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：本文研究同步稀疏近似（SSA）问题。该问题出现在雷达、传感器网络等需处理具有某种依赖关系的多信号的应用中。本文提出一种新方法，用于联合恢复具有相同支撑集的多个独立稀疏信号。我们对所提出的方法——自适应阈值同步迭代法（SIMAT）的收敛性进行了分析讨论。此外，通过数值实验，我们将该方法与其他组稀疏重构技术，即同步正交匹配追踪（SOMP）和自适应阈值分块迭代法（BIMAT）进行了比较。仿真结果表明，在信噪比（SNR）和成功率（SR）指标上，SIMAT优于这些算法。同时，SIMAT的复杂度远低于BIMAT，使其适用于MIMO雷达系统等实际应用。