Ternary image decomposition with automatic parameter selection via auto- and cross-correlation

This paper is devoted to the decomposition of images into cartoon, texture and noise components. A two-stage variational model is proposed which is parameter-free and both context- and noise-unaware. In the first stage, the additive white noise component is separated and then the denoised image is further split into cartoon and texture, in the second stage. Auto-correlation and cross-correlation principles represent the key aspects of the two variational stages. The solutions of the two optimisation problems are efficiently obtained by the alternating directions method of multipliers (ADMM). Numerical results show the potentiality of the proposed approach for decomposing images corrupted by different kinds of additive white noises.