Beyond worst-case reconstruction in deterministic compressed sensing

@article{Jafarpour2012BeyondWR,
  title={Beyond worst-case reconstruction in deterministic compressed sensing},
  author={Sina Jafarpour and Marco F. Duarte and A. Robert Calderbank},
  journal={2012 IEEE International Symposium on Information Theory Proceedings},
  year={2012},
  pages={1852-1856}
}
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… CONTINUE READING

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