Measurement Matrix Design for Sample-Efficient Binary Compressed Sensing
Measurement Matrix Design for Sample-Efficient Binary Compressed Sensing
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DOI：
10.1109/lsp.2022.3179230
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发表时间：
2022-01-01
影响因子：
3.9
通讯作者：
Pal, Piya
中科院分区：
文献类型：
--
作者：
Sarangi, Pulak;Pal, Piya
本文研究了用有限冲激响应滤波器从二进制值信号的卷积压缩测量中恢复二进制值信号的问题。我们证明了用一种计算高效的算法来获得精确恢复(无噪声)的最佳样本复杂度是可能的。我们通过采用算法-测量联合设计策略来实现这一点，其中测量矩阵被设计为滤波器的函数，从而可以通过使用顺序译码算法来恢复任意稀疏的二进制信号。这种依赖于过滤器的采样器设计可以克服与实施二进制约束相关的计算挑战，并使我们能够在“极端压缩”状态下操作，在这种情况下，测量的数量可以比稀疏程度小得多。
This letter investigates the problem of recovering a binary-valued signal from compressed measurements of its convolution with a known finite impulse response filter. We show that it is possible to attain optimum sample complexity for exact recovery (in absence of noise) with a computationally efficient algorithm. We achieve this by adopting an algorithm-measurement co-design strategy where the measurement matrix is designed as a function of the filter, such that the recovery of binary signals with arbitrary sparsity is possible by using a sequential decoding algorithm. Such a filter-dependent sampler design can overcome the computational challenges associated with enforcing binary constraints, and enable us to operate in "extreme compression" regimes, where the number of measurements can be much smaller than the sparsity level.