Efficient ordering of the Hadamard basis for single pixel imaging

Area of Science:

• Optics and Photonics
• Computational Imaging
• Signal Processing

Background:

• Single-pixel imaging (SPI) reconstructs images using a single photodetector by projecting spatial patterns onto a scene.
• Compressed sensing (CS) enables SPI with sub-Nyquist sampling using random patterns, but often yields lower spatial resolution.
• Hadamard pattern-based methods can reconstruct large images but require longer acquisition times.

Purpose of the Study:

• To develop an efficient strategy for ordering Hadamard basis patterns in single-pixel imaging.
• To enable image reconstruction at significantly reduced sampling rates.
• To enhance the trade-off between sampling rate, image quality, and computational complexity in SPI.

Main Methods:

• Proposed an efficient ordering strategy for Hadamard basis patterns based on relevance, from higher to lower.
• Constructed generalized two-dimensional basis vectors.
• Applied a zigzag ordering fashion to the basis vectors.
• Reconstructed images at very low sampling rates (as low as 8%).

Main Results:

• Achieved competitive image quality and computational complexity compared to state-of-the-art methods.
• Demonstrated effective image reconstruction at ultra-low sampling rates.
• Validated the proposed method through both simulations and experimental results.

Conclusions:

• The proposed Hadamard pattern ordering strategy offers an efficient approach for single-pixel imaging.
• This method significantly reduces the required sampling rate without compromising image quality.
• The findings present a competitive alternative to existing SPI techniques, particularly for applications requiring high efficiency and low data acquisition.