Pseudo complementary measurement for traditional single-pixel cameras

doi:10.1088/1674-1056/abb22b

Abstract

A traditional single-pixel camera needs a large number of measurements to reconstruct the object with compressive sensing computation. Compared with the 1/0 matrices in classical measurement, the 1/−1 matrices in the complementary measurement has better property for reconstruction computation and returns better reconstruction results. However, each row of the 1/−1 matrices needs two measurements with the traditional single-pixel camera which results into double measurements compared with the 1/0 matrices. In this paper, we consider the pseudo complementary measurement which only takes the same amount of measurements with the row number of some properly designed 1/0 matrix to compute the total luminous flux of the objective and derives the measurement data of the corresponding 1/−1 matrix in a mathematical way. The numerical simulation and experimental result show that the pseudo complementary measurement is an efficient tool for the traditional single-pixel camera imaging under low measurement rate, which can combine the advantages of the classical and complementary measurements and significantly improve the peak signal-to-noise ratio.

Keywords: computational imaging single-pixel camera

Received: 25 May 2020
Revised: 08 July 2020
Accepted manuscript online: 25 August 2020

Fund: the National Key Research and Development Program of China (Grant No. 2018YFB0504302), the Youth Innovation Promotion Association of Chinese Academy of Sciences, and the National Natural Science Foundation of China (Grant Nos. 11701545, 11971466, and 11991021).

Corresponding Authors: ^†Corresponding author. E-mail: yaoxuri@nssc.ac.cn

Cite this article:

Qian Dong(董乾), Xu-Ri Yao(姚旭日), Xin Liu(刘歆), Bing Liu(刘冰), and Guang-Jie Zhai(翟光杰)$ Pseudo complementary measurement for traditional single-pixel cameras 2020 Chin. Phys. B 29 114202

Fig. 1.

Single-pixel camera.

Fig. 2.

The reconstruction quality versus sampling rate of different matrices for head phantom picture. In (b), the “random”, “toeplitz” and “hadamard” mean the random, Toeplitz and Hadamard matrices, respectively; the “1/0” and “1/−1” mean the 1/0 and 1/−1 matrices, respectively. The “hadamard−1/0” matrix is made with the 1 part of the corresponding Hadamard matrix. The sampling rates are taken 0.1, 0.2, 0.3, …, 1.

Fig. 3.

The components in the 2048th row of A^T A of different matrices, where A ∈ ℝ^{1228 × 4096}.

Fig. 4.

Peak signal-to-noise ratio (PSNR) vs measurement rate of different measurements (matrices), noiseless case. The legends are the same as the ones in Fig. 2. The measurement rates are taken as 0.1, 0.2, 0.3, …, 1.

Algorithm 1:

Matrix generation based on Assumptions 1 and 2

Fig. 5.

The flow chart based on Algorithm 1 and Lemma 3.

Fig. 6.

The components in the 1st row of A^T A of the matrices. The dimension of A is listed in the sub-figures. The “new−1/0” matrix is designed by Algorithm 1 and Lemma 3, and the “new−1/−1 matrix” is computed based on Eq. (4).

Fig. 7.

PSNR vs measurement rate with the pseudo complementary measurement. The “new−1/−1” matrix is generated by Algorithm 1 and the other legends are the same as the ones in Fig. 4. The measurement rates are taken as 0.1, 0.2, 0.3, …, 1.

Table 1.

The reconstructed PSNR of the head phantom in Fig. 1(a).

Fig. 8.

The reconstructed image of the head phantom in Fig. 2(a). Here the measurement rate is 0.3, and σ is the standard deviation of the noise. The “new 1/−1” matrix is generated by Algorithm 1; the “rand.”, “toep.” and “hada.” mean the random, Toeplitz and Hadamard matrix respectively; the “1/0” and “1/−1” mean the 1/0 and 1/−1 matrices, respectively.

Fig. 9.

The original image in the experiment.

Fig. 10.

The reconstructed image of Fig. 9. Here the measurement rate is 0.3. The “new 1/−1” matrix is generated by Algorithm 1; the “rand.”, “toep.” and “hada.” mean the random, Toeplitz and Hadamard matrix respectively; the “1/0” and “1/−1” mean the 1/0 and 1/−1 matrices, respectively.

Table 2.

The reconstructed PSNR of Fig. 2(a).

[1]	Candès E J, Romberg J, Tao T 2006 IEEE Trans. Inform. Theory 52 489 DOI: 10.1109/TIT.2005.862083
[2]	Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289 DOI: 10.1109/TIT.2006.871582
[3]	Candès E J 2006 Proceedings of the International Congress of Mathematicians Madrid Spain 3 1433 DOI: 10.4171/022-3/69
[4]	Candès E J 2008 Comptes Rendus Mathematique 346 589 DOI: 10.1016/j.crma.2008.03.014
[5]	Romberg J 2008 IEEE Signal Process. Magaz. 25 14 DOI: 10.1109/MSP.2007.914729
[6]	Takhar D, Laska J, Wakin M B, Duarte M F, Baron D, Sarvotham S, Kelly K, Baraniuk R G 2006 IS&T/SPIE Computational Imaging IV 6065 606509 DOI: 10.1117/12.659602
[7]	Duarte M F, Davenport M A, Takbar D, Laska J N, Sun T, Kelly K F, Baraniuk R G 2008 IEEE Signal Process. Magaz. 25 83 DOI: 10.1109/MSP.2007.914730
[8]	Chan W L, Charan K, Takhar D, Kelly K F, Baraniuk R G, Mittleman D M 2008 Appl. Phys. Lett. 93 121105 DOI: 10.1063/1.2989126
[9]	Radwell N, Mitchell K J, Gibson G M, Edgar M P, Bowman R, Padgett M J 2014 Optica 1 285 DOI: 10.1364/OPTICA.1.000285
[10]	Edgar M P, Gibson G M, Bowman R W, Sun B, Radwell N, Mitchell K J, Welsh S S, Padgett M J 2015 Sci. Rep. 5 srep10669 DOI: 10.1038/srep10669
[11]	Howland G A, Dixon P B, Howell J C 2011 Appl. Opt. 50 5917 DOI: 10.1364/AO.50.005917
[12]	Sun M, Edgar M, Gibson G, Sun B, Radwell N, Lamb R N, Padgett M J 2016 Nat. Commun. 7 12010 DOI: 10.1038/ncomms12010
[13]	Li F, Chen H, Pediredla A, Yeh C, He K, Veeraraghavan A, Cossairt O 2017 Opt. Express 25 31096 DOI: 10.1364/OE.25.031096
[14]	Studer V, Bobin J, Chahid M, Mousavi H S, Candès J, Dahan M 2012 Proc. Natl. Acad. Sci. USA 109 E1679 DOI: 10.1073/pnas.1119511109
[15]	August Y, Vachman C, Rivenson Y, Stern A 2013 Appl. Opt. 52 D46 DOI: 10.1364/AO.52.000D46
[16]	Arce G R, Brady D J, Carin L, Arguello H, Kittle D S 2014 IEEE Signal Process. Magaz. 31 105 DOI: 10.1109/MSP.2013.2278763
[17]	Liu X, Yu W, Yao X, Dai B, Li L, Wang C, Zhai G 2016 Opt. Commun. 365 173 DOI: 10.1016/j.optcom.2015.12.020
[18]	Wang C, Liu X, Yu W, Yao X, Zheng F, Dong Q, Lan R, Sun Z, Zhai G 2017 Chin. Phys. Lett. 34 104203 DOI: 10.1088/0256-307X/34/10/104203
[19]	Gong W, Han S 2012 Phys. Lett. A 376 1519 DOI: 10.1016/j.physleta.2012.03.027
[20]	Yao X, Li L, Liu X, Yu W, Zhai G 2015 Chin. Phys. B 24 044203 DOI: 10.1088/1674-1056/24/4/044203
[21]	Wang P, Li W, Wang C, Bo Z, Gong W 2018 Chin. Phys. B 27 074202 DOI: 10.1088/1674-1056/27/7/074202
[22]	Yu W, Liu X, Yao X, Wang C, Zhai Y, Zhai G 2014 Sci. Rep. 4 5834 DOI: 10.1038/srep05834
[23]	Ferri F, Magatti D, Lugiato L A, Gatti A 2010 Phys. Rev. Lett. 104 253603 DOI: 10.1103/PhysRevLett.104.253603
[24]	Sun B, Welsh S S, Edgar M P, Shapiro J H, Padgett M J 2012 Opt. Express 20 16892 DOI: 10.1364/OE.20.016892
[25]	Soldevila F, Clemente P, Tajahuerce E, Uribe-Patarroyo N, Andrès P, Lancis J 2016 Sci. Rep. 6 29181 DOI: 10.1038/srep29181
[26]	Bian L, Suo J, Dai Q, Chen F 2018 J. Opt. Soc. Am. A 35 78 DOI: 10.1364/JOSAA.35.000078
[27]	Zhang G, Jiao S, Xu X, Wang L 2010 IEEE International Conference on Information and Automation (ICIA) 455 DOI: 10.1109/ICINFA.2010.5512379
[28]	Do T T, Tran T D, Gan L 2008 IEEE International Conference on Acoustics, Speech and Signal Processing 3369 DOI: 10.1109/ICIP.2010.5652780
[29]	Monajemi H, Jafarpour S, Gavish M, Collaboration S C, Donoho D L 2013 Proc. Natl. Acad. Sci. USA 110 1181 DOI: 10.1073/pnas.1219540110
[30]	Tsaig Y, Donoho D L 2006 Signal Process. 86 549 DOI: 10.1016/j.sigpro.2005.05.029
[31]	Bajwa W U, Haupt J D, Raz G M, Wright S J, Nowak R D 2007 IEEE/SP 14th Workshop on Statistical Signal Processing 294 DOI: 10.1109/SSP.2007.4301266
[32]	Rauhut H arXiv:0902.4394 [cs.IT]
[33]	Sebert F, Zou Y, Ying L 2008 IEEE ITAB International Conference on Information Technology and Applications in Biomedicine 47 DOI: 10.1109/ITAB.2008.4570587
[34]	Li C, Yin W, Jiang H, Zhang Y 2013 Comput. Optim. Appl. 56 507 DOI: 10.1007/s10589-013-9576-1

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