Abstract

A camera module employing spherical single-element lens imaging system (SSLIS) is introduced in this study. This type of imaging system can be used in compact digital cameras or mobile phone cameras, and it provides the advantages of simple design, reduced device bulkiness, and reduced manufacturing costs. When compared with conventional camera modules, our system produces radially variant blurred images, which can be satisfactorily restored by means of a polar domain deconvolution algorithm proposed in our previous study. In this study, we demonstrate an improved version of this algorithm that enables full-field-of-view (FOV) image restoration instead of the partial FOV restoration obtained via our previous algorithm. This improvement is realized by interpolating the upper and arc-shaped boundaries of the panoramic polar image such that the ringing artifacts around the center and four boundaries of the restored Cartesian image are greatly suppressed. The effectiveness of the improved algorithm is verified by image restoration of both computer simulated images and real-world scenes captured by the spherical single lens camera module. The quality of the restored image depends on the overall sparsity of all the point spread function (PSF) block Toeplitz with circulant blocks (BTCB) matrices used to restore a radially blurred image.

© 2012 OSA

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2011 (2)

Y. Zhang and T. Ueda, “Deblur of radially variant blurred image for single lens system,” IEEE J. Trans. Elect. Electron. Eng.6(S1), S7–S16 (2011).
[CrossRef]

Y. Zhang, I. Minema, and T. Ueda, “Analysis of radially restored images for spherical single lens cellphone camera,” IEEE Sens. J.11(11), 2834–2844 (2011).
[CrossRef]

2010 (2)

Y. Zhang and T. Ueda, “Field-dependent distortion coefficient and backward mapping for distortion correction of singlet lens cameras,” IEEE J. Trans. Elect. Electron. Eng.5(2), 203–210 (2010).
[CrossRef]

Y. Zhang and T. Ueda, “Design of a singlet lens and the corresponding aberration correction approaches for cell phone camera,” IEEE J. Trans. Elect. Electron. Eng.5(4), 474–485 (2010).
[CrossRef]

2005 (2)

W. Wang, J. Fang, and K. Varahramyan, “Compact variable-focusing microlens with integrated thermal actuator and sensor,” IEEE Photon. Technol. Lett.17(12), 2643–2645 (2005).
[CrossRef]

S. J. Reeves, “Fast image restoration without boundary artifacts,” IEEE Trans. Image Process.14(10), 1448–1453 (2005).
[CrossRef] [PubMed]

2004 (1)

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
[CrossRef]

1997 (1)

M. R. Banham and A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag.14(2), 24–41 (1997).
[CrossRef]

1996 (1)

J. G. Nagy, R. J. Plemmons, and T. C. Torgersen, “Iterative image restoration using approximate inverse preconditioning,” IEEE Trans. Image Process.5(7), 1151–1162 (1996).
[CrossRef] [PubMed]

1994 (1)

M. Hanke and J. Nagy, “Toeplitz approximate inverse preconditioner for banded Toeplitz matrices,” Numer. Alg.7(2), 183–199 (1994).
[CrossRef]

1993 (1)

R. H. Chan, J. G. Nagy, and R. J. Plemmons, “FFT-based preconditioners for Toeplitz-Block least squares problems,” SIAM J. Numer. Anal.30(6), 1740–1768 (1993).
[CrossRef]

1988 (1)

R. L. Lagendijk, J. Biemond, and D. E. Boekee, “Regularized iterative image restoration with ringing reduction,” IEEE Trans. Acoust. Speech36(12), 1874–1888 (1988).
[CrossRef]

1985 (1)

1980 (1)

Banham, M. R.

M. R. Banham and A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag.14(2), 24–41 (1997).
[CrossRef]

Biemond, J.

R. L. Lagendijk, J. Biemond, and D. E. Boekee, “Regularized iterative image restoration with ringing reduction,” IEEE Trans. Acoust. Speech36(12), 1874–1888 (1988).
[CrossRef]

Boekee, D. E.

R. L. Lagendijk, J. Biemond, and D. E. Boekee, “Regularized iterative image restoration with ringing reduction,” IEEE Trans. Acoust. Speech36(12), 1874–1888 (1988).
[CrossRef]

Chan, R. H.

R. H. Chan, J. G. Nagy, and R. J. Plemmons, “FFT-based preconditioners for Toeplitz-Block least squares problems,” SIAM J. Numer. Anal.30(6), 1740–1768 (1993).
[CrossRef]

Fang, J.

W. Wang, J. Fang, and K. Varahramyan, “Compact variable-focusing microlens with integrated thermal actuator and sensor,” IEEE Photon. Technol. Lett.17(12), 2643–2645 (2005).
[CrossRef]

Hanke, M.

M. Hanke and J. Nagy, “Toeplitz approximate inverse preconditioner for banded Toeplitz matrices,” Numer. Alg.7(2), 183–199 (1994).
[CrossRef]

Hendriks, B. H. W.

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
[CrossRef]

Hidaka, H.

Katsaggelos, A. K.

M. R. Banham and A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag.14(2), 24–41 (1997).
[CrossRef]

Koike, Y.

Kuiper, S.

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
[CrossRef]

Lagendijk, R. L.

R. L. Lagendijk, J. Biemond, and D. E. Boekee, “Regularized iterative image restoration with ringing reduction,” IEEE Trans. Acoust. Speech36(12), 1874–1888 (1988).
[CrossRef]

Minema, I.

Y. Zhang, I. Minema, and T. Ueda, “Analysis of radially restored images for spherical single lens cellphone camera,” IEEE Sens. J.11(11), 2834–2844 (2011).
[CrossRef]

Moore, D. T.

Nagy, J.

M. Hanke and J. Nagy, “Toeplitz approximate inverse preconditioner for banded Toeplitz matrices,” Numer. Alg.7(2), 183–199 (1994).
[CrossRef]

Nagy, J. G.

J. G. Nagy, R. J. Plemmons, and T. C. Torgersen, “Iterative image restoration using approximate inverse preconditioning,” IEEE Trans. Image Process.5(7), 1151–1162 (1996).
[CrossRef] [PubMed]

R. H. Chan, J. G. Nagy, and R. J. Plemmons, “FFT-based preconditioners for Toeplitz-Block least squares problems,” SIAM J. Numer. Anal.30(6), 1740–1768 (1993).
[CrossRef]

Ohtsuka, Y.

Plemmons, R. J.

J. G. Nagy, R. J. Plemmons, and T. C. Torgersen, “Iterative image restoration using approximate inverse preconditioning,” IEEE Trans. Image Process.5(7), 1151–1162 (1996).
[CrossRef] [PubMed]

R. H. Chan, J. G. Nagy, and R. J. Plemmons, “FFT-based preconditioners for Toeplitz-Block least squares problems,” SIAM J. Numer. Anal.30(6), 1740–1768 (1993).
[CrossRef]

Reeves, S. J.

S. J. Reeves, “Fast image restoration without boundary artifacts,” IEEE Trans. Image Process.14(10), 1448–1453 (2005).
[CrossRef] [PubMed]

Torgersen, T. C.

J. G. Nagy, R. J. Plemmons, and T. C. Torgersen, “Iterative image restoration using approximate inverse preconditioning,” IEEE Trans. Image Process.5(7), 1151–1162 (1996).
[CrossRef] [PubMed]

Ueda, T.

Y. Zhang and T. Ueda, “Deblur of radially variant blurred image for single lens system,” IEEE J. Trans. Elect. Electron. Eng.6(S1), S7–S16 (2011).
[CrossRef]

Y. Zhang, I. Minema, and T. Ueda, “Analysis of radially restored images for spherical single lens cellphone camera,” IEEE Sens. J.11(11), 2834–2844 (2011).
[CrossRef]

Y. Zhang and T. Ueda, “Field-dependent distortion coefficient and backward mapping for distortion correction of singlet lens cameras,” IEEE J. Trans. Elect. Electron. Eng.5(2), 203–210 (2010).
[CrossRef]

Y. Zhang and T. Ueda, “Design of a singlet lens and the corresponding aberration correction approaches for cell phone camera,” IEEE J. Trans. Elect. Electron. Eng.5(4), 474–485 (2010).
[CrossRef]

Varahramyan, K.

W. Wang, J. Fang, and K. Varahramyan, “Compact variable-focusing microlens with integrated thermal actuator and sensor,” IEEE Photon. Technol. Lett.17(12), 2643–2645 (2005).
[CrossRef]

Wang, W.

W. Wang, J. Fang, and K. Varahramyan, “Compact variable-focusing microlens with integrated thermal actuator and sensor,” IEEE Photon. Technol. Lett.17(12), 2643–2645 (2005).
[CrossRef]

Zhang, Y.

Y. Zhang and T. Ueda, “Deblur of radially variant blurred image for single lens system,” IEEE J. Trans. Elect. Electron. Eng.6(S1), S7–S16 (2011).
[CrossRef]

Y. Zhang, I. Minema, and T. Ueda, “Analysis of radially restored images for spherical single lens cellphone camera,” IEEE Sens. J.11(11), 2834–2844 (2011).
[CrossRef]

Y. Zhang and T. Ueda, “Field-dependent distortion coefficient and backward mapping for distortion correction of singlet lens cameras,” IEEE J. Trans. Elect. Electron. Eng.5(2), 203–210 (2010).
[CrossRef]

Y. Zhang and T. Ueda, “Design of a singlet lens and the corresponding aberration correction approaches for cell phone camera,” IEEE J. Trans. Elect. Electron. Eng.5(4), 474–485 (2010).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

S. Kuiper and B. H. W. Hendriks, “Variable-focus liquid lens for miniature cameras,” Appl. Phys. Lett.85(7), 1128–1130 (2004).
[CrossRef]

IEEE J. Trans. Elect. Electron. Eng. (3)

Y. Zhang and T. Ueda, “Field-dependent distortion coefficient and backward mapping for distortion correction of singlet lens cameras,” IEEE J. Trans. Elect. Electron. Eng.5(2), 203–210 (2010).
[CrossRef]

Y. Zhang and T. Ueda, “Design of a singlet lens and the corresponding aberration correction approaches for cell phone camera,” IEEE J. Trans. Elect. Electron. Eng.5(4), 474–485 (2010).
[CrossRef]

Y. Zhang and T. Ueda, “Deblur of radially variant blurred image for single lens system,” IEEE J. Trans. Elect. Electron. Eng.6(S1), S7–S16 (2011).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

W. Wang, J. Fang, and K. Varahramyan, “Compact variable-focusing microlens with integrated thermal actuator and sensor,” IEEE Photon. Technol. Lett.17(12), 2643–2645 (2005).
[CrossRef]

IEEE Sens. J. (1)

Y. Zhang, I. Minema, and T. Ueda, “Analysis of radially restored images for spherical single lens cellphone camera,” IEEE Sens. J.11(11), 2834–2844 (2011).
[CrossRef]

IEEE Signal Process. Mag. (1)

M. R. Banham and A. K. Katsaggelos, “Digital image restoration,” IEEE Signal Process. Mag.14(2), 24–41 (1997).
[CrossRef]

IEEE Trans. Acoust. Speech (1)

R. L. Lagendijk, J. Biemond, and D. E. Boekee, “Regularized iterative image restoration with ringing reduction,” IEEE Trans. Acoust. Speech36(12), 1874–1888 (1988).
[CrossRef]

IEEE Trans. Image Process. (2)

S. J. Reeves, “Fast image restoration without boundary artifacts,” IEEE Trans. Image Process.14(10), 1448–1453 (2005).
[CrossRef] [PubMed]

J. G. Nagy, R. J. Plemmons, and T. C. Torgersen, “Iterative image restoration using approximate inverse preconditioning,” IEEE Trans. Image Process.5(7), 1151–1162 (1996).
[CrossRef] [PubMed]

Numer. Alg. (1)

M. Hanke and J. Nagy, “Toeplitz approximate inverse preconditioner for banded Toeplitz matrices,” Numer. Alg.7(2), 183–199 (1994).
[CrossRef]

SIAM J. Numer. Anal. (1)

R. H. Chan, J. G. Nagy, and R. J. Plemmons, “FFT-based preconditioners for Toeplitz-Block least squares problems,” SIAM J. Numer. Anal.30(6), 1740–1768 (1993).
[CrossRef]

Other (1)

H. C. Andrews and B. R. Hunt, Digital Image Restoration (Prentice-Hall, 1977), Chap.6,7,8 and 9.

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