An adaptive fast iterative shrinkage threshold algorithm

Fast iterative shrinkage threshold algorithm (FISTA) is an efficient first-order optimization algorithm for Linear inverse problems. However, the algorithm employed a fixed iterative step size which limits the speed of calculation, This paper proposes an adaptive fast iterative shrinkage threshold algorithm (FISTA) by using a Barzilai-Borwein (BB) operator. The proposed Algorithm uses the previous iteration information to update the step size which can speed up the rate of the iteration. The numerical experimental results of Compressed Sensing and Image Denoising demonstrate that the proposed algorithm has a faster convergence rate and improves the efficiency of the calculation.