Iterative signal recovery from incomplete samples

Deanna Needell and Joel Tropp conducted a study where they employed a specific and universal model to task, called Compressive Sampling (CoSa). The aim in CoSa was to sample the given data by multiplying it by a matrix that projected it to a lower dimension. This way, few projections were expected to characterize the complete signal, giving a compression effect. The research in CoSa concentrated on the choice of the projections to apply, algorithms for recovering the data from the projections, and deriving bounds on the required number of projections to enable a recovery of the original data. The researchers proposed a greedy iterative pursuit algorithm, called CoSaMP and provided theoretical analysis of its performance, giving such a guarantee for its successful operation. CoSa and sparse approximation also posed an appealing model and ways to use it successfully for various tasks.