Parameter Estimation in Sparse Inverse Problems Using Bernoulli-Gaussian Prior
Pierre Barbault, Matthieu Kowalski, Charles Soussen
Abstract
Sparse coding is now one of the state-of-art approaches for solving inverse problems. In combination with (Fast) Iterative Shrinkage Thresholding Algorithm (ISTA), among other algorithms, one can efficiently get a nice estimator of the sought sparse signal. However, the major drawback of these methods is the tuning of the so-called hyperparameter. In this paper, we first provide an Expectation-Maximization (EM) algorithm to estimate the parameters of a Bernoulli-Gaussian model for denoising a sparse signal corrupted by a white Gaussian noise. Then, building on the Expectation-Maximization interpretation of ISTA, we provide a simple iterative algorithm to blindly estimate all the model parameters in the linear inverse problem context, including the hyperparameter involved in the popular ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> regularized minimization. Moreover, the algorithm directly yields an estimator of the sparse signal.
BibTeX
@inproceedings{icassp2022_parameterestimat,
title = {Parameter Estimation in Sparse Inverse Problems Using Bernoulli-Gaussian Prior},
author = {Pierre Barbault and Matthieu Kowalski and Charles Soussen},
booktitle = {ICASSP 2022},
year = {2022}
}