Sparse Bayesian image restoration with linear operator uncertainties with application to EEG signal recovery

Sparse signal/image recovery is a challenging topic that has captured a great interest during the last decades, especially in the biomedical field. Many techniques generally try to regularize the considered ill-posed inverse problem by defining appropriate priors for the target signal/image. The target regularization problem can then be solved either in a variational or Bayesian context. However, a little interest has been devoted to the uncertainties about the linear operator, which can drastically alter the reconstruction quality. In this paper, we propose a novel method for signal/image recovery that accounts and corrects the linear operator imprecisions. The proposed approach relies on a Bayesian formulation which is applied to EEG signal recovery. Our results show the promising potential of the proposed method compared to other regularization techniques which do not account for any error affecting the linear operator.