  Patch-based low-rank minimization for image processing attracts much
attention in recent years. The minimization of the matrix rank coupled with the
Frobenius norm data fidelity can be solved by the hard thresholding filter with
principle component analysis (PCA) or singular value decomposition (SVD). Based
on this idea, we propose a patch-based low-rank minimization method for image
denoising. The main denoising process is stated in three equivalent way: PCA,
SVD and low-rank minimization. Compared to recent patch-based sparse
representation methods, experiments demonstrate that the proposed method is
rather rapid, and it is effective for a variety of natural grayscale images and
color images, especially for texture parts in images. Further improvements of
this method are also given. In addition, due to the simplicity of this method,
we could provide an explanation of the choice of the threshold parameter,
estimation of PSNR values, and give other insights into this method.
