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.
