A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging

Ming-Jie Sun,Matthew P Edgar,Ling-Tong Meng,Neal Radwell,Miles J Padgett

doi:10.1038/s41598-017-03725-6

Ming-Jie Sun, Matthew P Edgar + Show 3 more

Open Access

https://doi.org/10.1038/s41598-017-03725-6

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Journal: Scientific Reports	Publication Date: Jun 14, 2017
Citations: 213	License type: open-access

Affiliation: Beihang University, University of Glasgow

Abstract

Single-pixel imaging is an alternate imaging technique particularly well-suited to imaging modalities such as hyper-spectral imaging, depth mapping, 3D profiling. However, the single-pixel technique requires sequential measurements resulting in a trade-off between spatial resolution and acquisition time, limiting real-time video applications to relatively low resolutions. Compressed sensing techniques can be used to improve this trade-off. However, in this low resolution regime, conventional compressed sensing techniques have limited impact due to lack of sparsity in the datasets. Here we present an alternative compressed sensing method in which we optimize the measurement order of the Hadamard basis, such that at discretized increments we obtain complete sampling for different spatial resolutions. In addition, this method uses deterministic acquisition, rather than the randomized sampling used in conventional compressed sensing. This so-called ‘Russian Dolls’ ordering also benefits from minimal computational overhead for image reconstruction. We find that this compressive approach performs as well as other compressive sensing techniques with greatly simplified post processing, resulting in significantly faster image reconstruction. Therefore, the proposed method may be useful for single-pixel imaging in the low resolution, high-frame rate regime, or video-rate acquisition.

Highlights

Imaging is one of the most ubiquitous and useful techniques for gathering information
Alternative compressive approaches have been explored for single-pixel video, such as evolutionary compressive sensing (ECS)[5, 11, 25], where the measured patterns are chosen based upon a priori knowledge of the scene, taken from the previous frame and requires no lengthy post-processing
We demonstrate an optimized ordering of the Hadamard basis, where we use the properties of general scenes to order the patterns such that any truncation of that pattern sequence will provide an optimal reconstruction

Summary

Introduction

Imaging is one of the most ubiquitous and useful techniques for gathering information. Improvements can be made by sampling a scene with patterns forming an orthogonal basis set, allowing, in principle, a perfect reconstruction of an N pixel image with N measurements[17, 18].

Results

Conclusion