Matrizes de Medida Determinísticas Ótimas para Amostragem Compressiva Usando Bases Biortogonais

Compressive Sensing (CS) allows for reconstructing sparse signals within a low acceptable error using far less measurements than stipulated by the Nyquist criterion. In the CS paradigm one usually employs random measurements by means of projections on a sensing matrix and reconstructs the signal from these measurements through l1 norm minimization. In this work, the use of deterministic sensing matrices is investigated, in the context of rate-distortion performance. Experimental results show that the use of deterministic sensing matrices provides better rate-distortion performance than the use of random ones when l1 norm minimization is employed for reconstruction. In addition, for the cases the signal is sparse on a biorthogonal basis, we propose a method for designing deterministic sensing matrices with minimum coherence, which provides further rate-distortion performance.