论文标题
在压缩感应矩阵上打破方形根瓶颈
On Compressed Sensing Matrices Breaking the Square-Root Bottleneck
论文作者
论文摘要
压缩传感是信号处理中著名的框架，并且具有许多实际应用。压缩感应中的具有挑战性的问题之一是构建具有限制等轴测特性（RIP）的确定性矩阵。到目前为止，只有少数出版物提供确定性的RIP矩阵，在稀疏度上击败了方形瓶颈。在本文中，我们研究了由高功率残基Modulo Prime定义的某些矩阵的RIP。此外，我们证明了广泛的普遍佩利图的猜想意味着这些矩阵的裂痕破坏了方形 - 根瓶颈。
Compressed sensing is a celebrated framework in signal processing and has many practical applications. One of challenging problems in compressed sensing is to construct deterministic matrices having 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.
