Variational blind deconvolution of multi-channel images

The fundamental problem of denoising and deblurring images is addressed in this study. The great difficulty in this task is due to the ill-posedness of the problem. We analyze multi-channel images to gain robustness and regularize the process by the Polyakov action, which provides an anisotropic smoothing term that uses inter-channel information. Blind deconvolution is then solved by an additional anisotropic regularization term of the same type for the kernel. It is shown that the Beltrami regularizer leads to better results than the total variation (TV) regularizer. An analytic comparison to the TV method is carried out and results on synthetic and real data are demonstrated.