An intrinsic mode function basis dictionary for auditory signal processing

As one important field of sparse representation, the research of dictionary learning attracts most researchers interest in signal processing study. Empirical Mode Decomposition (EMD), as an efficient and adaptive signal decomposition method that depends completely on the signal, is considered as an innovative and appropriative the basis function theory. The Intrinsic Mode Functions (IMFs) obtained by EMD are used as the basis of that expansion which can be linear or nonlinear as dictated by the data, and their linear combination is an efficient representation of the original signals. However, IMFs cannot directly engage in the sparse representation of signals, and their application to the auditory signal processing is quite limited. In this paper, we propose a universal algorithm for dictionary learning that transforms raw IMFs into valuable basis functions. The signals are decomposed into IMFs by EMD, then the general dictionary learning algorithm is implemented on these IMFs, finally, the IMF basis dictionary is learned. Experiments of sparse representation and reconstruction of speech signals are carried out to verify the effectiveness and efficiency of the proposed IMF basis dictionary. The results proved that the signal-to-noise ratio between the reconstructed speech signal and the original one is much higher comparing with other traditional dictionaries, and a better sparseness is achieved.