基于超拉普拉斯先验上的交叠组稀疏去除脉冲噪声方法
Removing Impulse Noise Method Based on Hyper Laplacian Prior on Overlapping Group Sparsity
摘要: 由于图像复原具有不适定性，寻找一个有意义的图像先验仍然是图像处理上的重要挑战。在本篇论文中，提出了一个基于超拉普拉斯先验的交叠组稀疏模型用于去除脉冲噪声，且对于数据保真项采取Lp (0 < p < 1)范数。超拉普拉斯先验更能拟合自然图像的先验，交叠组稀疏是在图像去噪和图像去模糊中应用广泛。虽然是一项简单而广泛的研究，但该正则化在成像科学中仍有需求。为解决非凸非光滑最小化问题，我们采用交替乘子方向法(ADMM)作为主要算法框架。对于子问题分别使用FFT算法和MM算法。通过数值实验验证，所提出的模型在PSNR和SSIM值上是有效的。
Abstract: Finding a meaningful image prior remains an important challenge in image processing due to the uncomfortable nature of image restoration. In this thesis, an overlapping group sparsity model based on a hyper-Laplacian prior is proposed for impulse noise removal, and the data fidelity term is taken to be the Lp (0 < p < 1) norm. The hyper-Laplacian prior is a better fit to the natural image prior, and overlapping group sparsity is widely used in image denoising and image deblurring. Alt-hough it is a simple and extensive study, the regularization is still in demand in imaging science. To solve the non-convex non-smooth minimization problem, the alternating multiplier direction method (ADMM) is used as the main algorithmic framework. For the subproblems, the FFT algo-rithm and the MM algorithm are used respectively. The proposed model is validated by numerical experiments for PSNR and SSIM values.
文章引用：白萍. 基于超拉普拉斯先验上的交叠组稀疏去除脉冲噪声方法[J]. 应用数学进展, 2023, 12(3): 879-891. https://doi.org/10.12677/AAM.2023.123090

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