Nuclear Norm Minus Frobenius Norm Minimization with Rank Residual Constraint for Image Denoising

Image denoising is an indispensable process of manifold high level tasks in image processing and computer vision. However, the traditional low-rank minimization-based methods suffer from a biased problem since only the noisy observation is used to estimate the underlying clean matrix. To overcome this issue, a new low-rank minimization-based method, called nuclear norm minus Frobenius norm rank residual minimization (NFRRM), is proposed for image denoising. The propose method transforms the ill-posed image denoising problem to rank residual minimization problems through excavating the nonlocal self-similarity prior. The proposed NFRRM model can perform an accurate estimation to the underlying clean matrix through treating each rank residual component flexibly. More importantly, the global optimum of the proposed NFRRM model can be obtained in closed-form. Extensive experiments demonstrate that the proposed NFRRM method outperforms many state-of-the-art image denoising methods.