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.
翻译:从多度测量矢量(MMV)和共同宽度属性中分散的信号回收,在信号、图像和视频处理方面有许多应用。当信号矩阵的快照具有时间关联性时,问题就变得更加严重。考虑到信号的时间相关性,我们提供了一个基于临界值、功能反馈和空格调整的迭接MMV算法框架。对精确恢复的趋同分析已经确立。与大多数在测量/溶解空间中选择指数的迭接贪婪算法不同,我们根据迭接序列所设定的正方位子空间范围确定指数。此外,还实施并分析了控制“尾料”能源迁移数量的功能反馈。人们看到,功能反馈原则能够降低迭代数,加快算法的趋同速度。数字实验表明,拟议的算法与其他最先进的算法相比,在效率、适应性和准确性方面有着明显的优势平衡。