论文标题
一点点统治所有这些：将重建以1位压缩感应化
One Bit to Rule Them All : Binarizing the Reconstruction in 1-bit Compressive Sensing
论文作者
论文摘要
这项工作着重于从其1位测量值中重建稀疏信号。上下文是1位压缩感之一，其中的测量值量相当于量化（抖动）随机预测。我们的主要贡献表明，除了测量过程外，我们还可以通过传感矩阵的二线化重建信号。测量和传感矩阵的这种二进制表示可以显着简化嵌入式系统上的硬件体系结构，从而实现更便宜，更有效的替代方案。在此框架内，给定一个尊重限制的等轴测特性（RIP）的传感矩阵，我们证明，对于任何稀疏信号，量化的投影后反射（QPBP）算法在测量数M增加时会达到o（m-1/2）等重建误差，例如O（M-1/2）。模拟突出了开发方案在不同感应场景中的实用性，包括随机的部分傅立叶传感。
This work focuses on the reconstruction of sparse signals from their 1-bit measurements. The context is the one of 1-bit compressive sensing where the measurements amount to quantizing (dithered) random projections. Our main contribution shows that, in addition to the measurement process, we can additionally reconstruct the signal with a binarization of the sensing matrix. This binary representation of both the measurements and sensing matrix can dramatically simplify the hardware architecture on embedded systems, enabling cheaper and more power efficient alternatives. Within this framework, given a sensing matrix respecting the restricted isometry property (RIP), we prove that for any sparse signal the quantized projected back-projection (QPBP) algorithm achieves a reconstruction error decaying like O(m-1/2)when the number of measurements m increases. Simulations highlight the practicality of the developed scheme for different sensing scenarios, including random partial Fourier sensing.
