Sparse solutions to linear inverse problems with multiple measurement vectors
Sparse solutions to linear inverse problems with multiple measurement vectors
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DOI：
10.1109/tsp.2005.849172
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发表时间：
2005-07-01
影响因子：
5.4
通讯作者：
Kreutz-Delgado, K
中科院分区：
文献类型：
--
作者：
Cotter, SF;Rao, BD;Kreutz-Delgado, K
我们解决的问题，找到稀疏解欠定方程组时，有多个测量向量具有相同的，但未知的，稀疏结构。单测量稀疏解问题在过去已经得到了广泛的研究。虽然已知是NP难的，但许多单测量次优算法已被制定，并在许多不同的应用中找到了实用性。在这里，我们深入考虑两类算法的扩展-匹配追踪（MP）和FOCal欠定系统求解器（FOCALS）-多个测量的情况下，使它们可以用于应用程序，如神经磁成像，其中多个测量向量是可用的，必须计算一个共同的稀疏结构的解决方案。成本函数适当的多个测量问题的开发，算法推导出基于其最小化。在测试用例字典上进行了仿真研究，以显示利用多个测量向量如何提高MP和FOOLS类算法的性能，并比较了它们的性能。
We address the problem of finding sparse solutions to an underdetermined system of equations when there are multiple measurement vectors having the same, but unknown, sparsity structure. The single measurement sparse solution problem has been extensively studied in the past. Although known to be NP-hard, many single-measurement suboptimal algorithms have been formulated that have found utility in many different applications. Here, we consider in depth the extension of two classes of algorithms-Matching Pursuit (MP) and FOCal Underdetermined System Solver (FOCUSS)-to the multiple measurement case so that they may be used in applications such as neuromagnetic imaging, where multiple measurement vectors are available, and solutions with a common sparsity structure must be computed. Cost functions appropriate to the multiple measurement problem are developed, and algorithms are derived based on their minimization. A simulation study is conducted on a test-case dictionary to show how the utilization of more than one measurement vector improves the performance of the MP and FOCUSS classes of algorithm, and their performances are compared.