Compressed sensing Fourier single pixel imaging algorithm based on joint discrete gradient and non-local self-similarity
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Compressed sensing Fourier single pixel imaging algorithm based on joint discrete gradient and non‑local self‑similarity priors Zhenyu Liang1 · Dabin Yu1 · Zhengdong Cheng1 · Xiang Zhai1 · Yangdi Hu1 Received: 19 March 2020 / Accepted: 31 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Fourier single-pixel imaging (FSI) has been proven capable of acquiring excellent image quality when is sampled the fully information in Fourier domain. However, when the sampling measurements is limited, image reconstruction by applying inverse Fourier transform algorithm would result in the severe ringing effect and the loss of image details. In this report, we propose a new algorithm for FSI reconstruction based on compressed sensing theory, which utilizes joint discrete gradient and non-local self-similarity priors, thus substantially using the prior knowledge of natural images in reconstruction process. Both the results of computational simulations and experiments demonstrate the efficacy of the proposed algorithm. Keywords Fourier single-pixel imaging · Compressed sensing · Nonlocal self-similarity regularization
1 Introduction Single-pixel imaging (SPI) (Duarte et al. 2008; Lamb 2010, Ma 2010; Pei et al. 2011) is an innovative computational imaging approach that allows one to capture an object scene using the single-pixel detector by measuring the correlation between the object and series of time-varying illumination patterns instead of the conventional 2-D imaging sensor. The illumination patterns are commonly generated by a spatial light modulator (SLM) or a digital micro-mirror device (DMD). The SPI architecture is essentially as same as ghost imaging (GI) architecture in optical sense (Gatti et al. 2004; Meyers et al. 2008; Shapiro 2008; Katz et al. 2009; Sun and Zhang 2019), and it is often considered to originate from GI. The object and the SLM are conjugated by the lens between them in both architectures. In terms of hardware complexity and industrial cost, SPI has some unique advantages in potential application prospects for the simplification and integration of future imaging systems, especially in the infrared (Radwell et al. 2014; Edgar et al. 2015; Tong et al. 2018) * Zhenyu Liang [email protected] 1
State Key Laboratory of Pulsed Power Laser Technology, National University of Defense Technology, Hefei 230037, China
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and terahertz band (Watts et al. 2013, 2014), where the pixel array sensor devices are immature and in three-dimensional imaging (Sun et al. 2016) that requires high sensitivity and resolution. With these features, the emergence of single-pixel imaging technology has brought new solutions to the problems of traditional imaging systems. Besides, SPI has been proven capable of applying in different fields such as multi-spectral imaging (Barducci et al. 2013; Jin et al. 2017), optical encryption (Clemente et al. 2010), etc. As a novel single-pixel imaging technique, Fourier single-pixel imag
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