Adaptive backtracking scheme for iterative shrinkage thresholding algorithms

Iterative shrinkage/thresholding algorithms (ISTAs) have recently been proposed to solve linear inverse problems arising in signal and image processing. The convergence rate of ISTAs relies on a scalar known as step size, which is unknown and expensive to compute in practice especially for large-scale problems. Usually a backtracking rule is employed to choose an appropriate step size which guarantees the convergence condition and speed up ISTAs at the same time. In this paper, we propose a new method to compute the step size exactly. Experimental results show the effectiveness of the proposed algorithm.