Reconstruction of Piecewise-Constant Sparse Signals for Modulo Sampling

TL;DR

This paper introduces a novel algorithm for modulo sampling that directly reconstructs residual signals, leveraging their sparsity and high-frequency features to improve accuracy over traditional difference-based methods.

Contribution

The paper presents a new reconstruction algorithm that avoids error propagation by directly estimating the residual signal in modulo sampling.

Findings

More accurate signal reconstruction compared to conventional methods

Utilizes high-frequency characteristics and sparsity of residual signals

Reduces error propagation in the reconstruction process

Abstract

Modulo sampling is a promising technology to preserve amplitude information that exceeds the observable range of analog-to-digital converters during the digitization of analog signals. Since conventional methods typically reconstruct the original signal by estimating the differences of the residual signal and computing their cumulative sum, each estimation error inevitably propagates through subsequent time samples. In this paper, to eliminate this error-propagation problem, we propose an algorithm that reconstructs the residual signal directly. The proposed method takes advantage of the high-frequency characteristics of the modulo samples and the sparsity of both the residual signal and its difference. Simulation results show that the proposed method reconstructs the original signal more accurately than a conventional method based on the differences of the residual signal.