  Low rank matrix approximation (LRMA) has drawn increasing attention in recent
years, due to its wide range of applications in computer vision and machine
learning. However, LRMA, achieved by nuclear norm minimization (NNM), tends to
over-shrink the rank components with the same threshold and ignore the
differences between rank components. To address this problem, we propose a
flexible and precise model named multi-band weighted $l_p$ norm minimization
(MBWPNM). The proposed MBWPNM not only gives more accurate approximation with a
Schatten $p$-norm, but also considers the prior knowledge where different rank
components have different importance. We analyze the solution of MBWPNM and
prove that MBWPNM is equivalent to a non-convex $l_p$ norm subproblems under
certain weight condition, whose global optimum can be solved by a generalized
soft-thresholding algorithm. We then adopt the MBWPNM algorithm to color and
multispectral image denoising. Extensive experiments on additive white Gaussian
noise removal and realistic noise removal demonstrate that the proposed MBWPNM
achieves a better performance than several state-of-art algorithms.
