Abstract
Single pixel imaging (SPI) captures images without array detectors or raster scanning. When combined with compressive sensing techniques it enables novel solutions for high-speed optical imaging and spectroscopy. However, when it comes to the real-time capture and analysis of a fast event, the challenge is the inherent trade-off between frame rate and image resolution. Due to the lack of sufficient sparsity and the intrinsic iterative process, conventional compressed sensing techniques have limited improvement in capturing natural scenes and displaying the images in real time. In this work, we demonstrate a novel alternative compressive imaging approach employing an efficient and easy-implementation sampling scheme based on reordering the deterministic Hadamard basis through their total variation. By this means, the number of measurements and acquisition are reduced significantly without needing complex minimization algorithms. We can recover a 128 × 128 image with a sampling ratio of 5% at the signal peak signal-to-noise ratio (PSNR) of 23.8 dB, achieving super sub-Nyquist sampling SPI. Compared to other widely used sampling e.g. standard Hadamard protocols and Gaussian matrix methods, this approach results in a significant improvement both in the compression ratio and image reconstruction quality, enabling SPI for high frame rate imaging or video applications.
Highlights
An optimal Hadamard basis for any super low sampling, and it can be deterministically described by mathematics
Numerical simulations demonstrate that the TV ordered Hadamard basis outperforms the CC order and other optimized Hadamard basis matrices as well as the Gaussian matrix in image reconstruction at super low sampling both for sparse images and natural images with regards to RMSE, PSNR and Structure similarity index (SSIM)
TVAL3 is the acronym of Total Variation minimization by Augmented Lagrangian and Alternating Direction Algorithms[18]
Summary
Our goal is to produce a new order Hadamard basis based on the normal-order Hadamard matrix so that any truncation of these mask sequences will provide an optimal reconstruction
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