Optimized Structural Compressed Sensing Matrices for Speech Compression

ABSTRACT

Traditionally, random sensing matrices such as Gaussian are widely used in Compressed Sensing (CS). The higher computational complexity and non-structure of matrix make it inappropriate for practical use. Hence, we have projected the application of structural sensing matrices in CS. Since these matrices impose structure and hence easy to implement in hardware. In this paper, we have proposed optimization method based on structural sensing matrices and Grassmannian frame theory. These proposed sensing matrices are DCT–Grassmannian sensing matrix, Hadamard–Grassmannian sensing matrix, and Walsh–Hadamard Grassmannian sensing matrix, respectively. These sensing matrices are optimized for minimal mutual coherence based on shrinkage method; which further improves the signal recovery performance of speech signal. The result demonstrates that the performance of the proposed optimization method based on structural sensing matrices is improved compared to conventional Elad’s method which employs the Gaussian sensing matrix. Furthermore, the result reveals that the proposed optimization method with Hadamard–Grassmannian sensing matrix yields better performance compared to conventional Elad’s method. Finally, speech quality is evaluated using subjective MOS and objective measures such as LLR and WSS. The result exhibited that the proposed optimization method based on Hadamard–Grassmannian sensing matrix and DCT–Grassmannian sensing matrix exhibits the better MOS, LLR, and WSS performance indicating the good quality of speech.

KEYWORDS:

• Compressed Sensing
• Discrete Wavelet Transform
• Log-likelihood Ratio
• Mean Opinion Score
• Optimization
• Weighted Spectral Slope

Acknowledgements

The authors wish to acknowledge the Dr Babasaheb Ambedkar Technological University, Lonere, Maharashtra, India for providing infrastructure for this research work. The authors would like to thank the anonymous reviewers for their constructive comments and questions which greatly improved the quality of the article.

Additional information

Notes on contributors

Yuvraj V Parkale

Yuvraj V Parkale received the BE degree in electronics and telecommunication engineering from the University of Pune, Maharashtra, India, and MTech degree in electronics and telecommunication engineering from Government College of Engineering, Pune (COEP), Maharashtra, India, in 2010. He is currently pursuing PhD degree in electronics and telecommunication engineering from Dr Babasaheb Ambedkar Technological University (DBATU), State Technical University, Lonere, Raigad, Maharashtra, India. His current research interests include compressed sensing (CS), optimization techniques and algorithms, signal processing, embedded systems, internet of things and machine learning.

Sanjay L Nalbalwar

Sanjay L Nalbalwar received his BE degree in computer science engineering (CSE) in 1990 and ME (electronics) in 1995 from SGGS College of Engineering and Technology, Nanded, Maharashtra, India. He has completed PhD from IIT Delhi in the year 2008. He has around 27 years of teaching experience and is working as a Professor & Head of Electronics and Telecommunication Engineering Department at Dr. Babasaheb Ambedkar Technological University, State Technical University, Maharashtra State, India. His area of interest includes multirate signal processing and wavelet, and stochastic process modeling. He is also working on various research projects in the area of biomedical signal processing, signal representation, signal matched wavelets, smart grid, passenger solar car, and wireless sensor network. E-mail: [email protected]