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.

本文提出了一种基于双重加权截断核范数减去截断 Frobenius 范数最小化的方法，通过利用噪声图像的非局部自相似性来聚合类似结构并构建一系列类似的补丁矩阵，每个组采用 DtNFM 模型来估计其去噪版本，提供了处理复杂噪声分布的足够灵活性，并通过 ADMM 框架最小化问题。