Name
Abstract | ||
|---|---|---|
In this paper we consider memoryless one-bit compressed sensing with randomly subsampled Gaussian circulant matrices. We show that in a small sparsity regime and for small enough accuracy delta, m similar or equal to delta(-4)s log(N/s delta) measurements suffice to reconstruct the direction of any s-sparse vector up to accuracy d via an efficient program. We derive this result by proving that partial Gaussian circulant matrices satisfy an l(1)/l(2) restricted isometry property property. Under a slightly worse dependence on delta, we establish stability with respect to approximate sparsity, as well as full vector recovery results, i.e., estimation of both vector norm and direction. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1093/imaiai/iaz017 | INFORMATION AND INFERENCE-A JOURNAL OF THE IMA |
Keywords | Field | DocType |
compressed sensing, quantization, circulant matrices, restricted isometry properties | Slightly worse,Discrete mathematics,Circulant matrix,Gaussian,Mathematics,Compressed sensing,Restricted isometry property | Journal |
Volume | Issue | ISSN |
9 | 3 | 2049-8764 |
Citations | PageRank | References |
5 | 0.47 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sjoerd Dirksen | 1 | 32 | 2.75 |
| Hans Christian Jung | 2 | 5 | 0.47 |
| Holger Rauhut | 3 | 816 | 67.21 |