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

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