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89
Compressive radar imaging
 Proc. 2007 IEEE Radar Conf
, 2007
"... Abstract—We introduce a new approach to radar imaging based on the concept of compressive sensing (CS). In CS, a lowdimensional, nonadaptive, linear projection is used to acquire an efficient representation of a compressible signal directly using just a few measurements. The signal is then reconstr ..."
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Cited by 104 (9 self)
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Abstract—We introduce a new approach to radar imaging based on the concept of compressive sensing (CS). In CS, a lowdimensional, nonadaptive, linear projection is used to acquire an efficient representation of a compressible signal directly using just a few measurements. The signal is then reconstructed by solving an inverse problem either through a linear program or a greedy pursuit. We demonstrate that CS has the potential to make two significant improvements to radar systems: (i) eliminating the need for the pulse compression matched filter at the receiver, and (ii) reducing the required receiver analogtodigital conversion bandwidth so that it need operate only at the radar reflectivity’s potentially low “information rate” rather than at its potentially high Nyquist rate. These ideas could enable the design of new, simplified radar systems, shifting the emphasis from expensive receiver hardware to smart signal recovery algorithms. I.
Fast Bayesian Matching Pursuit
"... Abstract—A lowcomplexity recursive procedure is presented for minimum mean squared error (MMSE) estimation in linear regression models. A Gaussian mixture is chosen as the prior on the unknown parameter vector. The algorithm returns both an approximate MMSE estimate of the parameter vector and a se ..."
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Cited by 38 (2 self)
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Abstract—A lowcomplexity recursive procedure is presented for minimum mean squared error (MMSE) estimation in linear regression models. A Gaussian mixture is chosen as the prior on the unknown parameter vector. The algorithm returns both an approximate MMSE estimate of the parameter vector and a set of high posterior probability mixing parameters. Emphasis is given to the case of a sparse parameter vector. Numerical simulations demonstrate estimation performance and illustrate the distinctions between MMSE estimation and MAP model selection. The set of high probability mixing parameters not only provides MAP basis selection, but also yields relative probabilities that reveal potential ambiguity in the sparse model. 1 I.
Fast Bayesian Matching Pursuit: Model Uncertainty and Parameter Estimation for Sparse Linear Models
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2009
"... A lowcomplexity recursive procedure is presented for model selection and minimum mean squared error (MMSE) estimation in linear regression. Emphasis is given to the case of a sparse parameter vector and fewer observations than unknown parameters. A Gaussian mixture is chosen as the prior on the un ..."
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Cited by 29 (3 self)
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A lowcomplexity recursive procedure is presented for model selection and minimum mean squared error (MMSE) estimation in linear regression. Emphasis is given to the case of a sparse parameter vector and fewer observations than unknown parameters. A Gaussian mixture is chosen as the prior on the unknown parameter vector. The algorithm returns both a set of high posterior probability mixing parameters and an approximate MMSE estimate of the parameter vector. Exact ratios of posterior probabilities serve to reveal potential ambiguity among multiple candidate solutions that are ambiguous due to observation noise or correlation among columns in the regressor matrix. Algorithm complexity is linear in the number of unknown coefficients, the number of observations and the number of nonzero coefficients. If hyperparameters are unknown, a maximum likelihood estimate is found by a generalized expectation maximization algorithm. Numerical simulations demonstrate estimation performance and illustrate the distinctions between MMSE estimation and maximum a posteriori probability model selection.
Compressed Synthetic Aperture Radar
, 2010
"... In this paper, we introduce a new synthetic aperture radar (SAR) imaging modality which can provide a highresolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. This new imaging scheme, ..."
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Cited by 24 (3 self)
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In this paper, we introduce a new synthetic aperture radar (SAR) imaging modality which can provide a highresolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. This new imaging scheme, requires no new hardware components and allows the aperture to be compressed. It also presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced onboard storage requirements.
SAR image simulation with application to target recognition
 Progress In Electromagnetics Research
, 2011
"... Abstract—This paper presents a novel synthetic aperture radar (SAR) image simulation approach to target recognition, which consists of two frameworks, referred to as the satellite SAR images simulation and the target recognition and identification. The images simulation makes use of the sensor and t ..."
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Cited by 22 (0 self)
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Abstract—This paper presents a novel synthetic aperture radar (SAR) image simulation approach to target recognition, which consists of two frameworks, referred to as the satellite SAR images simulation and the target recognition and identification. The images simulation makes use of the sensor and target geolocation relative to the Earth, movement of SAR sensor, SAR system parameters, radiometric and geometric characteristics of the target, and target radar cross section (RCS), orbital parameters estimation, SAR echo signal generation and image focusing to build SAR image database. A hybrid algorithm that combines the physical optics, physical diffraction theory, and shooting and bouncing rays was used to compute the RCS of complex radar targets. Such database is vital for aided target recognition and identification system Followed by reformulating the projection kernel in an optimization equation form, the target’s reflectivity field can be accurately estimated. Accordingly, the target’s features can be effectively enhanced and extracted, and the dominant scattering centers are well separated. Experimental results demonstrate that the simulated database developed in this paper is well suited for target recognition. Performance is extensively tested and evaluated from real images by Radarsat2 and TerraSARX. Effectiveness and efficiency of the proposed method are further confirmed.
Iterative image reconstruction in MRI with separate magnitude and phase regularization
 In Proc. IEEE Intl. Symp. Biomed. Imag
, 2004
"... Iterative methods for image reconstruction in MRI are useful in several applications, including reconstruction from nonCartesian kspace samples, compensation for magnetic field inhomogeneities, and imaging with multiple receive coils. Existing iterative MR image reconstruction methods are either u ..."
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Cited by 15 (6 self)
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Iterative methods for image reconstruction in MRI are useful in several applications, including reconstruction from nonCartesian kspace samples, compensation for magnetic field inhomogeneities, and imaging with multiple receive coils. Existing iterative MR image reconstruction methods are either unregularized, and therefore sensitive to noise, or have used regularization methods that smooth the complex valued image. These existing methods regularize the real and imaginary components of the image equally. In many MRI applications, including T ∗ 2weighted imaging as used in fMRI BOLD imaging, one expects most of the signal information of interest to be contained in the magnitude of the voxel value, whereas the phase values are expected to vary smoothly spatially. This paper proposes separate regularization of the magnitude and phase components, preserving the spatial resolution of the magnitude component while strongly regularizing the phase component. This leads to a nonconvex regularized leastsquares cost function. We describe a new iterative algorithm that monotonically decreases this cost function. The resulting images have reduced noise relative to conventional regularization methods. 1.
On the Relation between Sparse Reconstruction and Parameter Estimation with Model Order Selection
"... We examine the relationship between the classic problem of continuous parametric modeling and sparse reconstruction. Sparse reconstruction techniques have been successfully applied to a number of problems in signal and image modeling and reconstruction. These techniques apply to applications in whic ..."
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Cited by 9 (4 self)
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We examine the relationship between the classic problem of continuous parametric modeling and sparse reconstruction. Sparse reconstruction techniques have been successfully applied to a number of problems in signal and image modeling and reconstruction. These techniques apply to applications in which a measurement can be described as a linear combination of a small number of discrete additive components. In the sparse reconstruction context, order selection and parameter estimation is accomplished through a regularized leastsquares algorithm that prefers sparse solutions. Sparse reconstruction is closely related to compressed sensing, and recent results in the compressed sensing literature have provided fast reconstruction algorithms with guaranteed performance bounds for problems with certain structure. Parameter estimation problems, by contrast, typically involve a model in which the signal is composed of a small but unknown number of parameterized functions; model estimation entails both model order selection and parameter estimation, the latter usually involving a nonlinear optimization problem. In this paper we show an explicit connection between the two problem formulations and demonstrate how sparse reconstruction may be used to solve traditional continuous parameter estimation problems and unknown model order estimation problems. We further demonstrate that the structural assumptions used in compressive sensing—namely the Restricted Isometry Property—to guarantee reconstruction performance are not satisfied in the parameter estimation
Sparse Representation in Structured Dictionaries With Application to Synthetic Aperture Radar
"... Abstract—Sparse signal representations and approximations from overcomplete dictionaries have become an invaluable tool recently. In this paper, we develop a new, heuristic, graphstructured, sparse signal representation algorithm for overcomplete dictionaries that can be decomposed into subdictiona ..."
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Cited by 9 (0 self)
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Abstract—Sparse signal representations and approximations from overcomplete dictionaries have become an invaluable tool recently. In this paper, we develop a new, heuristic, graphstructured, sparse signal representation algorithm for overcomplete dictionaries that can be decomposed into subdictionaries and whose dictionary elements can be arranged in a hierarchy. Around this algorithm, we construct a methodology for advanced image formation in wideangle synthetic aperture radar (SAR), defining an approach for joint anisotropy characterization and image formation. Additionally, we develop a coordinate descent method for jointly optimizing a parameterized dictionary and recovering a sparse representation using that dictionary. The motivation is to characterize a phenomenon in wideangle SAR that has not been given much attention before: migratory scattering centers, i.e., scatterers whose apparent spatial location depends on aspect angle. Finally, we address the topic of recovering solutions that are sparse in more than one objective domain by introducing a suitable sparsifying cost function. We encode geometric objectives into SAR image formation through sparsity in two domains, including the normal parameter space of the Hough transform. Index Terms—Hough transforms, inverse problems, optimization methods, overcomplete dictionaries, sparse signal representations, synthetic aperture radar, tree searching. I.
AngleDoppler processing using sparse regularization
 Proc. IEEE Int. Conf. Acoust. Speech and Signal Process
"... The detection of moving objects on the ground by airborne radar is one application of spacetime adaptive processing (STAP). The goal is to estimate the position and velocity of objects. This paper considers the problem as a linear inverse problem and uses 1norm regularization to promote sparsity ..."
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Cited by 7 (1 self)
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The detection of moving objects on the ground by airborne radar is one application of spacetime adaptive processing (STAP). The goal is to estimate the position and velocity of objects. This paper considers the problem as a linear inverse problem and uses 1norm regularization to promote sparsity in the solution. It is proposed that the angleDoppler plane be explicitly segmented into the clutter ridge component and a nonclutterridge component. We propose that the second component be modeled as sparse — as the moving objects are assumed to be well isolated in the angleDoppler plane. Index Terms — GMTI, sparsity, radar, STAP, signal restoration, iterated thresholding.
Superresolution Source Localization through DataAdaptive Regularization
 In Adaptive Sensor Array Processing Workshop
, 2002
"... We address the task of source localization using a novel nonparametric dataadaptive approach based on regularized linear inverse problems with sparsity constraints. The class of penalty functions that we use for regularization favors sparsity of the reconstructions, thus producing superb resoluti ..."
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Cited by 5 (2 self)
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We address the task of source localization using a novel nonparametric dataadaptive approach based on regularized linear inverse problems with sparsity constraints. The class of penalty functions that we use for regularization favors sparsity of the reconstructions, thus producing superb resolution of the sources. We present a computationally efficient technique to carry out the numerical optimization of the resulting cost function. In comparison to conventional source localization methods, the proposed approach provides numerous improvements, including increased resolution, reduced sidelobes, and better robustness properties to noise, limited snapshots, and coherence of the sources. The method is developed for the general source localization scenario, encompassing nearfield and farfield, narrowband and broadband, and nonlinear array geometry cases. Simulation results manifest the capabilities of the approach.