Compressive sensing of localized signals: Application to Analog-to-Information conversion

Compressed sensing hinges on the sparsity of signals to allow their reconstruction starting from a limited number of measures. When reconstruction is possible, the SNR of the reconstructed signal depends on the energy collected in the acquisition. Hence, if the sparse signal to be acquired is known to concentrate its energy along a known subspace, an additional “rakeness” criterion arises for the design and optimization of the measurement basis. Formal and qualitative discussion of such a criterion is reported within the framework of a well-known Analog-to-Information conversion architecture and for signals localized in the frequency domain. Non-negligible improvements are shown by simulation.