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

Patch-based sparse representation and low-rank approximation for image processing attract 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, which learns compact dictionaries from similar patches with PCA or SVD, and applies simple hard thresholding filters to shrink the representation coefficients. Compared to recent patchbased sparse representation methods, experiments demonstrate that the proposed method is not only rather rapid, but also effective for a variety of natural images, especially for texture parts in images.