Full fractional total variation method for eliminating salt and pepper noise

This study introduces a hybrid filter developed to effectively eliminate salt and pepper noise, named TVFFS&P. The proposed filter is a combination of the Full Fractional Total Variation (TVFF) method, which is successful in removing Gaussian noise, and two linear filters. The TVFF method utilizes the solution of the heat diffusion equation by incorporating fractional derivative operators of different orders on time and spatial variables along with nonlocal length scale parameters. The integration of these two linear filters enhances the effectiveness of the proposed algorithm in overcoming salt and pepper noise. This hybrid approach demonstrates superior performance, particularly at high noise levels, compared to the state-of-the-art methods. Experimental results show that the TVFFS&P filter significantly reduces salt and pepper noise while maintaining strong performance in preserving image details.