  In this paper we combine the stochastic variance reduced gradient (SVRG)
method [17] with the primal dual fixed point method (PDFP) proposed in [7] to
solve a sum of two convex functions and one of which is linearly composite.
This type of problems are typically arisen in sparse signal and image
reconstruction. The proposed SVRG-PDFP can be seen as a generalization of
Prox-SVRG [37] originally designed for the minimization of a sum of two convex
functions. Based on some standard assumptions, we propose two variants, one is
for strongly convex objective function and the other is for general convex
cases. Convergence analysis shows that the convergence rate of SVRG-PDFP is
O(1/k) (here k is the iteration number) for general convex objective function
and linear for k strongly convex case. Numerical examples on machine learning
and CT image reconstruction are provided to show the effectiveness of the
algorithms.
