Accelerated iterative simultaneous hard thresholding algorithm for joint sparse optimization

Joint sparse optimization (JSO) leverages the shared sparsity structure across multiple measurement vectors to enhance the signal recovery capability in various applications. In this paper, we propose an accelerated iterative simultaneous hard thresholding algorithm with gradient-based momentum for the JSO, and establish its approximate global convergence under the simultaneous restricted isometry property. Numerical experiments on simulated data demonstrate that the proposed algorithm converges faster and exhibits superior stability compared to several existing simultaneous algorithms.