Image denoising via local and nonlocal circulant similarity

• Circulant similarity as a new prior is introduced for image denoising.
• Local circulant similarity is incorporated into weighted averaging filter.
• Patch filter is implemented by fast Fourier transform.
• Nonlocal grouping is used to perform circulant similarity along three dimensions.

A patch based image denoising method is developed in this paper by introducing a new type of image self-similarity. This self-similarity is obtained by cyclic shift, which is called “circulant similarity”. Given a corrupted image patch, it can be estimated by incorporating circulant similarity into a weighted averaging filter. By choosing an appropriate kernel as weight function, the patch filter is implemented by circular convolution, and can be efficiently solved using fast Fourier transform. In addition, the circulant similarity can be enhanced by using nonlocal modeling. We stack the similar image patches into 3D groups, and propose a denoising scheme based on group estimation across the patches. Numerical experiments demonstrate that the proposed method with local circulant similarity outperforms much its local filtering based counterparts, and the proposed method with nonlocal circulant similarity shows very competitive performance with state-of-the-art denoising method, especially on images corrupted by strong noise.