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

Due to the high flexibility and remarkable performance, low-rank approximation methods has been widely studied for color image denoising. However, those methods mostly ignore either the cross-channel difference or the spatial variation of noise, which limits their capacity in real world color image denoising. To overcome those drawbacks, this paper is proposed to denoise color images with a double-weighted truncated nuclear norm minus truncated Frobenius norm minimization (DtNFM) method. Through exploiting the nonlocal self-similarity of the noisy image, the similar structures are gathered and a series of similar patch matrices are constructed. For each group, the DtNFM model is conducted for estimating its denoised version. The denoised image would be obtained by concatenating all the denoised patch matrices. 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 problem resulted from DtNFM model, an accurate and effective algorithm is proposed by exploiting the framework of the alternating direction method of multipliers (ADMM). The generated subproblems are discussed in detail. And their global optima can be easily obtained in closed-form. Rigorous mathematical derivation proves that the solution sequences generated by the 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.