Low Complex Simple Measurement Matrix for Sparse Recovery of Speech Signal

Compressed Sensing (CS), the methodology of signal capturing, allows sampling at flexible rates below Nyquist, with the constraint that the sparsifying basis and the level of sparsity are known in advance for the signal of interest. Many speech codecs based on CS frame work are developed using Linear Predictive Coding (LPC), Discrete Cosine Transform (DCT) and Code Excited Linear Prediction (CELP). In most of them, Gaussian random matrix is used for deriving the observation vector which is computationally complex and has large memory requirements. In this paper, a modified binary sensing matrix, specifically for speech signal is proposed, which has low coherence with the sparsifying bases used for reconstruction. The Signal-to-Noise Ratio (SNR) improvement goes beyond 3-4 dB and it is more significant at very high compression ratios. The application of the proposed sensing matrix to CS based codecs using CELP and dynamic DCT&LPC bases shows significant improvement in the perceptual quality of the reconstructed speech. This enables the functioning of these codecs at lower bit rates without compromising the quality.