A modified PRP conjugate gradient method with inertial extrapolation for sparse signal reconstruction

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. PRPCG-IE is applied to two sparse signal reconstruction problems with noise, and preliminary experimental results demonstrate the effectiveness of PRPCG-IE.