An adaptive orthogonal sparsifying transform for speech signals

In this paper we consider the problem of representing a speech signal with an adaptive transform that captures the main features of the data. The transform is orthogonal by construction, and is found to give a sparse representation of the data being analysed. The orthogonality property implies that evaluation of both the forward and inverse transform involve a simple matrix multiplication. The proposed dictionary learning algorithm is compared to the K singular value decomposition (K-SVD) method, which is found to yield very sparse representations, at the cost of a high approximation error. The proposed algorithm is shown to have a much lower computational complexity than K-SVD, while the resulting signal representation remains relatively sparse.