Vectorial total variation based on arranged structure tensor for multichannel image restoration

Abstract

We propose a new regularization function, named as Arranged Structure tensor Total Variation (ASTV), for multichannel image restoration. Since the standard structure tensor is a matrix whose eigenvalues well encodes local neighborhood information of an image, there has been proposed vectorial total variation based on the structure tensor for image regularization. However, the correlation among the channels cannot be measured by the structure tensor because the discrete differences of all the channels are just summed up in the entries of the structure tensor. On the other hand, ASTV is based on a newly-defined arranged structure tensor that becomes an approximately low-rank matrix when multichannel images have strong correlation among their channels. This suggests that penalizing the nuclear norm of the arranged structure tensor is a reasonable regularization for multichannel images, leading to the definition of ASTV. Experimental results illustrate the advantage of ASTV over a state-of-the-art vectorial total variation based on the structure tensor.