Intelligent Sparse Representations for Speech ∗

We design a dictionary in which speech signals have a sparse representation. We utilize the property that speech is comprised of a fixed number of phonemes. The dictionary is a concatenation of the principal components of all these phonemes, and hence information about each phoneme is present in a block. Since any speech signal is a concatenation of phonemes, it can be represented as a linear combination of the columns of this dictionary. In particular, if we consider a small window of speech (containing no more than two phonemes), such a signal would ideally have a block sparse representation in the dictionary. The representation is obtained by solving a variation of the LASSO or basis pursuit denoising (BPDN) problem. We show that the representation is sparse enough to achieve compression. Finally, our intuition is that such a representation could also implicitly perform denoising.