Efficient adaptation of complex-valued noiselet sensing matrices for compressed single-pixel imaging

TL;DR

This paper introduces an efficient method for using complex-valued noiselet sensing matrices in single-pixel imaging, enabling real-time pattern generation with binary modulators and minimal measurements.

Contribution

It proposes a novel approach to adapt complex noiselet functions for binary single-pixel cameras, including a modified fast transform for real-time pattern computation.

Findings

Successful experimental verification with a single-pixel camera

Reduced number of measurements needed for object sampling

Real-time pattern generation using integer calculations

Abstract

Minimal mutual coherence of discrete noiselets and Haar wavelets makes this pair of bases an essential choice for the measurement and compression matrices in compressed-sensing-based single-pixel detectors. In this paper we propose an efficient way of using complex-valued and non-binary noiselet functions for object sampling in single-pixel cameras with binary spatial light modulators and incoherent illumination. The proposed method allows to determine m complex noiselet coefficients from m+1 binary sampling measurements. Further, we introduce a modification to the complex fast noiselet transform, which enables computationally-efficient real-time generation of the binary noiselet-based patterns using efficient integer calculations on bundled patterns. The proposed method is verified experimentally with a single-pixel camera system using a binary spatial light modulator.