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Sparse representation and reproduction of speech signals in complex Fourier basis

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Abstract

Sparse representation concerns the task of determining the most compact representation of a signal via a linear combination of bases of an overcomplete dictionary. As the problem is non-convex, it is common to consider approximate suboptimal solutions, and one such method is the orthogonal matching pursuit (OMP) algorithm. OMP is an iterative greedy algorithm, where at each step, the basis vector which is most correlated with the current residual is selected. For the most part, attention in the past has been directed towards using real-valued dictionaries as the considered signal of interest is also real-valued. From the perspective of speech representation, the use of complex dictionaries in sparse representation is intuitively appealing as audio signals are generally assumed to be a mixture of exponentials, with time-varying amplitudes and phases. However, sparse representation of speech signal based on complex dictionary is less investigated mainly because the measurements are normally real-valued. In this paper, we pursue this intuition by modelling the complex dictionary on the popular discrete Fourier transform, and then proceed to introduce a new orthogonalization mechanism in the OMP for such cases. The customization of the conventional OMP algorithm to the complex setting enables high-quality compact representation of the speech signals with low computational complexity. Results from experiments demonstrate that the proposed approach is able to retain high perceptual similarity of the reconstructed speech signals to the original ones.

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Availability of data and materials

The data that support the findings of this study are available from the TIMIT Speech corpus (Linguistic Data Consortium (LDC)) (Jankowski et al. 1990) but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of LDC.

Notes

  1. A basis vector is said to be active if the corresponding sparse coefficient is non-zero.

Abbreviations

OMP:

Orthogonal matching pursuit

DFT:

Discrete Fourier transform

PESQ:

Perceptual evaluation of speech quality

DCR:

Degradation category rating

MSE:

Mean-square error

DCT:

Discrete cosine transform

K-SVD:

K-means singular value decomposition

dB:

Desibel

DMOS:

Degradation mean opinion score

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Authors and Affiliations

  1. Faculty of Engineering and Technology, Multimedia University, 75450, Melaka, Malaysia

    Lee-Chung Kwek, Alan Wee-Chiat Tan, Heng-Siong Lim & Khaled A. Alaghbari

  2. Motorola Solutions Malaysia Sdn Bhd, 11900, Penang, Malaysia

    Cheah-Heng Tan

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  1. Lee-Chung Kwek
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  2. Alan Wee-Chiat Tan
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  3. Heng-Siong Lim
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  4. Cheah-Heng Tan
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  5. Khaled A. Alaghbari
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Correspondence to Khaled A. Alaghbari.

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Kwek, LC., Tan, A.WC., Lim, HS. et al. Sparse representation and reproduction of speech signals in complex Fourier basis. Int J Speech Technol 25, 211–217 (2022). https://doi.org/10.1007/s10772-021-09941-w

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