Generalized atom and dictionary design and compressive sensing for vocal signal expansion
Compressive sensing is to apply the sparsity of a signal in some domain to compress a signal. Its performance highly depends on the dictionary and the atoms one applies in the matching pursuit or the basis pursuit processes. In this paper, we generalize the atoms used in the dictionary by converting the phase into the higher order form, using Hermite-Gaussian functions instead of Gaussian functions, and applying harmonic combination. We call them higher-order atoms. This generalization can maximize the sparsity of a signal and is very helpful for improving the coding efficiency. Moreover, we also propose the time-frequency pursuit, which can be viewed as a mixture of the matching pursuit and the basis pursuit, to determine expansion coefficients. Simulations show that the proposed algorithm can much improve the coding efficiency of vocal signals and the bit rate is much less than that of MP3 and other compressive sensing based methods.