Parameter Estimation in Sparse Inverse Problems Using Bernoulli-Gaussian Prior

Pierre Barbault (1) , Matthieu Kowalski (1) , Charles Soussen (1)

1 L2S - Laboratoire des signaux et systèmes

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 0 regularized minimization. Moreover, the algorithm directly yields an estimator of the sparse signal.

Mots clés: Sparse coding; Inverse Problem; ISTA; Bernoulli-Gaussian model

Domaines: Traitement du signal et de l'image [eess.SP]

Pierre Barbault, Matthieu Kowalski, Charles Soussen. Parameter Estimation in Sparse Inverse Problems Using Bernoulli-Gaussian Prior. 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2022), May 2022, Singapore, Singapore. ⟨10.1109/icassp43922.2022.9746697⟩. ⟨hal-03576005⟩