A nonlocal filter for local denoising using the Wigner transform

Nonlocal means denoising (NLM) and block-matching and 3D filtering (BM3D) have become the most popular algorithms for image processing. The disadvantage of these methods is that they cannot be realized by hardware implementation. The Wigner distribution function (WDF) has advantages such as explicit physical meaning, spatial frequency distribution of each pixel, and suitability for optical implementation. In recent years, the wide-field imaging system has been used extensively in multiple situations such as aviation, medicine, and traffic. Large-field images often have multiple point spread functions (PSF) and local random noise. However, the results have shown that most nonlocal filters have inadequate effects on local noise filtering. This paper analytically examines the Wigner transform of a multi-Gaussian function and investigates the effects of cross-term and noise on filter reconstruction in image processing. Based on the results, a new space-variant filter with a simple mathematical formula is proposed and applied to local high-frequency noise filtering. Since the filter is closely related to the intensity distribution in the spatial and frequency domains, it provides a simple way to process local noise while simultaneously preserving the high-frequency information of the image.