Deconvolution of Spike Trains

Champagnat, Frédéric; Goussard, Yves; Gautier, S.; Idier, Jérôme

doi:10.1002/9780470611197.ch5

Cited by 3 publications

(1 citation statement)

References 35 publications

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“…MMAP estimation consists of minimizing the marginal posterior likelihood p(q | y) after marginalizing out the signal coefficients r [7]. It is a natural estimator for applications where the support may bear more interest than the amplitudes, e.g., for source localization of brain activity using Magneto/ElectroEncephalography (M/EEG) [8], [9], [10].…”

Section: Introductionmentioning

confidence: 99%

Marginal MAP Estimation of a Bernoulli-Gaussian Signal: Continuous Relaxation Approach

Barbault,

Kowalski,

Soussen

2023

2023 31st European Signal Processing Conference (EUSIPCO)

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We focus on recovering the support of sparse signals for sparse inverse problems. Using a Bernoulli-Gaussian prior to model sparsity, we propose to estimate the support of the sparse signal using the so-called Marginal Maximum a Posteriori estimate after marginalizing out the values of the nonzero coefficients. To this end, we propose an Expectation-Maximization procedure in which the discrete optimization problem in the Mstep is relaxed into a continuous problem. Empirical assessment with simulated Bernoulli-Gaussian data using magnetoencephalographic lead field matrix shows that this approach outperforms the usual ℓ0 Joint Maximum a Posteriori estimation in Type-I and Type-II error for support recovery, as well as in SNR for signal estimation Index Terms-Sparse coding, inverse problem, Bernoulli-Gaussian model, Marginal-MAP, Joint-MAP.

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Section: Introductionmentioning

confidence: 99%

Marginal MAP Estimation of a Bernoulli-Gaussian Signal: Continuous Relaxation Approach

Barbault,

Kowalski,

Soussen

2023

2023 31st European Signal Processing Conference (EUSIPCO)

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Analysis of Force‐Volume Images in Atomic Force Microscopy Using Sparse Approximation

Soussen

Brie

Francius

et al. 2015

Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing

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Ultrasonic non destructive testing based on sparse deconvolution

Soussen

Idier²,

Carcreff

et al. 2012

J. Phys.: Conf. Ser.

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The acoustic modality yields non destructive testing techniques of choice for indepth investigation. Given a precise model of acoustic wave propagation in materials of possibly complex structures, acoustical imaging amounts to the so-called acoustic wave inversion. A less ambitious approach consists in processing pulse-echo data (typically, A-or B-scans) to detect localised echoes with the maximum temporal (and lateral) precision. This is a resolution enhancement problem, and more precisely a sparse deconvolution problem which is naturally addressed in the inversion framework. The paper focuses on the main sparse deconvolution methods and algorithms, with a view to apply them to ultrasonic non-destructive testing.

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Deconvolution of Spike Trains

Cited by 3 publications

References 35 publications

Marginal MAP Estimation of a Bernoulli-Gaussian Signal: Continuous Relaxation Approach

Marginal MAP Estimation of a Bernoulli-Gaussian Signal: Continuous Relaxation Approach

Analysis of Force‐Volume Images in Atomic Force Microscopy Using Sparse Approximation

Ultrasonic non destructive testing based on sparse deconvolution

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