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37
COMPRESSIVE RADAR WITH OFFGRID TARGETS: A PERTURBATION APPROACH
"... Abstract. Compressed sensing (CS) schemes are proposed for monostatic as well as synthetic aperture radar (SAR) imaging with chirped signals and UltraNarrowband (UNB) continuous waveforms. In particular, a simple, perturbation method is developed to reduce the gridding error for offgrid targets. A ..."
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Abstract. Compressed sensing (CS) schemes are proposed for monostatic as well as synthetic aperture radar (SAR) imaging with chirped signals and UltraNarrowband (UNB) continuous waveforms. In particular, a simple, perturbation method is developed to reduce the gridding error for offgrid targets. A coherence bound is obtained for the resulting measurement matrix. A greedy pursuit algorithm, SupportConstrained Orthogonal Matching Pursuit (SCOMP), is proposed to take advantage of the support constraint in the perturbation formulation and proved to have the capacity of determining the offgrid targets to the grid accuracy under favorable conditions. Alternatively, the Locally Optimized Thresholding (LOT) is proposed to enhance the performance of the CS method, Basis Pursuit (BP). For the advantages of higher signaltonoise ratio and signaltointerference ratio, it is proposed that Spotlight SAR imaging be implemented with CS techniques and multifrequency UNB waveforms. Numerical simulations show promising results of the proposed approach and algorithms. 1.
The Polyphase Random Demodulator for Wideband Compressive Sensing
, 2011
"... Compressive sensing (CS) provides a mathematical platform for designing analogtodigital converters (ADCs) that sample signals at subNyquist rates. In particular, the framework espouses a linear sensing system coupled with a nonlinear, iterative computational recovery algorithm. A central proble ..."
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Compressive sensing (CS) provides a mathematical platform for designing analogtodigital converters (ADCs) that sample signals at subNyquist rates. In particular, the framework espouses a linear sensing system coupled with a nonlinear, iterative computational recovery algorithm. A central problem within this platform is the design of practical hardware systems that can be easily calibrated and coupled with computational recovery algorithms. In this paper, we propose a new CSADC that resolves some of the practical issues present in prior work. We dub this new system the polyphase random demodulator.
Superresolution Line Spectrum Estimation with
"... Abstract—We address the problem of superresolution line spectrum estimation of an undersampled signal with block prior information. The component frequencies of the signal are assumed to take arbitrary continuous values in known frequency blocks. We formulate a general semidefinite program to recov ..."
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Abstract—We address the problem of superresolution line spectrum estimation of an undersampled signal with block prior information. The component frequencies of the signal are assumed to take arbitrary continuous values in known frequency blocks. We formulate a general semidefinite program to recover these continuousvalued frequencies using theories of positive trigonometric polynomials. The proposed semidefinite program achieves superresolution frequency recovery by taking advantage of known structures of frequency blocks. Numerical experiments show great performance enhancements using our method. Keywords—superresolution, block priors, structured sparsity, positive trigonometric polynomials, spectral estimation I.
OffGrid Compressed Sensing for GMTI using SAR Images
"... Abstract—The choice of the grid for generating the sparsity inducing basis or rather a corresponding dictionary is a central point of compressed sensing and sparse approximation. A poorly chosen grid corrupts the reconstruction performance. Here we consider the problem of ground moving target indica ..."
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Abstract—The choice of the grid for generating the sparsity inducing basis or rather a corresponding dictionary is a central point of compressed sensing and sparse approximation. A poorly chosen grid corrupts the reconstruction performance. Here we consider the problem of ground moving target indication from several – already processed – synthetic aperture radar images and apply a recently introduced method for reducing the effect of the grid. I.
ORTHOGONAL MATCHING PURSUIT WITH DICTIONARY REFINEMENT FOR MULTITONE SIGNAL RECOVERY
"... Abstract. In this paper, we propose a lowcost algorithm for recovering multitone signals from compressive measurements. We introduce a simple and efficient modification to orthogonal matching pursuit. Our approach uses a DFT basis, but refines the frequency estimate obtained at each iteration via a ..."
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Abstract. In this paper, we propose a lowcost algorithm for recovering multitone signals from compressive measurements. We introduce a simple and efficient modification to orthogonal matching pursuit. Our approach uses a DFT basis, but refines the frequency estimate obtained at each iteration via a simple gradient descent. We find that by adapting the dictionary in this manner we can realize the benefits of an overcomplete DFT frame without incurring the increased computation. Numerical simulations show that this approach not only outperforms traditional OMP, it even outperforms `1minimization unless we incur the computational cost of using a highly overcomplete DFT frame. Key words. Compressive sensing, multitone signals, overcomplete DFT frames, gradient descent, orthogonal matching pursuit 1. Introduction. Compressive
JOINT SPARSITY AND FREQUENCY ESTIMATION FOR SPECTRAL COMPRESSIVE SENSING
"... Parameter estimation from compressively sensed signals has recently received some attention. We here also consider this problem in the context of frequency sparse signals which are encountered in many application. Existing methods perform the estimation using finite dictionaries or incorporate vari ..."
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Parameter estimation from compressively sensed signals has recently received some attention. We here also consider this problem in the context of frequency sparse signals which are encountered in many application. Existing methods perform the estimation using finite dictionaries or incorporate various interpolation techniques to estimate the continuous frequency parameters. In this paper, we show that solving the problem in a probabilistic framework instead produces an asymptotically efficient estimator which outperforms existing methods in terms of estimation accuracy while still having a low computational complexity. Moreover, the proposed algorithm is also able to make inference about the sparsity level of the measured signal. The simulation code is available online. Index Terms — Compressive sensing, sinusoidal models, model order comparison, spectral estimation. 1.
Efficient Structured Matrix Rank Minimization
"... We study the problem of finding structured lowrank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use the full SVD; nor (b) resort to augmented Lagrangian techni ..."
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We study the problem of finding structured lowrank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use the full SVD; nor (b) resort to augmented Lagrangian techniques; nor (c) solve linear systems per iteration. Instead, we formulate the problem differently so that it is amenable to a generalized conditional gradient method, which results in a practical improvement with low per iteration computational cost. Numerical results show that our approach significantly outperforms stateoftheart competitors in terms of running time, while effectively recovering low rank solutions in stochastic system realization and spectral compressed sensing problems. 1
A PROBABILISTIC ANALYSIS OF THE COMPRESSIVE MATCHED FILTER
"... In this paper we study the “compressive matched filter, ” a correlationbased technique for estimating the unknown delay and amplitude of a signal using only a small number of randomly chosen (and possibly noisy) frequencydomain samples of that signal. To study the performance of this estimator, we ..."
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In this paper we study the “compressive matched filter, ” a correlationbased technique for estimating the unknown delay and amplitude of a signal using only a small number of randomly chosen (and possibly noisy) frequencydomain samples of that signal. To study the performance of this estimator, we model its output as a random process and—borrowing from analytical techniques that have been used to derive stateoftheart signal recovery bounds in the field of compressive sensing— we derive a lower bound on the number of samples needed to guarantee successful operation of the compressive matched filter. Our analysis allows the roles of time and frequency to be exchanged, and we study the particular problem of estimating the frequency of a pure sinusoidal tone from a small number of random samples in the time domain. Thus, for signals parameterized by an unknown translation in either the time or frequency domain, our theoretical bounds and experimental results confirm that random measurements provide an economical means for capturing and recovering such information.
Sparse Methods for Model . . .
, 2012
"... In additive component model estimation problems, the number of additive components (model order) and values of the model parameters in each of the additive components are estimated. Traditional methods typically estimate parameters for a set of models with fixed order; parameter estimation is perfor ..."
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In additive component model estimation problems, the number of additive components (model order) and values of the model parameters in each of the additive components are estimated. Traditional methods typically estimate parameters for a set of models with fixed order; parameter estimation is performed over a continuous space when parameters are not discrete. The model order is estimated as the minimizer, over the set of fixed model orders, of a cost function compromising between signal fit to measurements and model complexity. This dissertation explores dictionarybased estimation methods for joint model order and parameter estimation. In dictionary estimation, the continuous parameter space is discretized, forming a dictionary. Each column of the dictionary is a model component at a sampled parameter value, and a linear combination of a subset of columns is used to represent the model. It is assumed that the model consists of a small number of components, and a sparse reconstruction algorithm is used to select a sparse superposition of columns to represent the signal. The number of columns selected is the estimated model order, and the parameters of each column are the
A MULTITAPERRANDOM DEMODULATOR MODEL FOR NARROWBAND COMPRESSIVE SPECTRAL ESTIMATION
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