Sub-linear time compressed sensing using sparse-graph codes

We consider the problem of recovering the support of an arbitrary K-sparse N-length vector in the presence of noise, where the sparsity K = O(N δ ) is sub-linear in N for some 0 <; δ <; 1. A new family of sparse measurement matrices is introduced with a low-complexity recovery algorithm, which...

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Vydáno v:Proceedings / IEEE International Symposium on Information Theory s. 1645 - 1649
Hlavní autoři: Xiao Li, Pawar, Sameer, Ramchandran, Kannan
Médium: Konferenční příspěvek Journal Article
Jazyk:angličtina
Vydáno: IEEE 01.06.2015
Témata:
Bipartite graph
Color
Complexity
Compressed sensing
Computation
Decoding
Design engineering
Estimation
Mathematical analysis
Noise measurement
Recovery
Showcases
Sparse matrices
Vectors (mathematics)
ISSN:2157-8095, 2157-8117
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Shrnutí:We consider the problem of recovering the support of an arbitrary K-sparse N-length vector in the presence of noise, where the sparsity K = O(N δ ) is sub-linear in N for some 0 <; δ <; 1. A new family of sparse measurement matrices is introduced with a low-complexity recovery algorithm, which achieves a sub-linear measurement cost O(K log 1.3̇ N) and sub-linear computational complexity O(K log 1.3̇ N). Our measurement system is designed to capture observations of the signal through the parity constraints of sparse-graph codes, and to recover the signal by using a simple peeling decoder. We formally connect general sparse recovery problems with sparse-graph decoding, and showcase our design in terms of the measurement cost, computational complexity and recovery performance.
Bibliografie:ObjectType-Article-2
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ObjectType-Conference-1
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SourceType-Conference Papers & Proceedings-2
ISSN:2157-8095
2157-8117
DOI:10.1109/ISIT.2015.7282735