Sparse sources are separated sources

Sparse representations are being used to solve problems previously thought insolvable. For example, we can separate more sources than sensors using an appropriate transformation of the mixtures into a domain where the sources are sparse. But what do we mean by sparse? What attributes should a sparse measure have? And how can we use this sparsity to separate sources? We investigate these questions and, as a result, conclude that sparse sources are separated sources, as long as you use the correct measure.