Expander ℓ0-decoding

Moreover, we observe Serial-ℓ0 and Parallel-ℓ0 to be able to solve large scale problems with a larger fraction of nonzeros than other algorithms when the number of measurements is substantially less than the signal length; in particular, they are able to reliably solve for a k-sparse vector x∈Rn from m expander measurements with n/m=103 and k/m up to four times greater than what is achievable by ℓ1-regularisation from dense Gaussian measurements. Additionally, due to their low computational complexity, Serial-ℓ0 and Parallel-ℓ0 are observed to be able to solve large problems sizes in substantially less time than other algorithms for compressed sensing. In particular, Parallel-ℓ0 is structured to take advantage of massively parallel architectures.