A Class Of Fast Proximal Gradient Algorithms For L₁ Regularized Least Squares Problems

The fast proximal gradient algorithm[Lecture notes for EE236C,University of California,Los Angeles,2013]uses the accelerated gradient idea,each iteration takes full advantage of the previous two points's information,which makes the algorithm have a faster convergence rate in solving linear inverse problems in the signal and image processing.In this article,we propose a class of fast proximal gradient gradient algorithms to solve l₁ regularized least squares problems.Based on the fast proximal gradient method,we modify the linear combination of the previous two points to a more general structure,give a sufficient condition for the unknown parameters in the class of fast proximal gradient gradient algorithms,and prove that the algorithms have a global rate of convergence O?1/k²?.The numerical experiments show that,the class of algorithms proposed in this paper not only give a more clear picture,but also have the smaller error value than the fast iterative shrinkage-thresholding algorithm's[SIAM Image Science,2009,2?1?:183-202]within the limits of the same iterative numbers.