A note on patch-based low-rank minimization for fast image denoising.

Patch-based low-rank minimization for image processing attracts muchattention in recent years. The minimization of the matrix rank coupled with theFrobenius norm data fidelity can be solved by the hard thresholding filter withprinciple component analysis (PCA) or singular value decomposition (SVD). Basedon this idea, we propose a patch-based low-rank minimization method for imagedenoising. The main denoising process is stated in three equivalent way: PCA,SVD and low-rank minimization. Compared to recent patch-based sparserepresentation methods, experiments demonstrate that the proposed method israther rapid, and it is effective for a variety of natural grayscale images andcolor images, especially for texture parts in images. Further improvements ofthis 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.