A Novel Truncated Norm Regularization Method for Multi-channel Color Image Denoising

Due to the high flexibility and remarkable performance, low-rank approximation has been widely studied for color image denoising. However, existing methods usually ignore the cross-channel difference or the spatial variation of noise, which limits their capacity in the task of real world color image denoising. To overcome these drawbacks, this paper proposes a double-weighted truncated nuclear norm minus truncated Frobenius norm minimization (DtNFM) model, and apply it to color image denoising through exploiting the nonlocal self-similarity prior. The proposed DtNFM model has two merits. First, it models and utilizes both the cross-channel difference and the spatial variation of noise. This provides sufficient flexibility for handling the complex distribution of noise in real world images. Second, the proposed DtNFM model provides a close approximation to the underlying clean matrix since it can treat different rank components flexibly. To solve the DtNFM model, an efficient algorithm is devised through exploiting the framework of alternating directions method of multipliers (ADMM). Meanwhile, the truncated nuclear norm minus truncated Frobenius norm regularized least squares subproblem is discussed in detail, and the results show that its global optimum can be directly obtained in closed form. Therefore, the DtNFM model can be efficiently solved by a single ADMM. Rigorous mathematical derivation proves that the solution sequences generated by our proposed algorithm converge to a single critical point. Extensive experiments on synthetic and real noise datasets demonstrate that the proposed method outperforms many state-of-the-art color image denoising methods. MATLAB code is available at https://github.com/wangzhi-swu/DtNFM.