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

@article{Feuillen2020OneBT, title={One Bit to Rule Them All : Binarizing the Reconstruction in 1-bit Compressive Sensing}, author={Thomas Feuillen and Mike E. Davies and Luc Vandendorpe and Laurent Jacques}, journal={ArXiv}, year={2020}, volume={abs/2008.07264} }

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…

## References

SHOWING 1-10 OF 18 REFERENCES

Quantized Compressive Sensing with RIP Matrices: The Benefit of Dithering

- Computer Science, MathematicsArXiv
- 2018

This work shows that, for a scalar and uniform quantization, provided that a uniform random vector, or "random dithering", is added to the compressive measurements of a low-complexity signal, a large class of random matrix constructions known to respect the restricted isometry property (RIP) are made "compatible" with this quantizer.

Flexible Multilayer Sparse Approximations of Matrices and Applications

- Mathematics, Computer ScienceIEEE Journal of Selected Topics in Signal Processing
- 2016

This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors.

A Mathematical Introduction to Compressive Sensing

- Computer ScienceApplied and Numerical Harmonic Analysis
- 2013

A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build and serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject.

Quantity over Quality: Dithered Quantization for Compressive Radar Systems

- Engineering, Computer Science2019 IEEE Radar Conference (RadarConf)
- 2019

A novel estimation scheme that can deal with strongly quantized received signals, going as low as 1-bit per signal sample is introduced, leveraging for this a dithered quantized compressive sensing framework that can be applied to classic radar processing and hardware.

SignProx: One-bit Proximal Algorithm for Nonconvex Stochastic Optimization

- Computer Science, MathematicsICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2019

This paper proposes a stochastic variant of the proximal-gradient method that also uses one-bit per update element, and proves the theoretical convergence of the method for non-convex optimization under a set of explicit assumptions.

1-bit Localization Scheme for Radar using Dithered Quantized Compressed Sensing

- Engineering, Computer Science
- 2018

A novel scheme allowing for 2D target localization using highly quantized 1-bit measurements from a Frequency Modulated Continuous Wave radar with two receiving antennas by inserting a dithering on the unquantized observations is presented.

Review of Analog-To-Digital Conversion Characteristics and Design Considerations for the Creation of Power-Efficient Hybrid Data Converters

- Computer Science
- 2018

Design challenges for low-power CMOS high-speed analog-to-digital converters (ADCs) are reviewed, and a hybrid ADC architecture is introduced for applications requiring 1 GS/s with 6–8 bit resolution and power consumption below 11 mW.

and L

- Jacques, “1-bit localization scheme for radar using dithered quantized compressed sensing,” 2018 5th International Workshop on Compressed Sensing applied to Radar, Multimodal Sensing, and Imaging (CoSeRa)
- 2018

and L

- Jacques, “Quantity over quality: Dithered quantization for compressive radar systems,” 2019 IEEE Radar Conference (RadarConf), pp. 1–6
- 2018

Foucart andH . Rauhut , Amathematical introduction to compressive sensing

- 2013