Name
Abstract | ||
|---|---|---|
In one-bit compressed sensing (1-bit CS), one attempts to estimate a structured parameter (signal) only using the sign of suitable linear measurements. In this paper, we investigate 1-bit CS problems for sparse signals using the recently proposed k-support norm. We show that the new estimator has a closed-form solution, so no optimization is needed. We establish consistency and recovery guarantees of the estimator for both Gaussian and sub-Gaussian random measurements. For Gaussian measurements, our estimator is comparable to the best known in the literature, along with guarantees on support recovery. For sub-Gaussian measurements, our estimator has an irreducible error which, unlike existing results, can be controlled by scaling the measurement vectors. In both cases, our analysis covers the setting of model misspecification, i.e., when the true sparsity is unknown. Experimental results illustrate several strengths of the new estimator. |
Year | Venue | Field |
|---|---|---|
2015 | JMLR Workshop and Conference Proceedings | Minimum-variance unbiased estimator,Mathematical optimization,Stein's unbiased risk estimate,Computer science,Minimax estimator,Bias of an estimator,Invariant estimator,Compressed sensing,Consistent estimator,Estimator |
DocType | Volume | ISSN |
Conference | 38 | 1938-7288 |
Citations | PageRank | References |
6 | 0.47 | 14 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sheng Chen | 1 | 56 | 11.04 |
| Arindam Banerjee | 2 | 31 | 3.77 |