Demonstration of Sparse Hadamard Single-Pixel Imaging Using the $H_{64}$ Basis

Overview

This repository presents a comprehensive framework for Sparse Hadamard Single-Pixel Imaging (SHSI) utilizing the $H_{64}$ Hadamard basis. The implementation encompasses:

• Generation of positive and negative sparse Hadamard speckle patterns derived from the $H_{64}$ matrix.
• Simulation of single-pixel imaging data acquisition employing these speckle patterns.
• High-fidelity image reconstruction via the SHSI algorithm.
• Evaluation of noise robustness through additive white Gaussian noise (AWGN) simulations.
• Quantitative assessment of reconstruction quality using Peak Signal-to-Noise Ratio (PSNR) metrics.

Repository Contents

• Generate_hadamard_matrix_random_64_H.m
  Script to generate sparse Hadamard speckle patterns based on the $H_{64}$ matrix. The patterns are saved as PNG images along with the corresponding row and column indices required for SHSI reconstruction, as outlined in Algorithm 1:

• Natural_Hadamard_Transform.m
  Function to generate Hadamard matrices of order $2^n$ via Sylvester's construction, yielding matrices in natural order.

• SHSI.m
  Main demonstration script that:

  • Loads the generated speckle patterns and associated indices.
  • Loads and preprocesses a test image (e.g., Cameraman).
  • Simulates single-pixel measurements using the speckle patterns.
  • Performs image reconstruction via SHSI.
  • Assesses noise robustness by adding AWGN and comparing noisy and noise-free reconstructions.
  • Computes and displays PSNR values for quantitative evaluation.

Usage Instructions

Requirements: MATLAB with Image Processing Toolbox and Communications Toolbox. The demo uses MATLAB's local cameraman.tif sample by default instead of redistributing a copied bitmap. To use an authorized custom image, set the cross-platform environment variable SHSI_TARGET_IMAGE before running the script.

setenv('SHSI_TARGET_IMAGE', fullfile(pwd, 'my_target.png'));

1. Generate Hadamard Speckle Patterns
   Run Generate_hadamard_matrix_random_64_H.m to generate and save the positive and negative sparse Hadamard speckle patterns based on the $H_{64}$ basis. The patterns and corresponding reconstruction indices will be stored under ./data/Random_Discrete_Hadamard_Postive_and_Negetive_matrix_64_H/.

2. Run the SHSI Reconstruction Demo
   Execute SHSI.m to simulate the single-pixel imaging acquisition and reconstruction process using the generated patterns.

Experimental Results

(a) Experimental setup for active single-pixel imaging, featuring two ground glasses as occluders.
(b) Target object: resolution testing board.
(c–i) Reconstruction results obtained via ADMM-based CS, THSI, THSI combined with the CC, mode one using the $H_8$ basis, mode one using the $H_{256}$ basis, and mode two utilizing the $H_{256}$ basis combined with the CC at varying sampling rates.

If useful please cite:

@article{han2025generalized,
  title={Generalized sparse Hadamard single-pixel Imaging},
  author={Han, Yuyuan and Wu, Peng and Xu, Hanxiong and Li, Bin and He, Yuchen and Liu, Jianbin and Chen, Hui and Zheng, Huaibin},
  journal={Optics Express},
  volume={33},
  number={20},
  pages={43324--43341},
  year={2025},
  publisher={Optica Publishing Group}
}

Licensing and asset provenance

The MATLAB source code is released under the MIT License. Generated illumination patterns under data/ are local outputs and are not committed. Reference figures and sample-image handling have separate provenance notes in ASSET_PROVENANCE.md; the MIT license must not be interpreted as relicensing third-party material.