The background scene is then obtained by projecting the CS measurement vector onto the L1 principal components followed by total-variation (TV) minimization image recovery. The proposed L1-norm procedure directly carries out low-rank background representation without reconstructing the video sequence and, at the same time, exhibits significant robustness against outliers in CS measurements compared to L2-norm PCA.
In this paper, a compressing and reconstruction method for a noise video based on Compressed Sensing (CS) theory is proposed. At first, the CS theory is presented. Then the noise video is estimated from noisy measurement by solving the convex minimization problem. The video recovery algorithms based on gradient-based method is used to compressing and reconstructing the noise signal. And a compressive sensing algorithm with gradient-based method is proposed. At last, the performance of the proposed approach is shown and compared with some conventional algorithms. Our method can obtain best results in terms of peak signal noise ratio (PSNR) than those achieved by common methods with only a little runtime.
In this paper, we use transmit/receive co-prime arrays for direction finding of mixed coherent and uncorrelated targets based on the concept of sum coarrays. The sum coarray is defined as the set of pair-wise sums of the position vectors of the elements in the transmit and receive apertures. The data measurements from the transmit/receive co-prime array are used to emulate observations at a virtual array, whose element positions are given by the sum coarray corresponding to the co-prime array. A group sparse reconstruction problem is formulated employing multiple snapshots, where each group corresponding to a specific angle of arrival extends across all the time samples. The number of resolvable targets for the proposed sparsity-based approach is limited by the number of elements in the sum coarray. Supporting simulation results are provided, which validate the effectiveness of the proposed direction finding method.