This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications which work with multiple signals maintaining some degree of dependency such as radar and sensor networks. In this paper, we introduce a new method towards joint recovery of several independent sparse signals with the same support. We provide an analytical discussion on the convergence of our method called Simultaneous Iterative Method with Adaptive Thresholding (SIMAT). Additionally, we compare our method with other group-sparse reconstruction techniques, i.e., Simultaneous Orthogonal Matching Pursuit (SOMP), and Block Iterative Method with Adaptive Thresholding (BIMAT) through numerical experiments. The simulation results demonstrate that SIMAT outperforms these algorithms in terms of the metrics Signal to Noise Ratio (SNR) and Success Rate (SR). Moreover, SIMAT is considerably less complicated than BIMAT, which makes it feasible for practical applications such as implementation in MIMO radar systems.

翻译：本文研究了同步稀疏逼近(SSA)问题。这个问题在许多应用中涉及多个信号，这些信号之间有一定的相关性，例如雷达和传感器网络。在本文中，我们提出了一种新方法，针对具有相同支撑的多个独立稀疏信号进行联合恢复。我们通过分析讨论了我们的方法，称为自适应阈值同步迭代方法(SIMAT)的收敛性。此外，我们通过数值实验将我们的方法与其他组稀疏重建技术 (即，同时正交匹配追踪(SOMP)和块迭代方法自适应阈值(BIMAT)) 进行了比较。仿真结果表明，SIMAT在信噪比(SNR)和成功率(SR)等指标方面优于这些算法。此外，SIMAT比BIMAT要简单得多，这使得它在实际应用中（如MIMO雷达系统的实现）是可行的。