Enhanced sampling schemes for MCMC based blind Bernoulli–Gaussian deconvolution

Ge, Di; Idier, Jérôme; Carpentier, Éric Le

doi:10.1016/j.sigpro.2010.08.009

Cited by 35 publications

(72 citation statements)

References 11 publications

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“…Most Bayesian BD approaches exploiting sparsity use a Bernoulli-Gaussian prior for the sparse sequence a, i.e., the b k are independent and Bernoulli distributed and the nonzero a k are Gaussian distributed [7], [8], [23]- [26]. However, here we will use a modified Bernoulli-Gaussian prior incorporating a hard minimum distance constraint that requires the temporal distance between any two nonzero a k (or two nonzero indicators b k = 1) to be not smaller than some prescribed minimum distance.…”

Section: Introductionmentioning

confidence: 99%

“…The Gibbs sampler is a simple and widely used MCMC method with interesting properties for BD [9], [24], [26], [31]; however, it is computationally inefficient when there are strong dependencies among the parameters [23], [32]. Such dependencies are caused by our minimum distance constraint, since a nonzero indicator b k determines all indicators within a certain neighborhood to be zero.…”

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: Introductionmentioning

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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“…Regarding the choice of the prior, a popular approach consists in modeling z as a continuous random variable whose distribution has a sharp peak at zero and heavy tails (e.g., Cauchy [22], Laplace [23], [24], t-Student Bernoulli-Gaussian (BG) models exist. A first approach, as considered in [27], [30], [31], [34], consists in assuming that the elements of z are independently drawn from Gaussian distributions whose variances are controlled by Bernoulli variables: a small variance enforces elements to be close to zero whereas a large one defines a non-informative prior on non-zero coefficients. Another model on z based on BG variables is as follows: the elements of the sparse vector are defined as the multiplication of Gaussian and Bernoulli variables.…”

Section: A Standard Sparse Representation Algorithmsmentioning

confidence: 99%

“…After convergence of the procedure defined in (36)- (41), probabilities q(x i , s i ) correspond to a meanfield approximation of p(x i , s i |y) (see (34)). Coming back to problem (19), an approximation of p(s i |y)…”

Section: Particularized To Model (5)-(6)-(8)mentioning

confidence: 99%

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Boltzmann Machine and Mean-Field Approximation for Structured Sparse Decompositions

Drémeau

Herzet

Daudet

2012

IEEE Trans. Signal Process.

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To cite this version:Angélique Drémeau, Cédric Herzet, Laurent Daudet. Boltzmann machine and mean-field approximation for structured sparse decompositions. Accepté à IEEE Trans. On Signal Processing. 2012. AbstractTaking advantage of the structures inherent in many sparse decompositions constitutes a promising research axis. In this paper, we address this problem from a Bayesian point of view. We exploit a Boltzmann machine, allowing to take a large variety of structures into account, and focus on the resolution of a marginalized maximum a posteriori problem. To solve this problem, we resort to a mean-field approximation and the "variational Bayes Expectation-Maximization" algorithm. This approach results in a soft procedure making no hard decision on the support or the values of the sparse representation. We show that this characteristic leads to an improvement of the performance over state-of-the-art algorithms. Index TermsStructured sparse representation, Bernoulli-Gaussian model, Boltzmann machine, mean-field approximation.

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