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

TL;DR

This paper introduces a fast, closed-form method for real-time single-pixel image reconstruction using Fourier domain regularization, enabling high-speed imaging with compressive measurements and binary sampling functions.

Contribution

The authors develop a novel, computationally efficient reconstruction technique based on matrix pseudoinverse and Fourier domain regularization, suitable for real-time single-pixel imaging.

Findings

Achieved real-time reconstruction at 11 Hz for 256x256 images.

Demonstrated effective binary sampling with cosine and Morlet basis functions.

Provided a practical alternative to slow l1-norm compressive sensing methods.

Abstract

We present a closed-form image reconstruction method for single pixel imaging based on the generalized inverse of the measurement matrix. Its numerical cost scales linearly with the number of measured samples. Regularization is obtained by minimizing the norms of the convolution between the reconstructed image and a set of spatial filters, and the final reconstruction formula can be expressed in terms of matrix pseudoinverse. At high compression this approach is an interesting alternative to the methods of compressive sensing based on l1-norm optimization, which are too slow for real-time applications. For instance, we demonstrate experimental single-pixel detection with real-time reconstruction obtained in parallel with the measurement at the frame rate of $11$ Hz for highly compressive measurements with the resolution of $256\times 256$. For this purpose, we preselect the sampling functions to match the average spectrum obtained with an image database. The sampling functions are selected from the Walsh-Hadamard basis, from the discrete cosine basis, or from a subset of Morlet wavelets convolved with white noise. We show that by incorporating the quadratic criterion into the closed-form reconstruction formula, we are able to use binary rather than continuous sampling reaching similar reconstruction quality as is obtained by minimizing the total variation. This makes it possible to use cosine or Morlet-based sampling with digital micromirror devices without advanced binarization methods.