Sparse signal recoveries from multiple measurement vectors (MMV) with joint sparsity property have many applications in signal, image, and video processing. The problem becomes much more involved when snapshots of the signal matrix are temporally correlated. With signal's temporal correlation in mind, we provide a framework of iterative MMV algorithms based on thresholding, functional feedback and null space tuning. Convergence analysis for exact recovery is established. Unlike most of iterative greedy algorithms that select indices in a measurement/solution space, we determine indices based on an orthogonal subspace spanned by the iterative sequence. In addition, a functional feedback that controls the amount of energy relocation from the “tails” is implemented and analyzed. It is seen that the principle of functional feedback is capable to lower the number of iteration and speed up the convergence of the algorithm. Numerical experiments demonstrate that the proposed algorithm has a clearly advantageous balance of efficiency, adaptivity and accuracy compared with other state-of-the-art algorithms.

中文翻译：

---

基于正交子空间的联合稀疏恢复快速迭代阈值算法


具有联合稀疏特性的多个测量向量 (MMV) 的稀疏信号恢复在信号、图像和视频处理中具有许多应用。当信号矩阵的快照在时间上相关时，问题变得更加复杂。考虑到信号的时间相关性，我们提供了基于阈值、功能反馈和零空间调整的迭代 MMV 算法框架。建立了精确回收率的收敛分析。与大多数在测量/解空间中选择索引的迭代贪婪算法不同，我们根据迭代序列跨越的正交子空间来确定索引。此外，还实现并分析了控制“尾部”能量重新分配量的功能反馈。可见，函数反馈原理能够减少迭代次数，加快算法的收敛速度。数值实验表明，与其他最先进的算法相比，所提出的算法在效率、适应性和准确性方面具有明显的优势。