Abstract

The subject of interest is the superresolution of atmospheric-turbulence-degraded, short-exposure imagery, where superresolution refers to the removal of blur caused by a diffraction-limited optical system along with recovery of some object spatial-frequency components outside the optical passband. Photon-limited space object images are of particular interest. Two strategies based on multiple exposures are explored. The first is known as deconvolution from wave-front sensing, where estimates of the optical transfer function (OTF) associated with each exposure are derived from wave-front-sensor data. New multiframe superresolution algorithms are presented that are based on Bayesian maximum a posteriori and maximum-likelihood formulations. The second strategy is known as blind deconvolution, in which the OTF associated with each frame is unknown and must be estimated. A new multiframe blind deconvolution algorithm is presented that is based on a Bayesian maximum-likelihood formulation with strict constraints incorporated by using nonlinear reparameterizations. Quantitative simulation of imaging through atmospheric turbulence and wave-front sensing are used to demonstrate the superresolution performance of the algorithms.

© 1998 Optical Society of America

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1996 (1)

D. Kundur, D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Proc. Mag. 13, 43–64 (1996).
[CrossRef]

1995 (7)

B. R. Hunt, “Superresolution of images: algorithms, principles, performance,” Int. J. Imaging Syst. Technol. 6, 297–304 (1995).
[CrossRef]

E. Thiébaut, J.-M. Conan, “Strict a priori constraints for maximum-likelihood blind deconvolution,” J. Opt. Soc. Am. A 12, 485–492 (1995).
[CrossRef]

H.-M. Adorf, R. N. Hook, L. B. Lucy, “HST image restoration developments at the ST-ECF,” Int. J. Imaging Syst. Technol. 6, 339–349 (1995).
[CrossRef]

H.-M. Adorf, “Hubble Space Telescope image restoration in its fourth year,” Inverse Probl. 11, 639–653 (1995).
[CrossRef]

T. E. Bell, “Electronics and the stars,” IEEE Spectr. 32, 16–24 (1995).
[CrossRef]

P. J. Bones, C. R. Parker, B. L. Satherly, R. W. Watson, “Deconvolution and phase retrieval with use of zero sheets,” J. Opt. Soc. Am. A 12, 1842–1857 (1995).
[CrossRef]

M. C. Roggeman, B. L. Ellerbroek, T. A. Rhoadarmer, “Widening the effective field of view of adaptive-optics telescopes by deconvolution from wave-front sensing: average and signal-to-noise ratio performance,” Appl. Opt. 34, 1432–1444 (1995).
[CrossRef]

1994 (3)

F. Tsumuraya, N. Miura, N. Baba, “Iterative blind deconvolution method using Lucy’s algorithm,” Astron. Astrophys. 282, 699–708 (1994).

B. L. Satherly, P. J. Bones, “Zero tracks for blind deconvolution of blurred ensembles,” Appl. Opt. 33, 2197–2205 (1994).
[CrossRef]

L. A. Thompson, “Adaptive optics in astronomy,” Phys. Today 47, 24–31 (1994).
[CrossRef]

1993 (3)

1992 (2)

1989 (1)

B. L. K. Davey, R. G. Lane, R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353–356 (1989).
[CrossRef]

1988 (3)

1987 (1)

1986 (1)

1983 (1)

1975 (1)

T. G. Stockham, T. M. Cannon, R. B. Ingebretsen, “Blind deconvolution through digital signal processing,” Proc. IEEE 63, 678–692 (1975).
[CrossRef]

1974 (3)

K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short exposure images,” Astrophys. J. 193, L45–48 (1974).
[CrossRef]

R. W. Gerchberg, “Superresolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–759 (1974).
[CrossRef]

1972 (1)

1970 (1)

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

1969 (1)

Y. Biraud, “A new approach for increasing the resolving power by data processing,” Astron. Astrophys. 1, 124–127 (1969).

1968 (1)

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear filtering of multiplied and convolved signals,” Proc. IEEE 56, 1264–1291 (1968).
[CrossRef]

1966 (2)

Adorf, H.-M.

H.-M. Adorf, R. N. Hook, L. B. Lucy, “HST image restoration developments at the ST-ECF,” Int. J. Imaging Syst. Technol. 6, 339–349 (1995).
[CrossRef]

H.-M. Adorf, “Hubble Space Telescope image restoration in its fourth year,” Inverse Probl. 11, 639–653 (1995).
[CrossRef]

Andrews, H. C.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Angel, J. R. P.

E. K. Hege, J. R. P. Angel, M. Cheselka, M. Lloyd–Hart, “Simulation of aperture synthesis with the Large Binocular Telescope,” in Advanced Imaging Technologies and Commercial Applications, N. Clark, J. D. Gonglewski, eds., Proc. SPIE2566, 144–155 (1995).
[CrossRef]

Ayers, G. R.

Baba, N.

F. Tsumuraya, N. Miura, N. Baba, “Iterative blind deconvolution method using Lucy’s algorithm,” Astron. Astrophys. 282, 699–708 (1994).

Bates, R. H. T.

B. L. K. Davey, R. G. Lane, R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353–356 (1989).
[CrossRef]

R. G. Lane, R. H. T. Bates, “Automatic multidimensional deconvolution,” J. Opt. Soc. Am. A 4, 180–188 (1987).
[CrossRef]

Beland, R. R.

R. R. Beland, “Propagation through atmospheric optical turbulence,” The Infrared and Electro-Optical Handbook. Vol. 2: Atmospheric Propagation of Radiation, F. G. Smith, ed. (SPIE Optical Engineering Press: Bellingham, Wash., 1993), pp. 157–232.

Bell, T. E.

T. E. Bell, “Electronics and the stars,” IEEE Spectr. 32, 16–24 (1995).
[CrossRef]

Biraud, Y.

Y. Biraud, “A new approach for increasing the resolving power by data processing,” Astron. Astrophys. 1, 124–127 (1969).

Bones, P. J.

Cannon, T. M.

T. G. Stockham, T. M. Cannon, R. B. Ingebretsen, “Blind deconvolution through digital signal processing,” Proc. IEEE 63, 678–692 (1975).
[CrossRef]

Cheselka, M.

E. K. Hege, J. R. P. Angel, M. Cheselka, M. Lloyd–Hart, “Simulation of aperture synthesis with the Large Binocular Telescope,” in Advanced Imaging Technologies and Commercial Applications, N. Clark, J. D. Gonglewski, eds., Proc. SPIE2566, 144–155 (1995).
[CrossRef]

Christou, J. C.

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

J. C. Christou, E. K. Hege, S. M. Jefferies, “Speckle deconvolution imaging using an iterative algorithm,” in Advanced Imaging Technologies and Commercial Applications, N. Clark, J. D. Gonglewski, eds., Proc. SPIE2566, 134–143 (1995).
[CrossRef]

J. C. Christou, “Blind deconvolution post-processing of images corrected by adaptive optics,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 226–234 (1995).
[CrossRef]

Conan, J.-M.

E. Thiébaut, J.-M. Conan, “Strict a priori constraints for maximum-likelihood blind deconvolution,” J. Opt. Soc. Am. A 12, 485–492 (1995).
[CrossRef]

J.-M. Conan, V. Michau, G. Rousset, “Signal-to-noise ratio and bias of various deconvolution from wavefront sensing estimators,” Image Propagation through the Atmosphere, L. R. Bissonnette, C. Dainty, eds., Proc. SPIE2828, 332–339 (1996).
[CrossRef]

Dainty, J. C.

Davey, B. L. K.

B. L. K. Davey, R. G. Lane, R. H. T. Bates, “Blind deconvolution of noisy complex-valued image,” Opt. Commun. 69, 353–356 (1989).
[CrossRef]

Delaney, P. A.

D. O. Walsh, P. A. Delaney, M. W. Marcellin, “Non-iterative implementation of a class of iterative signal restoration algorithms,” in Proceedings of the International Conference on Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), pp. 1672–1675.

Ellerbroek, B. L.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

Fried, D. L.

Gerchberg, R. W.

R. W. Gerchberg, “Superresolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

Gilliland, R. L.

R. J. Hanisch, R. L. White, R. L. Gilliland, “Deconvolution of Hubble Space Telescope images and spectra,” in Deconvolution of Images and Spectra, P. A. Jansson, ed. (Academic, New York, 1997).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hanisch, R. J.

R. J. Hanisch, R. L. White, “HST image restoration: current capabilities and future prospects,” in Very High Angular Resolution Imaging, J. G. Robertson, W. J. Tango, eds. (Kluwer, Dordrecht, The Netherlands, 1994), pp. 61–69.

R. J. Hanisch, R. L. White, R. L. Gilliland, “Deconvolution of Hubble Space Telescope images and spectra,” in Deconvolution of Images and Spectra, P. A. Jansson, ed. (Academic, New York, 1997).

Hanke, M.

M. Hanke, Conjugate-Gradient Type Methods for Ill-Posed Problems (Wiley, New York, 1995).

Hatzinakos, D.

D. Kundur, D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Proc. Mag. 13, 43–64 (1996).
[CrossRef]

Hege, E. K.

J. C. Christou, E. K. Hege, S. M. Jefferies, “Speckle deconvolution imaging using an iterative algorithm,” in Advanced Imaging Technologies and Commercial Applications, N. Clark, J. D. Gonglewski, eds., Proc. SPIE2566, 134–143 (1995).
[CrossRef]

E. K. Hege, J. R. P. Angel, M. Cheselka, M. Lloyd–Hart, “Simulation of aperture synthesis with the Large Binocular Telescope,” in Advanced Imaging Technologies and Commercial Applications, N. Clark, J. D. Gonglewski, eds., Proc. SPIE2566, 144–155 (1995).
[CrossRef]

Holmes, T. J.

Hook, R. N.

H.-M. Adorf, R. N. Hook, L. B. Lucy, “HST image restoration developments at the ST-ECF,” Int. J. Imaging Syst. Technol. 6, 339–349 (1995).
[CrossRef]

Hunt, B. R.

B. R. Hunt, “Superresolution of images: algorithms, principles, performance,” Int. J. Imaging Syst. Technol. 6, 297–304 (1995).
[CrossRef]

P. J. Sementilli, B. R. Hunt, M. S. Nadar, “Analysis of the limit to superresolution in incoherent imaging,” J. Opt. Soc. Am. A 10, 2265–2276 (1993).
[CrossRef]

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

B. R. Hunt, P. J. Sementilli, “Description of a Poisson imagery superresolution algorithm,” in Astronomical Data Analysis Software and Systems I, D. Worral, C. Biemesderfer, J. Barnes, eds. (Astronomy Society of the Pacific, San Francisco, Calif., 1992), pp. 196–199.

Ingebretsen, R. B.

T. G. Stockham, T. M. Cannon, R. B. Ingebretsen, “Blind deconvolution through digital signal processing,” Proc. IEEE 63, 678–692 (1975).
[CrossRef]

Jansson, P. A.

P. A. Jansson, “Modern constrained nonlinear methods,” in Deconvolution of Images and Spectra, P. A. Jansson, ed. (Academic, New York, 1997).

P. A. Jansson, “Traditional linear deconvolution methods,” in Deconvolution of Images and Spectra, P. A. Jansson, ed. (Academic, New York, 1997).

Jefferies, S. M.

S. M. Jefferies, J. C. Christou, “Restoration of astronomical images by iterative blind deconvolution,” Astrophys. J. 415, 862–874 (1993).
[CrossRef]

J. C. Christou, E. K. Hege, S. M. Jefferies, “Speckle deconvolution imaging using an iterative algorithm,” in Advanced Imaging Technologies and Commercial Applications, N. Clark, J. D. Gonglewski, eds., Proc. SPIE2566, 134–143 (1995).
[CrossRef]

Knox, K. T.

K. T. Knox, B. J. Thompson, “Recovery of images from atmospherically degraded short exposure images,” Astrophys. J. 193, L45–48 (1974).
[CrossRef]

Kundur, D.

D. Kundur, D. Hatzinakos, “Blind image deconvolution,” IEEE Signal Proc. Mag. 13, 43–64 (1996).
[CrossRef]

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Lane, R. G.

Lloyd–Hart, M.

E. K. Hege, J. R. P. Angel, M. Cheselka, M. Lloyd–Hart, “Simulation of aperture synthesis with the Large Binocular Telescope,” in Advanced Imaging Technologies and Commercial Applications, N. Clark, J. D. Gonglewski, eds., Proc. SPIE2566, 144–155 (1995).
[CrossRef]

Lohman, A. W.

Lucy, L. B.

H.-M. Adorf, R. N. Hook, L. B. Lucy, “HST image restoration developments at the ST-ECF,” Int. J. Imaging Syst. Technol. 6, 339–349 (1995).
[CrossRef]

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–759 (1974).
[CrossRef]

Marcellin, M. W.

D. O. Walsh, P. A. Delaney, M. W. Marcellin, “Non-iterative implementation of a class of iterative signal restoration algorithms,” in Proceedings of the International Conference on Speech, and Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1996), pp. 1672–1675.

Meinel, E. S.

Michau, V.

J.-M. Conan, V. Michau, G. Rousset, “Signal-to-noise ratio and bias of various deconvolution from wavefront sensing estimators,” Image Propagation through the Atmosphere, L. R. Bissonnette, C. Dainty, eds., Proc. SPIE2828, 332–339 (1996).
[CrossRef]

Miura, N.

F. Tsumuraya, N. Miura, N. Baba, “Iterative blind deconvolution method using Lucy’s algorithm,” Astron. Astrophys. 282, 699–708 (1994).

Nadar, M. S.

Noll, R. J.

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66, 207–211 (1966).
[CrossRef]

Northcott, M. J.

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear filtering of multiplied and convolved signals,” Proc. IEEE 56, 1264–1291 (1968).
[CrossRef]

Parker, C. R.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, 1988).

Rhoadarmer, T. A.

Richardson, W. H.

Roddier, F.

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. XIX, pp. 281–376.

Roggeman, M. C.

Rousset, G.

J.-M. Conan, V. Michau, G. Rousset, “Signal-to-noise ratio and bias of various deconvolution from wavefront sensing estimators,” Image Propagation through the Atmosphere, L. R. Bissonnette, C. Dainty, eds., Proc. SPIE2828, 332–339 (1996).
[CrossRef]

Satherly, B. L.

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, T. G. Stockham, “Nonlinear filtering of multiplied and convolved signals,” Proc. IEEE 56, 1264–1291 (1968).
[CrossRef]

Schulz, T. J.

Sementilli, P. J.

P. J. Sementilli, B. R. Hunt, M. S. Nadar, “Analysis of the limit to superresolution in incoherent imaging,” J. Opt. Soc. Am. A 10, 2265–2276 (1993).
[CrossRef]

B. R. Hunt, P. J. Sementilli, “Description of a Poisson imagery superresolution algorithm,” in Astronomical Data Analysis Software and Systems I, D. Worral, C. Biemesderfer, J. Barnes, eds. (Astronomy Society of the Pacific, San Francisco, Calif., 1992), pp. 196–199.

P. J. Sementilli, “Suppression of artifacts in super-resolved images,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1993).

Shewchuk, J. R.

J. R. Shewchuk, “An introduction to the conjugate-gradient method without the agonizing pain,” (Carnegie Mellon University, School of Computer Science, Pittsburgh, Pa., 1994).

Stockham, T. G.

T. G. Stockham, T. M. Cannon, R. B. Ingebretsen, “Blind deconvolution through digital signal processing,” Proc. IEEE 63, 678–692 (1975).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Original OCNR5 satellite object and sample tilt-corrected simulated short-exposure images for different visual magnitudes mv (r0=10 cm). Clockwise from upper left: OCNR5 object, mv=0-frame, mv=4-frame, mv=8-frame images.

Fig. 2
Fig. 2

Spectra of images from Fig. 1. Clockwise from upper left: OCNR5 object spectrum, mv=0-frame spectrum, mv=4-frame spectrum, mv=8-frame spectrum. All spectra are range compressed with log10(1+|·|2).

Fig. 3
Fig. 3

Restoration of a simulated OCNR5 satellite object of visual magnitude mv=4 by use of the multiframe incremental PMAP algorithm with varying number of frames (r0=10 cm). Clockwise from upper left: OCNR5 object, 10-frame restoration, 50-frame restoration, 200-frame restoration.

Fig. 4
Fig. 4

Spectra of images from Fig. 3. Clockwise from upper left: OCNR5 object spectrum, 10-frame-restoration spectrum, 50-frame-restoration spectrum, 200-frame-restoration spectrum. All spectra are range compressed with log10(1+|·|2).

Fig. 5
Fig. 5

Restoration of a simulated OCNR5 satellite object of visual magnitude mv=4 by use of the multiframe maximum-likelihood blind deconvolution algorithm with varying number of frames (r0=10 cm). Clockwise from upper left: OCNR5 object, 10-frame restoration, 50-frame restoration, 200-frame restoration.

Fig. 6
Fig. 6

Spectra of images from Fig. 5. Clockwise from upper left: OCNR5 object spectrum, 10-frame-restoration spectrum, 50-frame-restoration spectrum, 200-frame-restoration spectrum. All spectra are range compressed with log10(1+|·|2).

Tables (1)

Tables Icon

Table 1 Expected Image and Subaperture Photon Counts As a Function of Object Visual Magnitudea

Equations (41)

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

g(x, y)=L{f(ξ, η)}n(x, y),
g(x, y)=--h(x-ξ, y-η)f(ξ, η)dξdηn(x, y)=(h*f)(x, y)n(x, y),
p(f, {hk}|{gk})=p({gk}|f, {hk})p(f, {hk})p({gk}).
fˆ=arg maxf,h p({gk}|f, {hk}),
fˆ=arg maxf,h p({gk}|f, {hk})p(f, {hk}).
fˆ=arg maxf p({gk}|f)p(f)
=arg maxf p(f)kp(gk|f)
=arg maxf k ln p(gk|f)+ln pf(f)
k fij[ln p(gk|f)]fˆ+fij[ln p(f)]fˆ=0.
fijn+1=f¯ijnk exp1Kgk(fn*hk)-1*hk+ij,
fijn+1=fijnk exp1Kgk(fn*hk)-1*hk+ij.
fijn+1=fijn expg((n))K(fn*h((n))K)-1*h((n))K+ij,
fˆ=arg minf[-ln p({gk}|f)],
J(f)=-kx,y ln p((gk)xy|f)-kx,y{(gk)xy ln[(f*hk)xy]-(f*hk)xy}.
J(f)fij=-kgk(f*hk)-1*hk+ij,
J(f)ϕif=J(f)fijfijϕij=-2ϕijkgk(f*hk)-1*hk+ij.
(hk)ij=(ξ*ψk)ij2i,j(ξ*ψk)ij2,
J(f, {hk})(ψk)ij=m,n J(f, {hk})(hk)mn(hk)mn(ψk)ij=-2i,j(ξ*ψk)ij2×(ξ*ψk)gkf*hk-1*f+*ξ+ij-[(ξ*ψk)*ξ+]ijm,n×gkf*hk-1*f+mn(hk)mn,
σ=0.86πη2nlsar0lsa>r00.74πη2nlsar0,
E=ψ(u, v)-i=1N ciei(u, v)2,
f0=1Kk=1Kgk
fijn+1=fijn+1kexp1Kgk(fn*hk)-1*hk+ij(baseline)
fijn+1=fijn expg((n))K(f*h((n))K)-1*h((n))K+ij(incremental).
J(ϕn)=-kx,y((gk)xy ln{[(ϕn)2*hk]xy}-[(ϕn)2*hk]xy),
J(ϕn)|ij=J(fn)ϕijn=J(fn)fijnfijnϕijn=-2ϕijnkgk[(ϕn)2*hk]-1*hk+ij,
n=0,
ϕn=fn=1Kk=1kgk,
dn=rn-J(ϕn).
ϕn+1=ϕn+αndn.
rn+1=-(Jϕn+1)βn+1=max(rn+1)T(rn+1-rn)(rn)Trn, 0(the PolakRibière form),
dn+1=rn+1+βn+1dn.
J(ϕn, ψ1n, , ψkn)=-kx,y(gk)xy ln(ϕn)2*(ξ*ψkn)2i,j(ξ*ψkn)ij2xy-(ϕn)2*(ξ*ψkn)2ij(ξ*ψkn)ij2xy,
J(ϕn)|ij=J(fn)ϕijn=J(fn)fijnfijnϕijn=-2ϕijnkgk[(ϕn)2*hk]-1*hk+ij,
J(ψkn)|ij=J(f, {hk})(ψk)ij=-2i,j(ξ*ψk)ij2×(ξ*ψk)gkf*hk-1*f+*ξ+ij-[(ξ*ψk)*ξ+]ij×mngkf*hk-1*f+mn(hk)mn
n=0,
ϕn=fn=1Kk=1Kgk,
dn=rn=-J(ϕn:ψ1n: ψKn).
[ϕn+1 : ψ1n+1 :  : ψKn+1]=[ϕn : ψ1n :  : ψKn]+αndn.
rn+1=-J(ϕn+1 : ψ1n+1 :  : ψKn+1),
βn+1=max(rn+1)T(rn+1-rn)(rn)Trn, 0(thePolakRibièreform),
dn+1=rn+1+βn+1dn.

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