TY - JOUR
T1 - Superset technique for approximate recovery in one-bit compressed sensing
AU - Flodin, Larkin
AU - Gandikota, Venkata
AU - Mazumdar, Arya
N1 - Funding Information:
Acknowledgements: This research is supported in part by NSF CCF awards 1618512, 1642658, and 1642550 and the UMass Center for Data Science.
Publisher Copyright:
© 2019 Neural information processing systems foundation. All rights reserved.
PY - 2019
Y1 - 2019
N2 - One-bit compressed sensing (1bCS) is a method of signal acquisition under extreme measurement quantization that gives important insights on the limits of signal compression and analog-to-digital conversion. The setting is also equivalent to the problem of learning a sparse hyperplane-classifier. In this paper, we propose a generic approach for signal recovery in nonadaptive 1bCS that leads to improved sample complexity for approximate recovery for a variety of signal models, including nonnegative signals and binary signals. We construct 1bCS matrices that are universal - i.e. work for all signals under a model - and at the same time recover very general random sparse signals with high probability. In our approach, we divide the set of samples (measurements) into two parts, and use the first part to recover the superset of the support of a sparse vector. The second set of measurements is then used to approximate the signal within the superset. While support recovery in 1bCS is well-studied, recovery of superset of the support requires fewer samples, which then leads to an overall reduction in sample complexity for approximate recovery.
AB - One-bit compressed sensing (1bCS) is a method of signal acquisition under extreme measurement quantization that gives important insights on the limits of signal compression and analog-to-digital conversion. The setting is also equivalent to the problem of learning a sparse hyperplane-classifier. In this paper, we propose a generic approach for signal recovery in nonadaptive 1bCS that leads to improved sample complexity for approximate recovery for a variety of signal models, including nonnegative signals and binary signals. We construct 1bCS matrices that are universal - i.e. work for all signals under a model - and at the same time recover very general random sparse signals with high probability. In our approach, we divide the set of samples (measurements) into two parts, and use the first part to recover the superset of the support of a sparse vector. The second set of measurements is then used to approximate the signal within the superset. While support recovery in 1bCS is well-studied, recovery of superset of the support requires fewer samples, which then leads to an overall reduction in sample complexity for approximate recovery.
UR - http://www.scopus.com/inward/record.url?scp=85090173380&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85090173380&partnerID=8YFLogxK
M3 - Conference Article
AN - SCOPUS:85090173380
SN - 1049-5258
VL - 32
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
T2 - 33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019
Y2 - 8 December 2019 through 14 December 2019
ER -