Chaotic Analog-to-Information Conversion: Principle and Reconstructability with Parameter Identifiability

TL;DR

This paper introduces a chaos-based analog-to-information conversion system that leverages chaotic systems for sparse signal acquisition and reconstruction, analyzing its reconstructability through parameter identifiability and sensitivity matrix properties.

Contribution

It presents a novel chaos-based sampling method for sparse signals and provides a theoretical analysis of its reconstructability using parameter identifiability concepts.

Findings

Reconstructability depends on the linear independence of sensitivity matrix columns.

The method successfully reconstructs sparse signals using Lorenz system simulations.

Sensitivity matrix analysis guides conditions for local reconstructability.

Abstract

This paper proposes a chaos-based analog-to-information conversion system for the acquisition and reconstruction of sparse analog signals. The sparse signal acts as an excitation term of a continuous-time chaotic system and the compressive measurements are performed by sampling chaotic system outputs. The reconstruction is realized through the estimation of the sparse coefficients with principle of chaotic parameter estimation. With the deterministic formulation, the analysis on the reconstructability is conducted via the sensitivity matrix from the parameter identifiability of chaotic systems. For the sparsity-regularized nonlinear least squares estimation, it is shown that the sparse signal is locally reconstructable if the columns of the sparsity-regularized sensitivity matrix are linearly independent. A Lorenz system excited by the sparse multitone signal is taken as an example to illustrate the principle and the performance.