Sparse Signal Blind Deconvolution using Bayesian MAP Estimation
Jack Bourdin White, Abdeldjalil Aïssa El Bey, Matthieu Arzel, Jean-Marc Leveau · 2025
Blind deconvolution tackles the issue of recovering a signal from a convolution between an initial signal and a filter with an unknown kernel. To address the ill-posed nature of blind deconvolution, we leverage the sparse characteristics of the signals in a pre-existent dictionary. Rather than imposing sparsity directly on the signal using L0 or L1 penalties, we express it as a prior on the signal’s covariance matrix. The hierarchical prior acts like a decoupling between the signal and its sparsity, making estimation a classical a posteriori problem. The proposition revolves around a maximum a posteriori estimation in an Expectation - Maximization framework for alternate optimization of the signal and the filter. We give simulation results in comparison with MAP oracle values for any sparse basis.