Design of optimal matrices for compressive sensing: Application to environmental sounds

In a compressive sensing context, we propose a solution for a full learning of the dictionary composed of the sparsity basis and the measurement matrix. The sparsity basis learning process is achieved using Empirical Mode Decomposition (EMD) and Hilbert transformation. EMD being a data-driven decomposition method, the resulting sparsity basis shows high sparsifying capacities. On the other hand, a gradient method is applied for the design of the measurement matrix. The method integrates the dictionary normalization into the target function. It is shown to support large scale problems and to have a good convergence and high performance. The evaluation of the whole approach is done on a set of environmental sounds, and is based on a couple of key criteria: sparsity degree and incoherence. Experimental results demonstrate that our approach achieves well with regards to mutual coherence reduction and signal reconstruction at low sparsity degrees.