Deterministic Construction of Compressed Sensing Matrices via Algebraic Curves | IEEE Journals & Magazine | IEEE Xplore

Deterministic Construction of Compressed Sensing Matrices via Algebraic Curves


Abstract:

Compressed sensing is a sampling technique which provides a fundamentally new approach to data acquisition. Comparing with traditional methods, compressed sensing makes f...Show More

Abstract:

Compressed sensing is a sampling technique which provides a fundamentally new approach to data acquisition. Comparing with traditional methods, compressed sensing makes full use of sparsity so that a sparse signal can be reconstructed from very few measurements. A central problem in compressed sensing is the construction of sensing matrices. While random sensing matrices have been studied intensively, only a few deterministic constructions are known. Inspired by algebraic geometry codes, we introduce a new deterministic construction via algebraic curves over finite fields, which is a natural generalization of DeVore's construction using polynomials over finite fields. The diversity of algebraic curves provides numerous choices for sensing matrices. By choosing appropriate curves, we are able to construct binary sensing matrices which are superior to Devore's ones. We hope this connection between algebraic geometry and compressed sensing will provide a new point of view and stimulate further research in both areas.
Published in: IEEE Transactions on Information Theory ( Volume: 58, Issue: 8, August 2012)
Page(s): 5035 - 5041
Date of Publication: 24 April 2012

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