NDLI: Beyond worst-case reconstruction in deterministic compressed sensing

Content Provider	IEEE Xplore Digital Library
Author	Jafarpour, S. Duarte, M.F. Calderbank, R.
Copyright Year	2012
Description	Author affiliation: Multimedia Research Group, Yahoo! Research (Jafarpour, S.) \|\| Department of Electrical and Computer Engineering, University of Massachusetts-Amherst (Duarte, M.F.) \|\| Department of Computer Science, Duke University (Calderbank, R.)
Abstract	The role of random measurement in compressive sensing is analogous to the role of random codes in coding theory. In coding theory, decoders that can correct beyond the minimum distance of a code allow random codes to achieve the Shannon limit. In compressed sensing, the counterpart of minimum distance is the spark of the measurement matrix, i.e., the size of the smallest set of linearly dependent columns. This paper constructs a family of measurement matrices where the columns are formed by exponentiating codewords from a classical binary error-correcting code of block length M. The columns can be partitioned into mutually unbiased bases, and the spark of the corresponding measurement matrix is shown to be O(√M) by identifying a configuration of columns that plays a role similar to that of the Dirac comb in classical Fourier analysis. Further, an explicit basis for the null space of these measurement matrices is given in terms of indicator functions of binary self-dual codes. Reliable reconstruction of k-sparse inputs is shown for k of order M/log(M) which is best possible and far beyond the worst case lower bound provided by the spark.
Starting Page	1852
Ending Page	1856
File Size	152545
Page Count	5
File Format	PDF
ISBN	9781467325806
ISSN	21578117
e-ISBN	9781467325790
e-ISBN	9781467325783
DOI	10.1109/ISIT.2012.6283601
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-07-01
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Vectors Null space Symmetric matrices Sensors Coherence Compressed sensing Sparse matrices
Content Type	Text
Resource Type	Article

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