Sparse Signal Recovery from a Mixture of Linear and Magnitude-Only Measurements.
Sparse Signal Recovery from a Mixture of Linear and Magnitude-Only Measurements.
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DOI：
10.1109/lsp.2015.2393295
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发表时间：
2015-09
影响因子：
3.9
通讯作者：
Tarokh V
中科院分区：
文献类型：
--
作者：
Akçakaya M;Tarokh V
我们认为，从线性和幅度的组合（无相）测量的精确稀疏信号恢复的问题。k稀疏信号x ∈ n被测量为r = Bx和y =| CX|，其中B ∈ Σ m1×n和C ∈ Σ m2×n是测量矩阵，| · |是元素的绝对值。我们证明，如果max（2 m1，1）+ m2 ≥ 4k − 1，那么一组通用测量就足以精确地恢复每个k-稀疏x，从而在线性测量和仅幅度测量的数量之间建立权衡。
We consider the problem of exact sparse signal recovery from a combination of linear and magnitude-only (phaseless) measurements. A k-sparse signal x ∈ ℂn is measured as r = Bx and y = |Cx|, where B ∈ ℂm1×n and C ∈ ℂm2×n are measurement matrices and | · | is the element-wise absolute value. We show that if max(2m1, 1) + m2 ≥ 4k − 1, then a set of generic measurements are sufficient to recover every k-sparse x exactly, establishing the trade-off between the number of linear and magnitude-only measurements.