Image Deblurring in the Presence of Salt-and-Pepper Noise

The problem of image deblurring in the presence of salt and pepper noise is considered. Standard image deconvolution algorithms, that are designed for Gaussian noise, do not perform well in this case. Median type filtering is a common method for salt and pepper noise removal. Deblurring an image that has been preprocessed by median-type filtering is however difficult, due to the amplification (in the deconvolution stage) of median-induced distortion. A unified variational approach to salt and pepper noise removal and image deblurring is presented. An objective functional that represents the goals of deblurring, noiserobustness and compliance with the piecewise-smooth image model is formulated. A modified L data fidelity term integrates deblurring with robustness to outliers. Elements from the Mumford-Shah functional, that favor piecewise smooth images with simple edge-sets, are used for regularization. Promising experimental results are shown for several blur models.