Group-based image decomposition using 3-D cartoon and texture priors

We propose a novel image decomposition method to decompose an image into its cartoon and texture components. To exploit the nonlocal self-similarity of cartoon-plus-texture images, we construct groups by stacking together similar image patches into 3-D arrays and consider group as the basic unit of decomposition. We decompose each group via a convex optimization model consisting of 3-D cartoon and texture priors. These priors characterize the local properties of the cartoon and texture components and the nonlocal similarity within each component in a unified and natural manner. We develop the alternating direction method of multipliers (ADMM) to efficiently solve the proposed model. For further improvement, we investigate an adaptive rule for the estimation of the regularization parameter. The proposed method is also extended to tackle noisy images. Numerical experiments confirm that the performance of the proposed method is competitive with some of the state-of-the-art schemes.