Weighted Schatten p-Norm Minimization for Image Denoising and Background Subtraction

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Authors Yuan Xie, Shuhang Gu, Yan Liu, Wangmeng Zuo, Wensheng Zhang, and Lei Zhang
Journal/Conference Name IEEE Transactions on Image Processing
Paper Category
Paper Abstract Low rank matrix approximation (LRMA), which aims to recover the underlying low rank matrix from its degraded observation, has a wide range of applications in computer vision. The latest LRMA methods resort to using the nuclear norm minimization (NNM) as a convex relaxation of the nonconvex rank minimization. However, NNM tends to over-shrink the rank components and treats the different rank components equally, limiting its flexibility in practical applications. We propose a more flexible model, namely the Weighted Schattenp-Norm Minimization (WSNM), to generalize the NNM to the Schattenp-norm minimization with weights assigned to different singular values. The proposed WSNM not only gives better approximation to the original low-rank assumption, but also considers the importance of different rank components. We analyze the solution of WSNM and prove that, under certain weights permutation, WSNM can be equivalently transformed into independent non-convex lp-norm subproblems, whose global optimum can be efficiently solved by generalized iterated shrinkage algorithm. We apply WSNM to typical low-level vision problems, e.g., image denoising and background subtraction. Extensive experimental results show, both qualitatively and quantitatively, that the proposed WSNM can more effectively remove noise, and model complex and dynamic scenes compared with state-of-the-art methods.
Date of publication 2016
Code Programming Language MATLAB

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