Rician noise removal via weighted nuclear norm penalization
| Autor: | Xiaoxia Liu, Jiapeng Tian, Jian Lu, Zhenwei Hu, Qingtang Jiang, Yuru Zou |
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| Rok vydání: | 2021 |
| Předmět: |
Applied Mathematics
010102 general mathematics ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION Matrix norm Low-rank approximation Image processing 010103 numerical & computational mathematics Lipschitz continuity 01 natural sciences Regularization (mathematics) Image (mathematics) Convergence (routing) Maximum a posteriori estimation 0101 mathematics Algorithm Mathematics |
| Zdroj: | Applied and Computational Harmonic Analysis. 53:180-198 |
| ISSN: | 1063-5203 |
| Popis: | Rician noise is a common noise that naturally appears in Magnetic Resonance Imaging (MRI) images. Low rank matrix approximation approaches have been widely used in image processing, which takes advantage of the non-local self-similarity between patches in a natural image. The weighted nuclear norm minimization method as a low rank matrix approximation approach has shown to be an effective approach for image denoising. Inspired by this, we propose in this paper a maximum a posteriori (MAP) model with the weighted nuclear norm as a regularization constraint to remove Rician noise. The MAP data fidelity term has a Lipschitz continuous gradient and the weighted nuclear norm can be efficiently minimized. We propose an iterative weighted nuclear norm minimization algorithm (IWNNM) to solve the proposed non-convex model and analyze the convergence of our algorithm. The computational results show that our proposed method is promising in restoring images corrupted with Rician noise. |
| Databáze: | OpenAIRE |
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