Abstract

Modern cameras typically use an array of millions of detector pixels to capture images. By contrast, single-pixel cameras use a sequence of mask patterns to filter the scene along with the corresponding measurements of the transmitted intensity which is recorded using a single-pixel detector. This review considers the development of single-pixel cameras from the seminal work of Duarte et al. up to the present state of the art. We cover the variety of hardware configurations, design of mask patterns and the associated reconstruction algorithms, many of which relate to the field of compressed sensing and, more recently, machine learning. Overall, single-pixel cameras lend themselves to imaging at non-visible wavelengths and with precise timing or depth resolution. We discuss the suitability of single-pixel cameras for different application areas, including infrared imaging and 3D situation awareness for autonomous vehicles.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (1)

2019 (4)

S. Jiao, J. Feng, Y. Gao, T. Lei, Z. Xie, and X. Yuan, “Optical machine learning with incoherent light and a single-pixel detector,” Opt. Lett. 44(21), 5186–5189 (2019).
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N. Radwell, S. D. Johnson, M. P. Edgar, C. F. Higham, R. Murray-Smith, and M. J. Padgett, “Deep learning optimized single-pixel lidar,” Appl. Phys. Lett. 115(23), 231101 (2019).
[Crossref]

M.-J. Sun and J.-M. Zhang, “Single-pixel imaging and its application in three-dimensional reconstruction: a brief review,” Sensors 19(3), 732 (2019).
[Crossref]

G. Barbastathis, A. Ozcan, and G. Situ, “On the use of deep learning for computational imaging,” Optica 6(8), 921–943 (2019).
[Crossref]

2018 (6)

K. Pieper, A. Bergmann, R. Dengler, and C. Rockstuhl, “Using a pseudo-thermal light source to teach spatial coherence,” Eur. J. Phys. 39(4), 045303 (2018).
[Crossref]

Z.-H. Xu, W. Chen, J. Penuelas, M. Padgett, and M.-J. Sun, “1000 fps computational ghost imaging using LED-based structured illumination,” Opt. Express 26(3), 2427–2434 (2018).
[Crossref]

C. F. Higham, R. Murray-Smith, M. J. Padgett, and M. P. Edgar, “Deep learning for real-time single-pixel video,” Sci. Rep. 8(1), 2369 (2018).
[Crossref]

A.-X. Zhang, Y.-H. He, L.-A. Wu, L.-M. Chen, and B.-B. Wang, “Tabletop x-ray ghost imaging with ultra-low radiation,” Optica 5(4), 374–377 (2018).
[Crossref]

T. Shimobaba, Y. Endo, T. Nishitsuji, T. Takahashi, Y. Nagahama, S. Hasegawa, M. Sano, R. Hirayama, T. Kakue, A. Shiraki, and T. Ito, “Computational ghost imaging using deep learning,” Opt. Commun. 413, 147–151 (2018).
[Crossref]

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost imaging based on deep learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

2017 (4)

2016 (6)

M.-J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref]

C. A. Metzler, A. Maleki, and R. G. Baraniuk, “From denoising to compressed sensing,” IEEE Trans. Inf. Theory 62(9), 5117–5144 (2016).
[Crossref]

R. I. Khakimov, B. M. Henson, D. K. Shin, S. S. Hodgman, R. G. Dall, K. G. H. Baldwin, and A. G. Truscott, “Ghost imaging with atoms,” Nature 540(7631), 100–103 (2016).
[Crossref]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard X rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

S. M. Hornett, R. I. Stantchev, M. Z. Vardaki, C. Beckerleg, and E. Hendry, “Subwavelength terahertz imaging of graphene photoconductivity,” Nano Lett. 16(11), 7019–7024 (2016).
[Crossref]

2015 (4)

W.-K. Yu, X.-F. Liu, X.-R. Yao, C. Wang, Y. Zhai, and G.-J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4(1), 5834 (2015).
[Crossref]

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5(1), 10669 (2015).
[Crossref]

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6(1), 6225 (2015).
[Crossref]

R. S. Aspden, N. R. Gemmell, P. A. Morris, D. S. Tasca, L. Mertens, M. G. Tanner, R. A. Kirkwood, A. Ruggeri, A. Tosi, R. W. Boyd, G. S. Buller, R. H. Hadfield, and M. J. Padgett, “Photon-sparse microscopy: visible light imaging using infrared illumination,” Optica 2(12), 1049–1052 (2015).
[Crossref]

2014 (3)

2013 (3)

2012 (3)

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proc. Natl. Acad. Sci. 109(26), E1679–E1687 (2012).
[Crossref]

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20(15), 16892–16901 (2012).
[Crossref]

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inf. Process. 11(4), 949–993 (2012).
[Crossref]

2011 (2)

2010 (3)

F. Ferri, D. Magatti, L. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref]

M. A. Davenport, P. T. Boufounos, M. B. Wakin, and R. G. Baraniuk, “Signal processing with compressive measurements,” IEEE J. Sel. Topics Signal Process. 4(2), 445–460 (2010).
[Crossref]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photonics 2(4), 405–450 (2010).
[Crossref]

2009 (2)

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

2008 (6)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
[Crossref]

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008).
[Crossref]

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93(12), 121105 (2008).
[Crossref]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

N. Lazaros, G. C. Sirakoulis, and A. Gasteratos, “Review of stereo vision algorithms: from software to hardware,” Int. J. Optomechatronics 2(4), 435–462 (2008).
[Crossref]

2007 (2)

Y. Y. Schechner, S. K. Nayar, and P. N. Belhumeur, “Multiplexing for optimal lighting,” IEEE Trans. Pattern Anal. Mach. Intell. 29(8), 1339–1354 (2007).
[Crossref]

E. Candès and J. Romberg, “Sparsity and incoherence in compressive sampling,” Inverse Prob. 23(3), 969–985 (2007).
[Crossref]

2006 (4)

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[Crossref]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Timeline of developments in single-pixel imaging. Publications are shown by year and highlight the modulation technology and sampling scheme used. It is interesting to note that systems based on a structured detection approach, and employ sampling schemes such as compressive sensing (CS) or machine learning (ML), are often termed single-pixel cameras, whereas those based on structured illumination are often referred to as computational ghost imaging. The following references are shown: Sen 2005 [6], Candès 2006 [4], Candès 2007 [19], Duarte 2008 [5], Howland 2011 [20], Howland 2013 [21], Shrekenhamer 2013 [14], Yu 2014 [17], Hornett 2016 [15], Stantchev 2017 [22], Higham 2018 [23], Gatti 2004 [24], Valencia 2005 [25], Shapiro 2008 [26], Katz 2009 [27], Bromberg 2009 [28], Ferri 2010 [29], Sun 2013 [30], Zhang 2015 [31], Yu 2016 [11], Xu 2018 [32] and Radwell 2019 [33].
Fig. 2.
Fig. 2. Structured detection setup. a) A digital micromirror device (DMD) can be used to spatially filter light by selectively redirecting parts of an incident light beam at $\pm 24^\circ$ to the normal, corresponding to the individual DMD micromirrors being in the “on” or “off” state respectively. An object is flood-illuminated and imaged onto the DMD, where a sequence of binary patterns displayed on the DMD can be used to mask, or filter, the image. A single photodetector is used to measure the total filtered intensity for each mask pattern, allowing an image of the object to be reconstructed. b) Each pattern in the sequence is then multiplied by the corresponding single-pixel intensity measurement to give a set of weighted patterns that can be summed to reconstruct the image.
Fig. 3.
Fig. 3. Structured illumination with time-of-flight. a) In an alternative configuration, the DMD is used to project a sequence of light patterns onto a scene and the single-pixel detector measures the total back scattered intensity. For both structured illumination and structured detection a pulsed laser can be used as the illumination source to perform temporal resolution measurements using a single-pixel detector (as shown here). Recording the temporal form of the back scattered light provides a measure of the distance travelled by the light and hence depth of the scene. b) Similar to the structured detection scheme, the sequence of projected patterns and the corresponding intensity measurements allows an image to be reconstructed. In the case where a pulsed laser is used, the additional time-of-flight information from the broadened back scattered pulse allows a depth map of the scene to be constructed.
Fig. 4.
Fig. 4. A comparison of the patterns used for single-pixel imaging to reconstruct a $16\times 16$ image. The random binary patterns will require a greater number of measurements to reconstruct an image with high accuracy. Examples are shown of an image ($128\times 128$) with the number of samples equal to the number of pixels ($N$), and also for 10 and 100 times the number of pixels. Patterns were measured with a differential measurement using a 50% split in the binary selection. The Hadamard patterns and Fourier patterns are orthogonal and fully sample the image, a noiseless sampling will reproduce the ground truth image with $N$ and $4\times N$ patterns respectively.
Fig. 5.
Fig. 5. The sampling frequencies for the Hadamard and Fourier sampling methods [67], based on a $128\times 128$ image. Reducing the number of patterns used to reconstruct the image produces a lower quality image, as shown by the $\mathit {PSNR}$ values for each image.
Fig. 6.
Fig. 6. An example of single-pixel imaging using deep-learning. a) The reconstruction from Hadamard sampling using a reduced number of patterns (4%). b) The reconstruction using a trained neural-network using a deep-learned patterns set. c) Examples of the deep-learned pattern sampling basis. The method applied has been presented in Higham et al. [23].

Equations (11)

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O ( x , y ) , M = 1 M m = 1 M S m P ( x , y ) , m
H 2 = [ 1 1 1 1 ] ,
H 2 k = [ H 2 k 1 H 2 k 1 H 2 k 1 H 2 k 1 ]
O = H S
M S E = 1 m n i = 0 m 1 j = 0 n 1 ( I GT ( i , j ) I ( i , j ) ) 2 .
P S N R = 10 log 10 ( M A X I GT 2 M S E ) .
P ( u , v ) = cos ( 2 π ( u x N + v y N ) + ϕ )
F ( u , v ) = ( D π D 0 ) i ( D 3 π / 2 D π / 2 )
R T V ( O ) = i = 1 N ( | d I i ( O ) d x | + | d I i ( O ) d y | )
R T C ( O ) = i = 1 N ( | d 2 I i ( O ) d x 2 | + | d 2 I i ( O ) d y 2 | )
C = χ 2 M ( O ) + λ R ( O )