Structured sublinear compressive sensing via belief propagation
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- 作者：Wei Dai ; [Author Vitae] ; Olgica Milenkovic ; milenkov@uiuc.edu ; [Author Vitae] ; Hoa Vin Pham
- 关键词：Belief propagation ; Compressive sensing ; Low-density parity-check codes ; Orthogonal matching pursuit ; Restricted isometry constants ; Sparse approximation ; Subspace pursuit
- 刊名：Physical Communication
- 出版年：2012
- 出版时间：June, 2012
- 年：2012
- 卷：5
- 期：2
- 页码：76-90
- 全文大小：338 K
文摘
Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage cost of random sensing matrices. We propose a new structured compressive sensing scheme, based on codes of graphs, that allows for a joint design of structured sensing matrices and logarithmic-complexity reconstruction algorithms. The compressive sensing matrices can be shown to offer asymptotically optimal performance when used in combination with orthogonal matching pursuit (OMP) methods. For reduced-complexity greedy reconstruction schemes, we propose a new family of list-decoding belief propagation algorithms, as well as reinforced and multiple-basis belief propagation (BP) algorithms. Our simulation results indicate that reinforced BP CS schemes offer very good complexity-performance tradeoffs for very sparse signal vectors.