A coupled non-convex hybrid regularization and weak H^-1 image decomposition model for denoising application

Recently, many non-convex variational models have been developed to reduce staircase artifacts in the smooth regions of restored images. Among these models, the L^2 -norm is often used to capture high-frequency oscillation information in the image. However, this modeling method makes it difficult to separate the image structure component from the oscillation component. To address this problem, we propose a coupled non-convex hybrid regularization and weak H^-1 decomposition model for image denoising in this paper, which leverages non-convex TV and fractional-order TV regularizers to measure the structure and textural information of the image, respectively. Additionally, we employ weak H^-1 -space to model the oscillatory noisy component. By these modeling techniques, the proposed model effectively separates the high-frequency oscillation component and alleviates the staircase effect. To solve this non-convex minimization, an alternating direction method of multipliers combined with the majorization–minimization algorithm is introduced. Furthermore, we provide a detailed discussion on the convergence conditions of the proposed algorithm. Numerical experimental results demonstrate the feasibility of our decomposition model in denoising applications. Moreover, compared with other variational models, our proposed model exhibits excellent performance in terms of peak signal-to-noise ratio and structural similarity index values.