Multiscale Structure Tensor Total Variation for Image Recovery

Abstract

This paper proposes multiscale structure-tensor total variation (MSTV) for image recovery. Gradient vectors in local patches usually have similar directions, and thus each local gradient matrix (the set of gradient vectors) tends to be low rank. STV introduces this property by calculating the sum of nuclear norms from all the 10-cal gradient matrices over the input image. By STV regularization, fine textures are recovered efficiently. However, since STV only considers differences of vertically and horizontally adjacent pixels, if neighboring samples are not reliable due to severe degradation, a latent image cannot be recovered efficiently. In this work, we assume that, for any two target pixels in a local patch, two vectors consisting of multiple differences not only between each target and adjacent pixels but also each target and further distant pixels exhibit a similar direction. According to this assumption, our MSTV firstly applies wavelet-based multiscale decomposition to vertical/horizontal gradient vectors and then evaluates the sum of nuclear norms of all the local wavelet coefficients. Experimental results show that the MSTV improves both numerical reconstruction error and subjective visual quality, compared with the conventional STV.