An Iterative Hard Thresholding Algorithm based on Sparse Randomized Kaczmarz Method for Compressed Sensing

The paper proposes a novel signal reconstruction algorithm through substituting the gradient descent method in the iterative hard thresholding algorithm with a faster sparse randomized Kaczmarz method. By designing a series of gradually attenuated weights for the matrix rows whose indexes lie outside of the support set of the original sparse signal, we can focus the iterations on the effective support rows of the measurement matrix. The experiment results show that the proposed algorithm presents a faster convergence rate and more accurate reconstruction accuracy than the state-of-the-art algorithms. Meanwhile, the successful reconstruction probability of the proposed algorithm is higher than that of other algorithms. Moreover, the characteristics of the proposed signal reconstruction algorithm are also analyzed in detail through numerical experiments.