Cosparsity in Compressed Sensing

Analysis l(1)-recovery is a strategy of acquiring a signal, that is sparse in some transform domain, from incomplete observations. In this chapter we give an overview of the analysis sparsity model and present theoretical conditions that guarantee successful nonuniform and uniform recovery of signals from noisy measurements. We derive a bound on the number of Gaussian and subgaussian measurements by examining the provided theoretical guarantees under the additional assumption that the transform domain is generated by a frame, which means that there are just few nonzero inner products of a signal of interest with frame elements.