A sharpening median filter for Cauchy noise with wavelet based regularization

This paper presents a novel method for addressing Cauchy noise in image processing by incorporating a sharpening median filter based on wavelet regularization into a preprocessing model. The proposed approach leverages the noise removal capabilities of the median filter, the detail enhancement provided by the sharpening operator, and the image recovery properties of wavelet regularization. By applying the median filter and sharpening operator sequentially to the images, we obtain preprocessing results that are combined with wavelet regularization to derive an effective preprocessing model. The model is solved using the alternating direction multiplier method. Numerical experiments were conducted to compare the performance of the method under different noise levels and blurriness, with the results demonstrating superior peak signal-to-noise ratio (PSNR) and the measure of structural similarity (SSIM) values compared to existing methods.