The maximum a posteriori estimation model for signal recovery with mixed Gaussian and impulse noise

This paper presents a novel variational model to recover a signal corrupted by mixed Gaussian and impulse noise. We adopt a spike-and-slab distribution to model the mixed noise, enabling a probabilistic framework that facilitates the segmentation of the observed data into three distinct components: the original signal, Gaussian noise, and impulse noise. The proposed model including a novel data fidelity term is then derived by the maximum a posteriori estimation. This data fidelity term is not only proved to be optimal in terms of the maximum likelihood estimation but it can be simplified to the traditional counterpart applicable to a single type of noise. Numerical experiments demonstrate that the proposed model accurately captures the statistical characteristics of mixed Gaussian and impulse noise.