Image recovery by D-SET framework with improved BNN

Decomposed SET, namely Smooth, Edge, and Texture, (D-SET) recovery, is an image decomposition and recovery method which assumes images as the sum of smooth, edge, and texture components. All the components are obtained by solving an optimization problem consists of regularizations based on priori information of original images. In this paper, we apply BNN (block nuclear norm) to the regularization of texture components of D-SET. BNN is originally applied for cartoon-texture image decomposition, and its decomposition method regards a image as the sum of ideal cartoon and sub-texture components. BNN is defined as the sum of singular values of all possibility overlapped sub-blocks of sheared image, and BNN of texture components become small. On the other hand, D-SET uses Shift-Invariant Redundant Discrete Cosine Transform (RDCT) for the texture component. This work tries to obtain better recovery images by applying BNN instead of RDCT, and we also improve BNN itself by adjusting the shearing operations of BNN in a block-wise manner. The proposed method demonstrates more effective image recovery than the conventional D-SET.