A non-convex ternary variational decomposition and its application for image denoising

A non-convex ternary variational decomposition model is proposed in this study, which decomposes the image into three components including structure, texture and noise. In the model, a non-convex total variation (NTV) regulariser is utilised to model the structure component, and the weaker G and E spaces are used to model the texture and noise components, respectively. The proposed model provides a very sparse representation of the structure in total variation (TV) transform domain due to the use of non-convex regularisation and cleanly separates the texture and noise since two different weaker spaces are used to model these two components, respectively. In image denoising application, the proposed model can successfully remove noise while effectively preserving image edges and constructing textures. An alternating direction iteration algorithm combining with iteratively reweighted l(1) algorithm, projection algorithm and wavelet soft threshold algorithm is introduced to effectively solve the proposed model. Numerical results validate the model and the algorithm for both synthetic and real images. Furthermore, compared with several state-of-the-art image variational restoration models, the proposed model yields the best performance in terms of the peak signal to noise ratio (PSNR) and the mean structural similarity index (SSIM).