Salt and pepper noise removal is a common inverse problem in image processing. Traditional denoising methods have two limitations. First, noise characteristics are often not described accurately. For example, the noise location information is often ignored and the sparsity of the salt and pepper noise is often described by L1 norm, which cannot illustrate the sparse variables clearly. Second, conventional methods separate the contaminated image into a recovered image and a noise part, thus resulting in recovering an image with unsatisfied smooth parts and detail parts. In this study, we introduce a noise detection strategy to determine the position of the noise, and a non-convex sparsity regularization depicted by Lp quasi-norm is employed to describe the sparsity of the noise, thereby addressing the first limitation. The morphological component analysis framework with stationary Framelet transform is adopted to decompose the processed image into cartoon, texture, and noise parts to resolve the second limitation. Then, the alternating direction method of multipliers (ADMM) is employed to solve the proposed model. Finally, experiments are conducted to verify the proposed method and compare it with some current state-of-the-art denoising methods. The experimental results show that the proposed method can remove salt and pepper noise while preserving the details of the processed image.

翻译：椒盐噪声去除是图像处理中常见的逆问题。传统去噪方法存在两个局限性。首先，噪声特征往往无法被精确描述。例如，噪声位置信息常被忽略，且椒盐噪声的稀疏性通常采用L1范数描述，这无法清晰刻画稀疏变量。其次，传统方法将受污染图像分解为恢复图像和噪声分量，导致恢复图像的光滑区域与细节区域不尽人意。本研究引入噪声检测策略以确定噪声位置，并采用Lp拟范数描述的非凸稀疏正则化来刻画噪声的稀疏性，从而解决第一个局限性。采用基于平稳Framelet变换的形态分量分析框架，将处理图像分解为卡通、纹理和噪声分量，以解决第二个局限性。随后采用交替方向乘子法（ADMM）求解所提模型。最后，通过实验验证所提方法，并与当前若干先进去噪方法进行对比。实验结果表明，所提方法能在去除椒盐噪声的同时保持处理图像的细节。