Structure–texture image decomposition using a new non‐local TV‐Hilbert model

Abstract

Combining the advantages of the non‐local total variation (TV) and the Gabor function, a new Gabor function based non‐local TV‐Hilbert model is presented to separate the structure and texture components of the image. Computationally, by introducing the dual form of the non‐local TV, the authors reformulate the non‐local TV‐Hilbert minimisation problem into a convex–concave saddle‐point problem. In the aspect of solving algorithm, by transforming the Chambolle–Pock's first‐order primal–dual algorithm into a different equivalent form. The authors propose a proximal‐based primal–dual algorithm to solve the convex–concave saddle‐point problem. At last, experimental results demonstrate that the proposed new model outperforms several existing state‐of‐the‐art variational models.

Keywords

• proximal‐based primal–dual algorithm
• Chambolle–Pock's first‐order primal–dual algorithm
• convex–concave saddle‐point problem
• nonlocal TV‐Hilbert minimisation problem
• texture components
• Gabor function