  Color image denoising is frequently encountered in various image processing
and computer vision tasks. One traditional strategy is to convert the RGB image
to a less correlated color space and denoise each channel of the new space
separately. However, such a strategy can not fully exploit the correlated
information between channels and is inadequate to obtain satisfactory results.
To address this issue, this paper proposes a new multi-channel optimization
model for color image denoising under the nuclear norm minus Frobenius norm
minimization framework. Specifically, based on the block-matching, the color
image is decomposed into overlapping RGB patches. For each patch, we stack its
similar neighbors to form the corresponding patch matrix. The proposed model is
performed on the patch matrix to recover its noise-free version. During the
recovery process, a) a weight matrix is introduced to fully utilize the noise
difference between channels; b) the singular values are shrunk adaptively
without additionally assigning weights. With them, the proposed model can
achieve promising results while keeping simplicity. To solve the proposed
model, an accurate and effective algorithm is built based on the alternating
direction method of multipliers framework. The solution of each updating step
can be analytically expressed in closed-from. Rigorous theoretical analysis
proves the solution sequences generated by the proposed algorithm converge to
their respective stationary points. Experimental results on both synthetic and
real noise datasets demonstrate the proposed model outperforms state-of-the-art
models.
