A Blind Source Separation Perspective on Image Restoration

This paper re-investigates the physical image formation process leading to a new interpretation of the classic image restoration problem from a blind source separation (BSS) perspective. The observed distorted image is considered as a linear combination of a set of shifted version of the point spread function (PSF) with the weight coefficients determined by the actual image. The new interpretation brings two immediate benefits to the practice of image restoration. First, we can utilize the rich set of BSS methods to solve the blind image restoration problem. Second, the new formulation in terms of matrix product has the equivalent merit as the conventional matrix-vector notation in theoretical study of restoration algorithms. We develop a smoothness and block-decorrelation constrained nonnegative matrix factorization method (termed CNMF) to blindly recover both the PSF and the actual image. The experimental results compared to one of the state-of-the-art methods demonstrate the merit of the proposed approach.