Signal-to-noise ratio analysis of single-pixel detection multiplexing under photon-noise. Cases of Hadamard and Cosine positive modulation

TL;DR

This paper analyzes the signal-to-noise ratio in single-pixel detection multiplexing under photon noise, comparing Hadamard and Cosine modulation schemes to raster scanning, revealing limited SNR improvements for certain brightness conditions.

Contribution

It provides a theoretical comparison of SNR performance between single-pixel multiplexing and raster scanning under photon noise for Hadamard and Cosine patterns.

Findings

Single-pixel multiplexing does not always outperform raster scanning in SNR.

SNR improvement occurs only for brighter object pixels, at least $k$ times above the mean.

Hadamard and Cosine modulation schemes have similar SNR limitations under photon noise.

Abstract

In typical single-pixel detection multiplexing, an unknown object is sequentially illuminated with intensity patterns: the total signal is summed into a single-pixel detector and is then demultiplexed to retrieve the object. Because of measurement noise, the retrieved object differs from the ground truth by some error quantified by the signal-to-noise ratio (SNR). In situations where the noise only arises from the photon counting process, it has not been made clear if single-pixel detection multiplexing leads to a better SNR than simply scanning the object with a focused intensity spot - a modality known as raster scanning. This study theoretically assesses the SNR associated with certain types of single-pixel detection multiplexing, and compares it with raster scanning. In particular, we show that, under photon noise, when the positive intensity modulation is based on Hadamard or Cosine patterns, single-pixel detection multiplexing does not systematically improve the SNR as compared to raster scanning. Instead, it only improves the SNR on object pixels at least $k$ times brighter than the object mean signal $\bar{x}$, where $k$ is a constant that depends on the modulation scheme.