# Sparsity Promoting Reconstruction of Delta Modulated Voice Samples by Sequential Adaptive Thresholds

## TL;DR

This paper introduces IMATDM, a novel sparsity-promoting reconstruction method for delta modulated voice signals, which significantly improves signal quality over traditional lowpass filtering by leveraging adaptive thresholds and sparse signal assumptions.

## Contribution

The paper proposes a new iterative reconstruction algorithm, IMATDM, with adaptive thresholds for delta modulation signals, enhancing reconstruction quality by exploiting sparsity and noise suppression.

## Key findings

- IMATDM outperforms conventional lowpass filtering in SNR by 7.6 dB.
- The method effectively exploits signal sparsity and quantization noise suppression.
- Experimental results confirm improved reconstruction performance over existing sparsity methods.

## Abstract

In this paper, we propose the family of Iterative Methods with Adaptive Thresholding (IMAT) for sparsity promoting reconstruction of Delta Modulated (DM) voice signals. We suggest a novel missing sampling approach to delta modulation that facilitates sparsity promoting reconstruction of the original signal from a subset of DM samples with less quantization noise. Utilizing our proposed missing sampling approach to delta modulation, we provide an analytical discussion on the convergence of IMAT for DM coding technique. We also modify the basic IMAT algorithm and propose the Iterative Method with Adaptive Thresholding for Delta Modulation (IMATDM) algorithm for improved reconstruction performance for DM coded signals. Experimental results show that in terms of the reconstruction SNR, this novel method outperforms the conventional DM reconstruction techniques based on lowpass filtering. It is observed that by migrating from the conventional low pass reconstruction technique to the sparsity promoting reconstruction technique of IMATDM, the reconstruction performance is improved by an average of 7.6 dBs. This is due to the fact that the proposed IMATDM makes simultaneous use of both the sparse signal assumption and the quantization noise suppression effects by smoothing. The proposed IMATDM algorithm also outperforms some other sparsity promoting reconstruction methods.