A Sparsity-Based Method for the Estimation of Spectral Lines From Irregularly Sampled Data

Bourguignon, Sébastien; Carfantan, Hervé; Idier, Jérôme

doi:10.1109/jstsp.2007.910275

Cited by 84 publications

(122 citation statements)

References 34 publications

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“…We first consider the marginalization that corresponds to the marginal posterior p(b|x) underlying the MAP sequence detectorb (s) MAP in (15). Let q(b) denote the relative multiplicity of some b ∈ {0, 1} K in S, i.e., the number of occurrences of b in S normalized by the sample size |S| = M .…”

Section: A Sequence and Component Detectorsmentioning

confidence: 99%

“…The problem of blind deconvolution (BD) arises in many applications where some desired signal is to be recovered from a distorted observation, e.g., in digital communications [1]- [5], seismology [6]- [9], biomedical signal processing [10]- [13], and astronomy [14], [15]. The BD problem is ill-posed since different input sequences and impulse responses can provide the same observation.…”

Section: Introductionmentioning

confidence: 99%

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Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Distance Constraint: A Partially Collapsed Gibbs Sampler Method

Kail¹,

Tourneret

Hlawatsch³

et al. 2012

IEEE Trans. Signal Process.

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Abstract-For blind deconvolution of an unknown sparse sequence convolved with an unknown pulse, a powerful Bayesian method employs the Gibbs sampler in combination with a Bernoulli-Gaussian prior modeling sparsity. In this paper, we extend this method by introducing a minimum distance constraint for the pulses in the sequence. This is physically relevant in applications including layer detection, medical imaging, seismology, and multipath parameter estimation. We propose a Bayesian method for blind deconvolution that is based on a modified Bernoulli-Gaussian prior including a minimum distance constraint factor. The core of our method is a partially collapsed Gibbs sampler (PCGS) that tolerates and even exploits the strong local dependencies introduced by the minimum distance constraint. Simulation results demonstrate significant performance gains compared to a recently proposed PCGS. The main advantages of the minimum distance constraint are a substantial reduction of computational complexity and of the number of spurious components in the deconvolution result.

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Section: A Sequence and Component Detectorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Distance Constraint: A Partially Collapsed Gibbs Sampler Method

Kail¹,

Tourneret

Hlawatsch³

et al. 2012

IEEE Trans. Signal Process.

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show abstract

“…We let diag(a) denote the diagonal matrix with diagonal vector a, and tr(A) the matrix trace of A. We describe the structure of a matrix or vector by ordering elements within hard brackets, e.g., y = y(1) y (2) , while a set of elements is described using curly brackets, e.g., N = {1, 2, . .…”

Section: Notational Conventionsmentioning

confidence: 99%

“…Estimating a sparse parameter support for a high-dimensional regression problem has been the focus of much scientific attention during the last two decades, as this methodology has shown its usefulness in many applications, ranging from spectral analysis [1][2][3], array- [4][5][6] and audio processing [7][8][9], to biomedical modeling [10], and magnetic resonance imaging [11,12]. In its vanguard, notable contributions were done by, among others, Donoho et al [13] and Tibshirani et al [14].…”

Section: Introductionmentioning

confidence: 99%

Online group-sparse estimation using the covariance fitting criterion

Kronvall

Adalbjörnsson

Nadig

et al. 2017

2017 25th European Signal Processing Conference (EUSIPCO)

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In this paper, we present a time-recursive implementation of a recent hyperparameter-free group-sparse estimation technique. This is achieved by reformulating the original method, termed group-SPICE, as a square-root group-LASSO with a suitable regularization level, for which a time-recursive implementation is derived. Using a proximal gradient step for lowering the computational cost, the proposed method may effectively cope with data sequences consisting of both stationary and non-stationary signals, such as transients, and/or amplitude modulated signals. Numerical examples illustrates the efficacy of the proposed method for both coherent Gaussian dictionaries and for the multi-pitch estimation problem.

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“…However, due to uncertainty principle in RPRI signal processing, the nonparametric approaches such as CBP suffer from global leakage problems, which will lead to high sidelobe pedestal. Since random or irregular undersampling combined with the compressed sensing (CS) theory [11][12][13] provides a preferable approach for aliasing-free spectral analysis [14,15] with low sidelobe and high resolution, the recent signal processing methods for RPRI radar is also under the CS framework. For example, in [16] the random slow time undersampling and jittered slow time undersampling are introduced for the CS-based cross-range compression in synthetic aperture radar (SAR) imaging.…”

Section: Introductionmentioning

confidence: 99%

High Resolution Wideband Imaging of Fast Rotating Targets Based on Random Pri Radar

Liu¹,

Chen²,

Sui³

2018

PIER M

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Abstract-By exploiting the micro-motion features of fast rotating targets, wideband radar has been successfully applied to high resolution imaging. However, due to the traditional fixed pulse repetition interval (PRI), the target image may suffer from aliasing in some practical situations. In this paper, under the compressed sensing (CS) radar framework, an efficient wideband imaging scheme with random PRI signal is introduced for aliasing reduction. Considering that direct application of the CS theory will result in large-scale dictionaries and high computational complexity, we firstly generate a low resolution image by applying modified generalized Radon transform on range-slow time domain and then scale down the dictionary column by reserving the atoms corresponding to those strong scattering areas. Simulation results show that this scheme can achieve aliasing-free images with acceptable computational cost.

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A Sparsity-Based Method for the Estimation of Spectral Lines From Irregularly Sampled Data

Cited by 84 publications

References 34 publications

Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Distance Constraint: A Partially Collapsed Gibbs Sampler Method

Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Distance Constraint: A Partially Collapsed Gibbs Sampler Method

Online group-sparse estimation using the covariance fitting criterion

High Resolution Wideband Imaging of Fast Rotating Targets Based on Random Pri Radar

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