On Compressed Sensing Matrices Breaking the Square-Root Bottleneck
On Compressed Sensing Matrices Breaking the Square-Root Bottleneck
复制标题
DOI：
10.1109/itw46852.2021.9457623
复制
发表时间：
2020-10
期刊：
影响因子：
--
通讯作者：
Shohei Satake;Yujie Gu
中科院分区：
文献类型：
--
作者：
Shohei Satake;Yujie Gu
压缩感知是信号处理领域的一个重要框架，有着广泛的实际应用.压缩感知中最具挑战性的问题之一是构造具有约束等距性质的确定性矩阵。到目前为止，只有少数出版物提供了确定性RIP矩阵击败平方根瓶颈的稀疏水平。本文研究了模素数高次剩余定义的矩阵的RIP问题。此外，我们证明了广泛相信的广义Paley图猜想意味着这些矩阵有RIP打破平方根瓶颈。而且，由这些RIP矩阵实现的压缩比明显大于2。
Compressed sensing is a celebrated framework in signal processing and has many practical applications. One of the challenging problems in compressed sensing is to construct deterministic matrices having the restricted isometry property (RIP). So far, there are only a few publications providing deterministic RIP matrices beating the square-root bottleneck on the sparsity level. In this paper, we investigate RIP of certain matrices defined by higher power residues modulo primes. Moreover, we prove that the widely-believed generalized Paley graph conjecture implies that these matrices have RIP breaking the square-root bottleneck. Also the compression ratio realized by these RIP matrices is significantly larger than 2.