Optimizing Shrinkage Curves and Application in Image Denoising

A shrinkage curve optimization is proposed for weighted nuclear norm minimization and is adapted to image denoising. The proposed optimization method employs a penalty function utilizing the difference between a latent matrix and its observation and uses odd polynomials to shrink the singular values of the observation matrix. As a result, the coefficients of polynomial characterize the shrinkage operator fully. Furthermore, the Frobenius norm of the penalty function is converted into the corresponding spectral norm, and thus the parameter optimization problem can be easily solved by using off-and-shelf plain least-squares. In the practical application, the proposed denoising method does not work on the whole image at once, but rather a series of matrix termed Rank-Ordered Similar Matrix (ROSM). Simulation results on 256 noisy images demonstrate the effectiveness of the proposed algorithms.