Exact reconstruction of sparse signals via nonconvex minimization
Exact reconstruction of sparse signals via nonconvex minimization
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DOI：
10.1109/lsp.2007.898300
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发表时间：
2007-10-01
影响因子：
3.9
通讯作者：
Chartrand, Rick
中科院分区：
文献类型：
--
作者：
Chartrand, Rick
最近几位作者已经表明，它是可能的，以重建一个稀疏的信号，从更少的线性测量比传统的采样理论所预期的。所使用的方法涉及计算具有给定测量值的信号中的最小l（1）范数的信号。我们表明，通过用p < 1的l（p）范数替换l（1）范数，可以用更少的测量进行精确重建。我们在这个方向上给出一个定理，和许多数值例子，无论是在一个复杂的维度，和较大规模的例子在两个真实的维。
Several authors have shown recently that it is possible to reconstruct exactly a sparse signal from fewer linear measurements than would be expected from traditional sampling theory. The methods used involve computing the signal of minimum l(1) norm among those having the given measurements. We show that by replacing the l(1) norm with the l(p) norm with p < 1, exact reconstruction is possible with substantially fewer measurements. We give a theorem in this direction, and many numerical examples, both in one complex dimension, and larger-scale examples in two real dimensions.