Recovery of Sparse Signals via Modified Hard Thresholding Pursuit Algorithms

In this paper, we propose a modified version of the hard thresholding pursuit algorithm, called modified hard thresholding pursuit (MHTP), using a convex combination of the current and previous points. The convergence analysis, finite termination properties, and stability of the MHTP are established under the restricted isometry property of the measurement matrix. Simulations are performed in noiseless and noisy environments using synthetic data, in which the successful frequencies, average runtime, and phase transition of the MHTP are considered. Standard test images are also used to test the reconstruction capability of the MHTP in terms of the peak signal-to-noise ratio. Numerical results indicate that the MHTP is competitive with several mainstream thresholding and greedy algorithms, such as hard thresholding pursuit, compressive sampling matching pursuit, subspace pursuit, generalized orthogonal matching pursuit, and Newton-step-based hard thresholding pursuit, in terms of recovery capability and runtime.