LEMUR: Latent EM Unsupervised Regression for Sparse Inverse Problems
Résumé
Most methods for sparse signal recovery require to
set one or several hyperparameters. We propose an unsupervised
method to estimate the parameters of a Bernoulli-Gaussian (BG)
model describing sparse signals. The proposed method is first
derived for denoising problems, based on a maximum likelihood
(ML) approach. Then, an extention to general inverse problems is
achieved through a latent variable formulation. Two expectation-
maximization (EM) algorithms are then proposed to estimate the
signal together with the BG model parameters. Combining these
two approaches leads to the proposed LEMUR algorithm. All
proposed algorithms are then evaluated on extensive simulations
in terms of ability to recover the parameters and provide accurate
sparse signal estimates.
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