Sparse Recovery from Inaccurate Saturated Measurements
Sparse Recovery from Inaccurate Saturated Measurements
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DOI：
10.1007/s10440-018-0173-2
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发表时间：
2018-03
影响因子：
1.6
通讯作者：
S. Foucart;Jiangyuan Li
中科院分区：
文献类型：
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作者：
S. Foucart;Jiangyuan Li
本文研究了标准压缩感知问题的一种变体，其中稀疏向量是通过不准确的饱和测量获得的。饱和度函数通过发送绝对值较大的条目来加或减阈值，同时保持其他条目不变，从而按分量起作用。本研究的重点是预饱和误差的影响。精确饱和测量的现有理论，即，这种情况下，表现出两个政权取决于的大小，在这里被扩展。提出了一种基于凸优化的恢复方法，并证明了该方法对两种状态下的预饱和误差都具有鲁棒性。另一个忽略预饱和误差的程序也进行了分析，并显示出在小幅度政权是强大的。
This article studies a variation of the standard compressive sensing problem, in which sparse vectorsare acquired through inaccurate saturated measurements,. The saturation functionacts componentwise by sending entries that are large in absolute value to plus-or-minus a threshold while keeping the other entries unchanged. The present study focuses on the effect of the presaturation error. The existing theory for accurate saturated measurements, i.e., the case, which exhibits two regimes depending on the magnitude of, is extended here. A recovery procedure based on convex optimization is proposed and shown to be robust to presaturation error in both regimes. Another procedure ignoring the presaturation error is also analyzed and shown to be robust in the small magnitude regime.