Iterative Hard Thresholding Based on Randomized Kaczmarz Method

The iterative hard thresholding methods have been recently developed to deal with the sparse regularization problems arising in compressed sensing and other sparse signal processing methods. The methods are attractive due to their simplicity. In this paper, we propose acceleration schemes for iterative hard thresholding methods based on randomized Kaczmarz method. The speedup is achieved by replacing the gradient step in the iterative hard thresholding methods with a randomized Kaczmarz algorithm. Numerical experiments with the sparse signal recovery show the simplicity and effectiveness of the proposed algorithms.