Block Sparse Estimator for Grid Matching in Single Snapshot DoA Estimation

Jagannath, Rakshith; Hari, K.V.S.

doi:10.1109/lsp.2013.2279124

Cited by 53 publications

(24 citation statements)

References 9 publications

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“…Therefore, we now turn to a possibly simpler model. Following an approach widely used in the literature [28,19,29,22,30], we also investigate a first-derivativebased signal model which will be later compared with the parametric model. Indeed, in the parametric model, the Fourier dictionary F is not linear wrt the grid mismatch vector ε.…”

Section: Bayesian Modelmentioning

confidence: 99%

Bayesian sparse Fourier representation of off-grid targets with application to experimental radar data

et al. 2015

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sparse Fourier representation of off-grid targets with application to experimental radar data. Signal Processing, Elsevier, 2015Elsevier, , vol. 111, pp. 261-273. <10.1016Elsevier, /j.sigpro.2014 Any correspondence concerning this service should be sent to the repository administrator: AbstractThe problem considered is the estimation of a finite number of cisoids embedded in white noise, using a sparse signal representation (SSR) approach, a problem which is relevant in many radar applications. Many SSR algorithms have been developed in order to solve this problem, but they usually are sensitive to grid mismatch. In this paper, two Bayesian algorithms are presented, which are robust towards grid mismatch: a first method uses a Fourier dictionary directly parametrized by the grid mismatch while the second one employs a first-order Taylor approximation to relate linearly the grid mismatch and the sparse vector. The main strength of these algorithms lies in the use of a mixed-type distribution which decorrelates sparsity level and target power. Besides, both methods are implemented through a Monte-Carlo Markov chain algorithm. They are successfully evaluated on synthetic and experimental radar data, and compared to a benchmark algorithm.

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Section: Bayesian Modelmentioning

confidence: 99%

Bayesian sparse Fourier representation of off-grid targets with application to experimental radar data

et al. 2015

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“…Unlike these contributions, we assume that our CS model is corrupted by a BM degradation. In [33], the Bayesian lower bound in the specific case of direction of arrival estimation is derived in case of structured BM. Our Bayesian lower bound, taking into account datadependence on the noise, provides new insights into the MSE saturation.…”

Section: Introductionmentioning

confidence: 99%

Compressed Sensing with Basis Mismatch: Performance Bounds and Sparse-Based Estimator

Bernhardt

Boyer

Marcos

et al. 2016

IEEE Trans. Signal Process.

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Compressed sensing (CS) is a promising emerging domain which outperforms the classical limit of the Shannon sampling theory if the measurement vector can be approximated as the linear combination of few basis vectors extracted from a redundant dictionary matrix. Unfortunately, in realistic scenario, the knowledge of this basis or equivalently of the entire dictionary is often uncertain, i.e. corrupted by a Basis Mismatch (BM) error. The consequence of the BM problem is that the estimation accuracy in terms of Bayesian Mean Square Error (BMSE) of popular sparse-based estimators collapses even if the support is perfectly estimated and in the high Signal to Noise Ratio (SNR) regime. This saturation effect considerably limits the effective viability of these estimation schemes. In the first part of this work, the Bayesian Cramér-Rao Bound (BCRB) is derived for CS model with unstructured BM. We show that the BCRB foresees the saturation effect of the estimation accuracy of standard sparsebased estimators as for instance the OMP, Cosamp or the BP. In addition, we provide an approximation of this BMSE threshold. In the second part and in the context of the structured BM model, a new estimation scheme called Bias-Correction Estimator (BiCE) is proposed and its statistical properties are studied. The BiCE acts as a post-processing estimation layer for any sparsebased estimator and mitigates considerably the BM degradation. Finally, the BiCE (i) is a blind algorithm, i.e., is unaware of the uncorrupted dictionary matrix, (ii) is generic since it can be associated to any sparse-based estimator, (iii) is fast, i.e., the additional computational cost remains low and (iv) has good statistical properties. To illustrate our results and propositions, the BiCE is applied in the challenging context of the compressive sampling of non-bandlimited impulsive signals.

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“…Compressive sensing [1]- [3] is a promising solution to tackle the related new challenges, in that it allows for retrieving sparse signals with fewer samples than classical data acquisition theory requires [4]. CS has been successfully exploited in many realistic applications, such as channel estimation [5,6], equalization [7], sampling in magnetic resonance imaging [8], high-resolution radar imaging [9], and array processing [10]. Along with the CS theory, Rémy a large collection of sparse recovery estimators has emerged [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…In addition, reference [38] discuses some identifiability issues for sparse signals. In [10], a BCRB is derived for the CS model but in the particular scenario of the off-grid problem.…”

Section: Introductionmentioning

confidence: 99%

Large-System Estimation Performance in Noisy Compressed Sensing With Random Support of Known Cardinality—A Bayesian Analysis

Boyer

Couillet

Fleury

et al. 2016

IEEE Trans. Signal Process.

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Compressed sensing (CS) enables measurement reconstruction by using sampling rates below the Nyquist rate, as long as the amplitude vector of interest is sparse. In this work, we first derive and analyze the Bayesian Cramér-Rao Bound (BCRB) for the amplitude vector when the set of indices (the support) of its non-zero entries is known. We consider the following context: (i) The dictionary is non-stochastic but randomly generated; (ii) the number of measurements and the support cardinality grow to infinity in a controlled manner, i.e. the ratio of these quantities converges to a constant; (iii) the support is random; and (iv) the vector of non-zero amplitudes follow a multidimensional generalized normal distribution. Using results from random matrix theory, we obtain closed-form approximations of the BCRB. These approximations can be formulated in a very compact form in low and high SNR regimes. Secondly, we provide a statistical analysis of the variance and the statistical efficiency of the oracle linear mean-square-error (LMMSE) estimator. Finally, we present results from numerical investigations in the context of non-bandlimited finite-rate-of-innovation (FRI) signal sampling. We show that the performance of Bayesian mean square error (BMSE) estimators that are aware of the cardinality of the support, such as OMP and CoSaMP, are in good agreement with the developed lower bounds in the high SNR regime. Conversely, sparse estimators exploiting only the knowledge of the parameter vector and the noise variance in form of a-priori distributions of these parameters, like LASSO and BPDN, are not efficient at high SNR. However, at low SNR their BMSE is lower than that of the former estimators and may be close to the BCRB.

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Block Sparse Estimator for Grid Matching in Single Snapshot DoA Estimation

Cited by 53 publications

References 9 publications

Bayesian sparse Fourier representation of off-grid targets with application to experimental radar data

Bayesian sparse Fourier representation of off-grid targets with application to experimental radar data

Compressed Sensing with Basis Mismatch: Performance Bounds and Sparse-Based Estimator

Large-System Estimation Performance in Noisy Compressed Sensing With Random Support of Known Cardinality—A Bayesian Analysis

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