期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 57, 期 8, 页码 3721-3748出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2010.2050803
关键词
Analog compression; compressed sensing; information measures; Renyi information dimension; Shannon theory; source coding
资金
- National Science Foundation [CCF-0635154, CCF-0728445]
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1016625] Funding Source: National Science Foundation
In Shannon theory, lossless source coding deals with the optimal compression of discrete sources. Compressed sensing is a lossless coding strategy for analog sources by means of multiplication by real-valued matrices. In this paper we study almost lossless analog compression for analog memoryless sources in an information-theoretic framework, in which the compressor or decompressor is constrained by various regularity conditions, in particular linearity of the compressor and Lipschitz continuity of the decompressor. The fundamental limit is shown to the information dimension proposed by Renyi in 1959.
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