Multiplicative speckle noise removal is a challenging task in image processing. Motivated by the performance of anisotropic diffusion in additive noise removal and the structure of the standard deviation of a compressed speckle noisy image, we address this problem with anisotropic diffusion theories. Firstly, an anisotropic diffusion model based on image statistics, including information on the gradient of the image, gray levels, and noise standard deviation of the image, is proposed. Although the proposed model can effectively remove multiplicative speckle noise, it does not consider the noise at the edge during the denoising process. Hence, we decompose the divergence term in order to make the diffusion at the edge occur along the boundaries rather than perpendicular to the boundaries, and improve the model to meet our requirements. Secondly, the iteration stopping criteria based on kurtosis and correlation in view of the lack of ground truth in real image experiments, is proposed. The optimal values of the parameters in the model are obtained by learning. To improve the denoising effect, post-processing is performed. Finally, the simulation results show that the proposed model can effectively remove the speckle noise and retain minute details of the images for the real ultrasound and RGB color images.

Blind image inpainting is a challenging task in image processing. Motivated by the excellent performance of low dimensional manifold model (LDMM) in image inpainting for large-scale pixels missing, we introduce a novel blind inpainting model to repair images with missing pixels or damaged with impulse noise, in spite of the unknown locations of the corrupted pixels. We applied logarithmic transformation to separate the image and binary mask. LDMM regularization and l0 norm regularization were applied respectively to simultaneously estimate the image and the mask. The resulted minimization problem was then solved by the split Bregman algorithm. The simulation results showed that the proposed model, compared with the existing ones, can effectively restore the image with large uniform and non-uniform missing rate.