Single-pixel imaging with Morlet wavelet correlated random patterns

TL;DR

This paper introduces a novel sampling scheme for single-pixel imaging using Morlet wavelet correlated random patterns, significantly reducing measurement time and improving image quality at low compression rates.

Contribution

The paper proposes a new sampling method based on Morlet wavelet convolved with white noise, enhancing efficiency and image quality in single-pixel imaging.

Findings

Improved image quality over Walsh-Hadamard and noiselet sampling methods.

Enables single-pixel imaging at compression rates of a few percent.

Numerical and experimental validation of the proposed method.

Abstract

Single-pixel imaging is an indirect imaging technique which utilizes simplified optical hardware and advanced computational methods. It offers novel solutions for hyper-spectral imaging, polarimetric imaging, three-dimensional imaging, holographic imaging, optical encryption and imaging through scattering media. The main limitations for its use come from relatively high measurement and reconstruction times. In this paper we propose to reduce the required signal acquisition time by using a novel sampling scheme based on a random selection of Morlet wavelets convolved with white noise. While such functions exhibit random properties, they are locally determined by Morlet wavelet parameters. The proposed method is equivalent to random sampling of the properly selected part of the feature space, which maps the measured images accurately both in the spatial and spatial frequency domains. We compare both numerically and experimentally the image quality obtained with our sampling protocol against widely-used sampling with Walsh-Hadamard or noiselet functions. The results show considerable improvement over the former methods, enabling single-pixel imaging at low compression rates on the order of a few percent.