Multiplicative noise removal and blind inpainting of ultrasound images based on a new variational framework

Image inpainting and denoising are two important preprocessing steps widely used in image and visual analysis. In this paper, by the maximum a posterior estimation, we present a new framework to remove multiplicative noise and artifacts simultaneously, when the locations of the artifacts/damaged pixels are unknown. By taking into account the statistical distribution of multiplicative noise as Gamma or Rayleigh noise, we give the special data fidelity term. To suppress the noise and repair the missing intensities, the proposed method applies spatial regularization to the desirable image, and ℓ 0 norm regularization to the artifacts. We introduce three typical spatial regularization: total variation, second-order total generalized variation (TGV) and fractional-order total variation (FOTV) for smoothing images. Due to the non-convexity and non-differentiability of the proposed minimization problem, we introduce additional auxiliary variables to simplify the original problem, and then use the alternating direction method of multipliers to solve it. A set of experiments on synthetic images and real medical ultrasound images show that the proposed method can efficiently remove the multiplicative noise, and more importantly fill in the missing pixels very well. Compared to other similar method, the TGV and FOTV regularization can not only preserve edges and texture details of the image but also avoid the staircase effect.