A Time‐Fractional Equation With the Gray Level Indicator for Image Multiplicative Noise Removal

ABSTRACT Synthetic aperture radar (SAR) images suffer from multiplicative noise, which significantly degrades their quality and visual effect. To address this issue, we propose a time‐fractional equation with a gray level indicator for SAR image denoising. By introducing the time‐fractional derivative, the model effectively interpolates between the heat and wave equations, preserving valuable information in highly oscillatory regions. Moreover, the fractional‐order derivative operator possesses nonlocal properties, allowing for the inclusion of information from nonlocal domains. In order to achieve better control over the diffusion process, we incorporate a gray level indicator into the diffusion coefficients of our model, which allows us to fully take into account the gray level information of the image. We also investigate the well‐posedness of the proposed model. Experiments on natural and real SAR images demonstrate the superiority of our method in removing multiplicative noise, particularly in highly oscillatory regions and texture‐rich images.