Restoration of Blurred Images Corrupted by Impulse Noise via Median Filters and ℓp-ℓq Minimization

This paper proposes a two-phase fully automatic scheme for restoring images that have been corrupted by blur, impulse noise, and, possibly, Gaussian noise. In a first phase, a median filter is used to partially correct most of the pixels that are contaminated by impulse noise. Then the image is restored by solving the ℓp-ℓq minimization. This problem consists of a fidelity term, that is defined in terms of a p-norm, and a regularization term, that is defined in terms of a q-norm. We allow 0 < p, q ≤ 2. In particular, the p-norm is not a norm when 0 < p < 1; similarly for the q-norm. The relative influence of the fidelity and regularization terms is determined by a regularization parameter. We describe how this parameter can be chosen without user interaction. The numerical scheme described in this paper can restore images that have been contaminated by blur and with up to 70% of the pixels contaminated by salt-and-pepper noise.