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Conference Papers Year : 2023

Marginal MAP estimation of a Bernoulli-Gaussian signal: continuous relaxation approach

Abstract

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 M-step 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.
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Dates and versions

hal-04383978 , version 1 (10-01-2024)

Identifiers

  • HAL Id : hal-04383978 , version 1

Cite

Pierre Barbault, Matthieu Kowalski, Charles Soussen. Marginal MAP estimation of a Bernoulli-Gaussian signal: continuous relaxation approach. EUSIPCO 2023 - the 31st European Signal Processing Conference, Sep 2023, Helsinki, Finland. pp.1833-1837. ⟨hal-04383978⟩
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