Howard, SD; Calderbank, AR; Searle, SJ, *A fast reconstruction algorithm for deterministic compressive sensing using second order reed-muller codes*,
CISS 2008, The 42nd Annual Conference on Information Sciences and Systems
(2008),
pp. 11-15 [doi] .
**Abstract:**

*This paper proposes a deterministic compressed sensing matrix that comes by design with a very fast reconstruction algorithm, in the sense that its complexity depends only on the number of measurements n and not on the signal dimension N. The matrix construction is based on the second order Reed-Muller codes and associated functions. This matrix does not have RIP uniformly with respect to all k-sparse vectors, but it acts as a near isometry on k-sparse vectors with very high probability. © 2008 IEEE.*