Real-time single-pixel video imaging with Fourier domain regularization

Area of Science:

• Optics and Imaging
• Computational Imaging
• Signal Processing

Background:

• Single-pixel imaging (SPI) systems capture images using a single-pixel detector.
• Traditional SPI reconstruction methods can be computationally intensive, limiting real-time applications.
• Compressive sensing (CS) methods, while effective, often suffer from slow reconstruction times due to l1-norm optimization.

Purpose of the Study:

• To introduce a novel closed-form image reconstruction method for SPI.
• To provide a computationally efficient alternative for real-time SPI applications.
• To explore regularization techniques and sampling strategies for improved reconstruction quality.

Main Methods:

• Utilized the generalized inverse of the measurement matrix for closed-form reconstruction.
• Employed regularization by minimizing convolution norms with spatial filters.
• Investigated various sampling bases including Walsh-Hadamard, discrete cosine, and Morlet wavelets.

Main Results:

• Achieved real-time image reconstruction at 11 Hz for 256x256 resolution with highly compressive measurements.
• Demonstrated that incorporating a quadratic criterion allows binary sampling with comparable quality to total variation minimization.
• Showcased the method's effectiveness as an alternative to slow l1-norm optimization in CS.

Conclusions:

• The proposed closed-form reconstruction method significantly enhances the speed of SPI.
• This approach enables real-time single-pixel imaging, overcoming limitations of existing CS techniques.
• The flexibility in sampling functions and the use of binary sampling open possibilities for hardware implementation.