One Bit to Rule Them All : Binarizing the Reconstruction in 1-bit Compressive Sensing

TL;DR

This paper introduces a method for reconstructing sparse signals from 1-bit measurements using a binarized sensing matrix, simplifying hardware and maintaining accurate recovery with theoretical guarantees.

Contribution

It demonstrates that both measurements and sensing matrices can be binarized in 1-bit compressive sensing, enabling hardware-efficient signal reconstruction with proven error bounds.

Findings

Reconstruction error decays as O(m^{-1/2}) with increasing measurements.

Binarized sensing matrices can satisfy RIP, ensuring accurate recovery.

Simulations confirm effectiveness in various sensing scenarios, including Fourier sensing.

Abstract

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.