It is widely known that the inertial technique of the heavy ball method can accelerate its convergence speed. In this paper, by embedding the inertial technique in the famous PRP conjugate gradient method, we propose a modified PRP conjugate gradient method with inertial extrapolation (PRPCG-IE) for sparse signal reconstruction. Its direction satisfies the sufficient descent property, which is independent of any line search. Global convergence of PRPCG-IE is established under some standard conditions. Finally, PRPCG-IE is applied to two sparse signal reconstruction problems with noise. Preliminary experimental results demonstrate the effectiveness of PRPCG-IE.
MSC. 90C25, 90C30