Ultrasound image denoising using backward diffusion and framelet regularization

•We propose a new model of ultrasound image denoising using backward diffusion and framelet regularization.•The fidelity term is deduced by using Maximum a Posteriori of the Rayleigh distribution of the noise.•The introduction of framelet regularization can remove noise and preserve edges in multiscale framework.•The Split Bregman algorithm is designed to simplify the minimization problem of the proposed model.

This paper introduces a novel variational method for ultrasound image denoising for speckle suppression and edge enhancement. This method is designed to utilize the favorable denoising properties of framelet regularization and edge enhancement of backward diffusion technique. The sparsity and multiresolution properties of the framelet is well suited for speckle noise reduction. The fidelity term of the method can be obtained by Maximum a Posteriori (MAP). The introduction of backward diffusion and framelet regularization makes it difficult to solve the variational energy function. To simplify minimization problem, the Split Bregman algorithm for the proposed model is proposed and then we use it for ultrasound image denoising. Experiment results validate the usefulness of the proposed method for ultrasound image denoising.