论文标题
保持阶段！仅相压感应中的信号恢复
Keep the phase! Signal recovery in phase-only compressive sensing
论文作者
论文摘要
我们证明，在“仅相位压缩传感”（PO-CS）方案中，可以从复杂随机测量的相位估算一个稀疏信号。如果传感矩阵是一个复杂的高斯随机矩阵，并且与信号稀疏性相比，我们可以完美地恢复这种信号的概率和全局未知的幅度，那么我们可以完美地恢复这样的信号。我们的方法包括将（非线性）PO-CS方案重新铸造为线性压缩传感模型。我们是根据信号归一化约束和相一致性约束构建的。实际上，我们从基础追求denoising计划中实现了稳定且强大的信号方向估计。在数值上，达到稳健的信号方向估计的估计值约为压缩感中信号恢复所需的测量次数的两倍。
We demonstrate that a sparse signal can be estimated from the phase of complex random measurements, in a "phase-only compressive sensing" (PO-CS) scenario. With high probability and up to a global unknown amplitude, we can perfectly recover such a signal if the sensing matrix is a complex Gaussian random matrix and the number of measurements is large compared to the signal sparsity. Our approach consists in recasting the (non-linear) PO-CS scheme as a linear compressive sensing model. We built it from a signal normalization constraint and a phase-consistency constraint. Practically, we achieve stable and robust signal direction estimation from the basis pursuit denoising program. Numerically, robust signal direction estimation is reached at about twice the number of measurements needed for signal recovery in compressive sensing.
