Cauchy diversity measures: a novel methodology for enhancing sparsity in compressed sensing

As a new enchanting theory, compressed sensing (CS) demonstrates that a sparse signal can be recovered through a surprisingly small number of linear measurements by solving a problem of ℓ₁ norm minimisation (which can be thought as a special case of the signomial diversity measures). However, the traditional CS model with ℓ₁ norm minimisation can not fully exploit the sparsity especially when the degree of sparsity increases or the measurements number reduces. In this study, the Cauchy diversity measures is incorporated into the proposed model to deal with the above difficulties. The simulation results demonstrate that under the same condition, this new model offers a superior reconstruction precision compared with the common used signomial diversity measures.