Fast L1 regularized iterative forward backward splitting with adaptive parameter selection for image restoration

We consider the L1 regularized iterative forward backward splitting (IFBS) algorithm for image restoration. The main aim of the paper is to develop a fast and adaptive method with an automatic selection of regularization parameter. The regularization parameter is updated in each iteration without requiring the initial value of the parameter. We establish analytically monotonicity results of the adaptive parameter. Such an algorithm corresponds to solving an adaptive iterative thresholding process. Experimental results demonstrate that the adaptive parameter method is efficient and provide competitive performance.