Preconditioning in the fast dual forward-backward splitting algorithm

The fast forward-backward splitting algorithm has been applied to many fields since it was created, such as signal processing, image processing, compressed sensing, model predictive control and so on. However, this doesn´t mean that the algorithm converges very fast in the practical problems, especially when applied to the ill-conditions. Thus, it´s necessary to speed up the algorithm to make it more effective when solving the concrete problems. In this paper, we improved the work of P. Giselsson [1] by a more simple and concise preconditioning method. We show that the performance of the fast forward-backward splitting algorithm can be significantly improved by preconditioning the problem data and solving the preconditioned problems. Besides, the numerical experiment also shows the improvements by preconditioning the problem data, comparing to the case that no preconditioning is used.