Cartoon–Texture Image Decomposition Using Least Squares and Low-Rank Regularization

In this paper, we propose a novel model for the decomposition of cartoon–texture images, which integrates the edge-aware weighted least squares (WLS) with low-rank regularization. Unlike conventional methodologies that depend on total variation-based penalty functions, our model represents cartoon images using an edge-preserving WLS penalty. This approach effectively enhances edges and suppresses texture through iterative updates of an edge-preserving weight matrix. For the texture component, we introduce a low-rank penalty function to capture the structured regularity of texture patterns. By leveraging the repetitive nature of texture, our low-rank models can accurately represent these components. We employ a prediction–correction approach based on a three-block separable alternating direction multiplier method to solve the minimization problem, providing closed-form solutions for all subproblems. We also provide a convergence proof for the proposed algorithm. Numerical experiments validate the efficacy of our proposed method in successfully separating cartoon and texture components while preserving edges.