A novel image denoising technique with Caputo type space–time fractional operators

Abstract

A novel image denoising model, namely Full Fractional Total Variation (TVFF), based on the Rudin-Osher-Fatemi (ROF) and the fractional total variation models is presented. The leading advantage of TVFF model is that it uses fractional derivatives with length scale parameters instead of ordinary derivatives with respect to both time and spatial variables in the diffusion equation. The Riesz–Caputo fractional derivative operator is used to disperse nonlocal influence throughout all directions, whereas the Caputo fractional derivative concept is employed for time fractional derivatives. Therefore, the influence of neighboring pixels is given greater weight compared to those situated farther away and this reflects the consideration behind denoising process better. Moreover, the numerical approach is constructed, and its stability and convergence properties are thoroughly examined. To show the superiority of our model, the denoised images are subjected to visual and numerical comparisons using metrics such as the Signal-to-Noise Ratio (SNR), the Structural Similarity Index Measure (SSIM) and the Edge-Retention Ratio (ERR). The performance of the TVFF method is evaluated under various types of noise, including Poisson, Speckle, and Salt & Pepper, and the results are compared with those obtained using Gauss and Median Filters. Furthermore, the proposed method is applied to both blind and synthetic images, thereby showcasing its versatility and applicability across diverse datasets. The outcomes showcase the substantial potential of our enhanced model as a versatile and efficient tool for image denoising.