Level crossing speech sampling and its sparsity promoting reconstruction using an iterative method with adaptive thresholding

The authors propose asynchronous level crossing (LC) A/D converters for low redundancy voice sampling. They propose to utilise the family of iterative methods with adaptive thresholding (IMAT) for reconstructing voice from non-uniform LC and adaptive LC (ALC) samples thereby promoting sparsity. The authors modify the basic IMAT algorithm and propose the iterative method with adaptive thresholding for level crossing (IMATLC) algorithm for improved reconstruction performance. To this end, the authors analytically derive the basic IMAT algorithm by applying the gradient descent and gradient projection optimisation techniques to the problem of square error minimisation subjected to sparsity. The simulation results indicate that the proposed IMATLC reconstruction method outperforms the conventional reconstruction method based on low-pass signal assumption by 6.56dBs in terms of reconstruction signal-to-noise ratio (SNR) for LC sampling. In this scenario, IMATLC outperforms orthogonal matching pursuit, least absolute shrinkage and selection operator and smoothed L0 sparsity promoting algorithms by average amounts of 12.13, 10.31, and 10.28dBs, respectively. Finally, the authors compare the performance of the proposed LC/ALC-based A/Ds with the conventional uniform sampling-based A/Ds and their random sampling-based counterparts both in terms of perceptual evaluation of speech quality and reconstruction SNR.