Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | 夏羽 博士, 杭州师范大学
| | Inviter: | 许志强 研究员 | Title:
| Signal and matrix recovery with correlated measurements | Time & Venue:
| 2019.8.27 14:00-15:00 N226 | Abstract:
| Restricted Isometry Property (RIP) is widely used in compressed sensing and matrix recovery. However, in practice, we often come across high-dimensional data from random or deterministic measurements with correlated entries. Here we analyze data recovery from correlated measurements with suitable tools instead of RIP. In compressed sensing, we introduce the restricted eigenvalue condition adapted to frame D for several classes of correlated matrices, and get the error bounds in the analysis LASSO and the analysis Dantzig Selector under sparse scenario. Besides, we discuss multichannel blind deconvolution problem which can be considered as matrix recovery problem by lifting method. Under deterministic subspace assumption, the measurements are highly correlated and RIP is violated. We derive tight condition for signal recovery, and present a non-convex algorithm with theoretical stability result. | |
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