| Abstract: |
| Synthetic aperture radar (SAR) images suffer from multiplicative noise, which significantly degrades their quality and visual effect. In this work, 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. |
|