Single-iteration algorithm for compressive sensing reconstruction

In the light of popular compressive sensing concept, this paper proposes a single-iteration reconstruction algorithm for recovering sparse signals from its incomplete set of observations. Compressive sensing assumes that a signal which is sparse in certain transform domain can be randomly sampled in another (dense) domain, taking lower number of samples than required by the sampling theorem. Then, using the optimization algorithms, the entire signal information can be recovered. In our case, instead of using ℓ₁-based methods or approximate greedy solutions, we propose a simple algorithm based on the analysis of noisy-effects that appear in the sparsity domain as a consequence of missing samples. The theory is proven on the examples.