Abstract

In nature, the compound eyes of arthropods have evolved towards a wide field of view (FOV), infinite depth of field and fast motion detection. However, compound eyes have inferior resolution when compared with the camera-type eyes of vertebrates, owing to inherent structural constraints such as the optical performance and the number of ommatidia. For resolution improvements, in this paper, we propose COMPUtational compound EYE (COMPU-EYE), a new design that increases acceptance angles and uses a modern digital signal processing (DSP) technique. We demonstrate that the proposed COMPU-EYE provides at least a four-fold improvement in resolution.

© 2016 Optical Society of America

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Corrections

29 January 2016: A correction was made to the author listing.


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References

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2015 (1)

2014 (2)

J. Fang, J. Li, Y. Shen, H. Li, and S. Li, “Super-Resolution Compressed Sensing: An Iterative Reweighted Algotirhm for Joint Parameter Learning and Sparse Signal Recovery,” IEEE Signal Process. Lett. 21(6), 761–765 (2014).
[Crossref]

C. Shi and F. Xu, “Post-digital image processing based on microlens array,” Proc. SPIE 92701K, 9270 (2014).

2013 (5)

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

A. Borst and J. Plett, “Optical devices: Seeing the world through an insect’s eyes,” Nature 497(7447), 47–48 (2013).
[Crossref] [PubMed]

D. Floreano, R. Pericet-Camara, S. Viollet, F. Ruffier, A. Brückner, R. Leitel, W. Buss, M. Menouni, F. Expert, R. Juston, M. K. Dobrzynski, G. L’Eplattenier, F. Recktenwald, H. A. Mallot, and N. Franceschini, “Miniature curved artificial compound eyes,” Proc. Natl. Acad. Sci. U.S.A. 110(23), 9267–9272 (2013).
[Crossref] [PubMed]

H. Zhang, L. Li, D. L. McCray, S. Scheiding, N. J. Naples, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann, and A. Y. Yi, “Development of a low cost high precision three-layer 3D artificial compound eye,” Opt. Express 21(19), 22232–22245 (2013).
[Crossref] [PubMed]

J. Oliver, W.-B. Lee, and H.-N. Lee, “Filters with random transmittance for improving resolution in filter-array-based spectrometers,” Opt. Express 21(4), 3969–3989 (2013).
[Crossref] [PubMed]

2012 (3)

2011 (4)

A. Chambolle and T. Pock, “A first-order primal-dual algorithm for convex problems with applications to imaging,” J. Math. Imaging Vis. 40(1), 120–145 (2011).
[Crossref]

E. J. Candès, Y. C. Eldar, D. Needell, and P. Randall, “Compressed sensing with coherent and redundant dictionaries,” Appl. Comput. Harmon. Anal. 31(1), 59–73 (2011).
[Crossref]

J. Yang and Y. Zhang, “Alternating direction algorithms for l1-problems in compressive sensing,” SIAM J. Sci. Comput. 33(1), 250–278 (2011).
[Crossref]

P. T. Gonzalez-Bellido, T. J. Wardill, and M. Juusola, “Compound eyes and retinal information processing in miniature dipteran species match their specific ecological demands,” Proc. Natl. Acad. Sci. U.S.A. 108(10), 4224–4229 (2011).
[Crossref] [PubMed]

2010 (3)

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Found. Trends Mach. Learn. 3(1), 1–122 (2010).
[Crossref]

D. P. Pulsifer, A. Lakhtakia, R. J. Martín-Palma, and C. G. Pantano, “Mass fabrication technique for polymeric replicas of arrays of insect corneas,” Bioinspir. Biomim. 5(3), 036001 (2010).
[Crossref] [PubMed]

H. Rauhut, “Compressive sensing and structured random matrices,” Theor. Found. Num. Meth. Sparse Recov. 9, 1–92 (2010).

2009 (1)

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

2008 (3)

J. Duparré, F. Wippermann, P. Dannberg, and A. Bräuer, “Artificial compound eye zoom camera,” Bioinspir. Biomim. 3(4), 046008 (2008).
[Crossref] [PubMed]

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454(7205), 748–753 (2008).
[Crossref] [PubMed]

W. Wang, M. J. Wainwright, and K. Ramchandran, “Information-theoretic limits on sparse signal recovery: Dense versus sparse measurement matrices,” IEEE Trans. Inf. Theory 56(6), 2969–2979 (2008).

2007 (1)

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
[Crossref]

2006 (8)

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

A. Brückner, J. Duparré, A. Bräuer, and A. Tünnermann, “Artificial compound eye applying hyperacuity,” Opt. Express 14(25), 12076–12084 (2006).
[Crossref] [PubMed]

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

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation,” IEEE T. Signal Process. 54(11), 4311–4322 (2006).

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

E. J. Candès and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[Crossref]

D. L. Donoho, M. Elad, and V. Temlyakov, “Stable recovery of sparse overcomplete representations in the presence of noise,” IEEE Trans. Inf. Theory 52(1), 6–18 (2006).
[Crossref]

K. H. Jeong, J. Kim, and L. P. Lee, “Biologically Inspired Artificial Compound Eyes,” Science 312(5773), 557–561 (2006).
[Crossref] [PubMed]

2004 (2)

2001 (1)

1997 (1)

M. F. Land, “Visual Acuity in Insects,” Annu. Rev. Entomol. 42(1), 147–177 (1997).
[Crossref] [PubMed]

1992 (1)

E. Watson, R. Muse, and F. Blommel, “Aliasing and blurring in microscaned imagery,” Proc. SPIE 1689, 242–250 (1992).
[Crossref]

1989 (1)

D.-E. Nilson, “Vision optics and evolution,” Bioscience 39(5), 298–307 (1989).
[Crossref]

1988 (1)

M. F. Land, “The optics of animal eyes,” Contemp. Phys. 29(5), 435–455 (1988).
[Crossref]

1952 (1)

H. B. Barlow, “The size of ommatidia in apposition eyes,” J. Exp. Biol. 29, 667–674 (1952).

Aharon, M.

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation,” IEEE T. Signal Process. 54(11), 4311–4322 (2006).

Baraniuk, R.

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24(4), 118–121 (2007).
[Crossref]

Barlow, H. B.

H. B. Barlow, “The size of ommatidia in apposition eyes,” J. Exp. Biol. 29, 667–674 (1952).

Beck, A.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

Blommel, F.

E. Watson, R. Muse, and F. Blommel, “Aliasing and blurring in microscaned imagery,” Proc. SPIE 1689, 242–250 (1992).
[Crossref]

Borst, A.

A. Borst and J. Plett, “Optical devices: Seeing the world through an insect’s eyes,” Nature 497(7447), 47–48 (2013).
[Crossref] [PubMed]

Boyd, S.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Found. Trends Mach. Learn. 3(1), 1–122 (2010).
[Crossref]

Bräuer, A.

J. Duparré, F. Wippermann, P. Dannberg, and A. Bräuer, “Artificial compound eye zoom camera,” Bioinspir. Biomim. 3(4), 046008 (2008).
[Crossref] [PubMed]

A. Brückner, J. Duparré, A. Bräuer, and A. Tünnermann, “Artificial compound eye applying hyperacuity,” Opt. Express 14(25), 12076–12084 (2006).
[Crossref] [PubMed]

Brückner, A.

D. Floreano, R. Pericet-Camara, S. Viollet, F. Ruffier, A. Brückner, R. Leitel, W. Buss, M. Menouni, F. Expert, R. Juston, M. K. Dobrzynski, G. L’Eplattenier, F. Recktenwald, H. A. Mallot, and N. Franceschini, “Miniature curved artificial compound eyes,” Proc. Natl. Acad. Sci. U.S.A. 110(23), 9267–9272 (2013).
[Crossref] [PubMed]

A. Brückner, J. Duparré, A. Bräuer, and A. Tünnermann, “Artificial compound eye applying hyperacuity,” Opt. Express 14(25), 12076–12084 (2006).
[Crossref] [PubMed]

Bruckstein, A.

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation,” IEEE T. Signal Process. 54(11), 4311–4322 (2006).

Buss, W.

D. Floreano, R. Pericet-Camara, S. Viollet, F. Ruffier, A. Brückner, R. Leitel, W. Buss, M. Menouni, F. Expert, R. Juston, M. K. Dobrzynski, G. L’Eplattenier, F. Recktenwald, H. A. Mallot, and N. Franceschini, “Miniature curved artificial compound eyes,” Proc. Natl. Acad. Sci. U.S.A. 110(23), 9267–9272 (2013).
[Crossref] [PubMed]

Candès, E. J.

E. J. Candès, Y. C. Eldar, D. Needell, and P. Randall, “Compressed sensing with coherent and redundant dictionaries,” Appl. Comput. Harmon. Anal. 31(1), 59–73 (2011).
[Crossref]

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

E. J. Candès and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[Crossref]

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

E. J. Candès, “Compressive sampling,” Proc. Int. Congr. Mathematicians3, 1433–1452 (2006).

Chambolle, A.

A. Chambolle and T. Pock, “A first-order primal-dual algorithm for convex problems with applications to imaging,” J. Math. Imaging Vis. 40(1), 120–145 (2011).
[Crossref]

Chartrand, R.

R. Chartrand, “Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data,” in IEEE International Symposium on Biomedical Imaging (IEEE, 2009), pp. 262–265.

Chen, F.

Choi, K. J.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

Choi, W.

Choi, W. M.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454(7205), 748–753 (2008).
[Crossref] [PubMed]

Chu, E.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Found. Trends Mach. Learn. 3(1), 1–122 (2010).
[Crossref]

Chung, E.

Crozier, K. B.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

Dannberg, P.

J. Duparré, F. Wippermann, P. Dannberg, and A. Bräuer, “Artificial compound eye zoom camera,” Bioinspir. Biomim. 3(4), 046008 (2008).
[Crossref] [PubMed]

Dobrzynski, M. K.

D. Floreano, R. Pericet-Camara, S. Viollet, F. Ruffier, A. Brückner, R. Leitel, W. Buss, M. Menouni, F. Expert, R. Juston, M. K. Dobrzynski, G. L’Eplattenier, F. Recktenwald, H. A. Mallot, and N. Franceschini, “Miniature curved artificial compound eyes,” Proc. Natl. Acad. Sci. U.S.A. 110(23), 9267–9272 (2013).
[Crossref] [PubMed]

Donoho, D. L.

D. L. Donoho, M. Elad, and V. Temlyakov, “Stable recovery of sparse overcomplete representations in the presence of noise,” IEEE Trans. Inf. Theory 52(1), 6–18 (2006).
[Crossref]

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

Duparré, J.

J. Duparré, F. Wippermann, P. Dannberg, and A. Bräuer, “Artificial compound eye zoom camera,” Bioinspir. Biomim. 3(4), 046008 (2008).
[Crossref] [PubMed]

A. Brückner, J. Duparré, A. Bräuer, and A. Tünnermann, “Artificial compound eye applying hyperacuity,” Opt. Express 14(25), 12076–12084 (2006).
[Crossref] [PubMed]

Eberhardt, R.

Eckstein, J.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Found. Trends Mach. Learn. 3(1), 1–122 (2010).
[Crossref]

Elad, M.

D. L. Donoho, M. Elad, and V. Temlyakov, “Stable recovery of sparse overcomplete representations in the presence of noise,” IEEE Trans. Inf. Theory 52(1), 6–18 (2006).
[Crossref]

M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation,” IEEE T. Signal Process. 54(11), 4311–4322 (2006).

Eldar, Y. C.

E. J. Candès, Y. C. Eldar, D. Needell, and P. Randall, “Compressed sensing with coherent and redundant dictionaries,” Appl. Comput. Harmon. Anal. 31(1), 59–73 (2011).
[Crossref]

Expert, F.

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Figures (8)

Fig. 1
Fig. 1 (a) Illustration of the hemispherical compound eye. (b) Structure of conventional compound eye with key parameters: the acceptance angle ( Δ φ ) and focal length (f) for each ommatidium, the interommatidial angle (), the diameter of a photodiode (d) and the radius of curvature of the compound eye (R) and of an individual microlens (r). (c) Compound eye imaging system
Fig. 2
Fig. 2 Imaging systems of a conventional compound eye and the proposed COMPU-EYE (a) The conventional compound eye consists of 8 × 8 ommatidia with Δϕ = 1.5° and Δφ = 1.5°. (b) COMPU-EYE consists of 8 × 8 ommatidia with Δϕ = 1.5° and Δφ = 8° as well as a DSP algorithm.
Fig. 3
Fig. 3 Effects of acceptance angles for the conventional compound eye (top row) and COMPU-EYE (bottom row) (a)(d) Ommatidial receptive fields overlapped with the object image. (b)(e) Number of observing ommatidia corresponding to pixels in the 8th row. (c)(f) Graphical representations of the measurement matrices.
Fig. 4
Fig. 4 NMSE against acceptance angle where M = 8 × 8 ommatidia with Δϕ = 1.5° and N = 16 × 16 pixels.
Fig. 5
Fig. 5 For M = 80 × 80 and Δϕ = 2.25°, (a) Output image of the conventional compound eye with Δφ = 2.25° (b) Image recovered by COMPU-EYE with Δφ = 60°. For M = 120 × 120 and Δϕ = 1.5°. (c) Output image of the conventional compound eye with Δφ = 1.5° (d) Image recovered by COMPU-EYE with Δφ = 60°.
Fig. 6
Fig. 6 For the compound eyes, M = 120 × 120 and Δϕ = 1.5°. (a) Object image of 8-bit grayscale image with 160 × 160 pixels (b) Output image of the conventional compound eye with Δφ = 1.5° and. (c) Image recovered by COMPU-EYE with Δφ = 60°.
Fig. 7
Fig. 7 Resolution test: (a) Conventional compound eye consisting of 80 × 80 ommatidia with Δφ = Δϕ = 2.25°. (b) COMPU-EYE consisting of 80 × 80 ommatidia with Δφ = 60° and Δϕ = 2.25°.
Fig. 8
Fig. 8 Depth test: Image recovered by COMPU-EYE consisting of 100 × 100 ommatidia with Δφ = 60° and Δϕ = 1.8°, where the dimension of the final object image is (a) 30 × 30 mm at 5 mm, (b) 60 × 60 mm at 10 mm, (c) 90 × 90 mm at 15 mm. The actual tiger picture is 30 × 30 mm.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

a i j = { 0 1 0 < a i j < 1 , , , j th pixel is invisible to i th ommatidium j th pixel is fully observed by i th ommatidium j th pixel is partially observed by i th ommatidium .
y = A x + n .
x ^ = arg min x x 0 subject to A x y 2 ε .
x ^ = arg min x x 1 subject to A x y 2 ε .

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