Multiplicative noise removal via combining total variation and wavelet frame

Total variation (TV) regularization has been proved effective for cartoon images restoration however it produces staircase effects, and properly wavelet frames were confirmed to provide a more smoothing approximation to the original image. In this paper, a new model for multiplicative noise removal was proposed, which combines wavelet frame-based regularization and TV regularization. A modified proximal linearized alternating direction method is developed to solve the proposed model, considering that adding a new regularization term to the TV model would yield more parameters, which will result in computational difficulties. For the new model, the existence of solution and the convergence property of the proposed algorithm are proved. Numerical experiments have proved that the proposed model has a superior performance in terms of the peak signal-to-noise ratio and the relative error values for non-piecewise constant images when compared with some state-of-the-art multiplicative noise removal models.