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

08/17/2020
by   Thomas Feuillen, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

01/17/2018

Quantized Compressive Sensing with RIP Matrices: The Benefit of Dithering

In Compressive Sensing theory and its applications, quantization of sign...
02/18/2020

Restricted Structural Random Matrix for Compressive Sensing

Compressive sensing (CS) is well-known for its unique functionalities of...
03/04/2017

Sparse Depth Sensing for Resource-Constrained Robots

We consider the case in which a robot has to navigate in an unknown envi...
12/05/2019

(l1,l2)-RIP and Projected Back-Projection Reconstruction for Phase-Only Measurements

This letter analyzes the performances of a simple reconstruction method,...
12/05/2017

Energy-Efficient Sensor Censoring for Compressive Distributed Sparse Signal Recovery

To strike a balance between energy efficiency and data quality control, ...
11/20/2012

Forest Sparsity for Multi-channel Compressive Sensing

In this paper, we investigate a new compressive sensing model for multi-...
01/04/2021

Discovering genetic networks using compressive sensing

A first analysis applying compressive sensing to a quantitative biologic...