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. 2018 Feb 5;8:2369. doi: 10.1038/s41598-018-20521-y

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Quantitative assessment of the reconstruction performance. Four different metrics have been used to assess the reconstruction performance (PSNR, peak signal-to-noise ratio (a), SSIM, structural similarity index (b), STD, standard deviation (c) and reconstruction rate (d)) using different reconstruction methods: compressive sensing l₁ minimisation using a pseudo-random basis (l_1rand), a Russian-Doll ordered Hadamard basis (l_1RD), an optimised order of the Hadamard basis (l_1OH); by performing a Fast Hadamard Transform when using the Russian-Doll ordered Hadamard basis (FHT_RD), the optimised order of the Hadamard basis (FHT_OH); as well as the novel methods proposed here employing deep learning (DL_OH and DL). In each case the three shaded bars depict different reconstruction resolutions 128 × 128 first column, 64 × 64 second column and 32 × 32 third column. In summary, we find that deep learning offers the best reconstruction quality, with an increase in the standard deviation at video rates.