Conjugate Gradient Hard Thresholding Pursuit Algorithm for Sparse Signal Recovery

Abstract

We propose a new iterative greedy algorithm to reconstruct sparse signals in Compressed Sensing. The algorithm, called Conjugate Gradient Hard Thresholding Pursuit (CGHTP), is a simple combination of Hard Thresholding Pursuit (HTP) and Conjugate Gradient Iterative Hard Thresholding (CGIHT). The conjugate gradient method with a fast asymptotic convergence rate is integrated into the HTP scheme that only uses simple line search, which accelerates the convergence of the iterative process. Moreover, an adaptive step size selection strategy, which constantly shrinks the step size until a convergence criterion is met, ensures that the algorithm has a stable and fast convergence rate without choosing step size. Finally, experiments on both Gaussian-signal and real-world images demonstrate the advantages of the proposed algorithm in convergence rate and reconstruction performance.

Joint Sparse Channel Recovery With Quantized Feedback for Multi-User Massive MIMO Systems

“…Overall, the proposed 2-step Q-PJOMP outperforms the other schemes, which is due to several reasons: firstly, Q-PJOMP is more efficient than the IHT based algorithm (Q-PJIHT). Secondly, since the choice of η is critical in IHT [45], a flexible gradient step size η is employed in the Q-PJIHT algorithm. The η is used as per sparsity level requirements in each iteration, contrary to a fixed-size of 0.01 used in [16].…”

“…The proposed work also selects the optimal step size (η) depending on the sparsity level and dictionary length M . Indeed, since IHT is a gradient descent based algorithm, its step size must be chosen optimally for better convergence [45].…”

“…Although standard IHT based algorithms are computationally simple and take less memory than standard OMP based methods, they have several challenges while dealing with the practical problem. As an example, the stable signal recovery highly depends on the selection of step size η, sparsity parameter [45] and number of iterations.…”