Momentum-Based Iterative Hard Thresholding Algorithm for Sparse Signal Recovery

The iterative hard thresholding (IHT) algorithm is widely used for recovering sparse signals in compressed sensing. Despite the development of numerous variants of this effective algorithm, its convergence rate and accuracy in finding the optimal solution still have room for enhancement. Aiming at this issue, we propose a momentum-based iterative hard thresholding (MIHT) algorithm by introducing a new iterative search direction derived from the momentum method, which uses historical iteration information to refine the search direction and thereby accelerate convergence. We establish a sufficient condition, in terms of $ (3s)$-order restricted isometry constant, to guarantee the convergence of MIHT. Excitingly, numerical experiments demonstrate that MIHT possesses an excellent recovery success rate and outperforms a wide range of existing IHT variants.