# Explicit Compression Degradation Estimations for Low‐Sampling Single‐Pixel Imaging using Hadamard Basis

## TL;DR

This paper introduces a new method to estimate image degradation in single-pixel imaging using self-supervised learning, improving low-sampling image reconstruction.

## Contribution

A self-supervised learning method is proposed to estimate explicit blur kernels for low-sampling single-pixel imaging.

## Key findings

- Explicit degradation models using blur kernels are estimated without labeled data or implicit priors.
- The method is validated through numerical simulations and experimental results in dynamic scenes.
- Deconvolution networks using kernel estimations improve SPI image quality at low sampling ratios.

## Abstract

Single‐pixel imaging (SPI) is a promising imaging modality that enables 2D image acquisition using 1D photocurrent measurements. In SPI, the number of measurements strongly restricts image quality. Compressive sensing methods allow SPI reconstruction using undersampled measurements. Recent studies have focused on restoration schemes using implicit prior assumptions or data‐driven approaches. However, explicit compression degradation models for SPI are still unclear. Here, a degradation estimation technique is presented to explicitly describe compressive sampling for low‐sampling SPI reconstruction using Hadamard basis patterns. The compression degradation models are reflected by the results at different sampling ratios. A self‐supervised learning method is proposed to estimate explicit degradation models, which are mainly composed of blur kernels. Blur kernels varying with sampling ratios and corresponding SPI results are numerically and experimentally demonstrated. Furthermore, this approach is demonstrated for single‐pixel video imaging in dynamic scenes. It is anticipated that the compression degradation estimation technique will further promote the practical application of SPI.

This study proposes a degradation estimation technique to explicitly describe compressive sampling for low‐sampling Hadamard single‐pixel imaging. Blur kernels in explicit degradation models are estimated by the self‐supervised learning method without labeled data and implicit priors. Results of single‐pixel simulations and experiments are restored by using the deconvolution network and the kernel estimations.