Explicit constructions for compressed sensing of sparse signals
Explicit constructions for compressed sensing of sparse signals
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发表时间：
2008-01
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通讯作者：
P. Indyk
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作者：
P. Indyk
近年来，人们发现了一种获得n维矢量(或信号)的简洁近似表示的新方法。对于任何信号x，x的简明表示等于Ax，其中A是精心选择的Rxn实矩阵，R≪n。通常，A是从Rxn矩阵上的某个分布中随机选择的。向量Ax通常被称为x的测量向量或示意图。虽然Ax的维度比x短得多，但它包含了大量关于x的有用信息。
Over the recent years, a new approach for obtaining a succinct approximate representation of n-dimensional vectors (or signals) has been discovered. For any signal x, the succinct representation of x is equal to Ax, where A is a carefully chosen R x n real matrix, R ≪ n. Often, A is chosen at random from some distribution over R x n matrices. The vector Ax is often refered to as the measurement vector or a sketch of x. Although the dimension of Ax is much shorter than of x, it contains plenty of useful information about x.