Image Restoration with Faithful Residuals

It is common in image restoration to obtain residuals that does not agree with our knowledge about the noise process, even if we accept a small deviation due to the bias in the restored image. We discuss how this information can be further used, leading to more faithful residuals. Based on the regularization approach, we introduce penalty terms so the sample covariance of the residuals match the covariance structure in the noise. This is tested on artificial noisy images with and without blur. The simulation results shows sharper edges and a better restoration in difficult areas. We achieve best results with a weak model for the local spatial smoothness. Actually, a spatially smooth restoration can be obtained without any model for the local spatial smoothness of the true image. 1 Introduction The problem of image restoration is one of many inverse problems that occurs in imaging. The most popular methods for trying to solve such ill--posed or ill--conditioned problems, are by using t..