论文标题
相位在复杂压缩感中的重要性
The importance of phase in complex compressive sensing
论文作者
论文摘要
我们考虑了从复杂随机测量阶段估算实际低复杂性信号（例如稀疏矢量或低级数矩阵）的问题。我们表明，在这种“仅相结合的压缩感”（PO-CS）方案中，如果传感矩阵是一个复杂的高斯随机矩阵，并且与信号空间的复杂性水平相比，如果传感矩阵是一个复杂的高斯随机矩阵，我们可以完美地恢复具有很高概率的信号，并达到全局未知幅度。我们的方法是通过将（非线性）PO-CS方案重新铸造为根据信号归一化约束构建的线性压缩感测模型的来进行的，并且相一致性约束施加任何信号估计以匹配测量域中观察到的阶段。实际上，从压缩传感文献的任何“实例最佳”算法（例如基础追求denoising）中实现了稳定且稳健的信号方向估计。通过证明与此等效线性模型相关的矩阵可以很好地满足高概率的限制性等轴测特性，从而确保了这一点。我们最终从实验上观察到，在压缩传感中，信号恢复所需的测量数量大约是稳健的信号方向恢复。
We consider the question of estimating a real low-complexity signal (such as a sparse vector or a low-rank matrix) from the phase of complex random measurements. We show that in this "phase-only compressive sensing" (PO-CS) scenario, we can perfectly recover such a signal with high probability and up to global unknown amplitude if the sensing matrix is a complex Gaussian random matrix and if the number of measurements is large compared to the complexity level of the signal space. Our approach proceeds by recasting the (non-linear) PO-CS scheme as a linear compressive sensing model built from a signal normalization constraint, and a phase-consistency constraint imposing any signal estimate to match the observed phases in the measurement domain. Practically, stable and robust signal direction estimation is achieved from any "instance optimal" algorithm of the compressive sensing literature (such as basis pursuit denoising). This is ensured by proving that the matrix associated with this equivalent linear model satisfies with high probability the restricted isometry property under the above condition on the number of measurements. We finally observe experimentally that robust signal direction recovery is reached at about twice the number of measurements needed for signal recovery in compressive sensing.
