Abstract

Deconvolution from wave-front sensing is a powerful and low-cost high-resolution imaging technique designed to compensate for the image degradation due to atmospheric turbulence. It is based on a simultaneous recording of short-exposure images and wave-front sensor (WFS) data. Conventional data processing consists of a sequential estimation of the wave fronts given the WFS data and then of the object given the reconstructed wave fronts and the images. However, the object estimation does not take into account the wave-front reconstruction errors. A joint estimation of the object and the respective wave fronts has therefore been proposed to overcome this limitation. The aim of our study is to derive and validate a robust joint estimation approach, called myopic deconvolution from wave-front sensing. Our estimator uses all data simultaneously in a coherent Bayesian framework. It takes into account the noise in the images and in the WFS measurements and the available a priori information on the object to be restored as well as on the wave fronts. Regarding the a priori information on the object, an edge-preserving prior is implemented and validated. This method is validated on simulations and on experimental astronomical data.

© 2001 Optical Society of America

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1999 (2)

T. Fusco, J.-P. Véran, J.-M. Conan, L. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” Astron. Astrophys., Suppl. Ser. 134, 1–10 (1999).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, L. Mugnier, G. Rousset, “Efficient phase estimation for large-field-of-view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
[CrossRef]

1998 (2)

S. D. Ford, B. M. Welsh, M. C. Roggemann, “Constrained least-squares estimation in deconvolution from wave-front sensing,” Opt. Commun. 151, 93–100 (1998).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

1997 (1)

1996 (1)

Y.-L. You, M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Processing 5, 416–428 (1996).
[CrossRef]

1995 (1)

1994 (4)

1993 (4)

C. Bouman, K. Sauer, “A generalized Gaussian image model for edge-preserving MAP estimation,” IEEE Trans. Image Process. 2, 296–310 (1993).
[CrossRef] [PubMed]

D. W. Tyler, C. L. Matson, “Speckle imaging detector optimization and comparison,” Opt. Eng. 32, 864–869 (1993).
[CrossRef]

T. J. Schulz, “Multiframe blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10, 1064–1073 (1993).
[CrossRef]

B. M. Welsh, R. N. VonNiederhausern, “Performance analysis of the self-referenced speckle-holography image-reconstruction technique,” Appl. Opt. 32, 5071–5078 (1993).
[CrossRef] [PubMed]

1992 (1)

1990 (4)

1989 (1)

G. Demoment, “Image reconstruction and restoration: overview of common estimation structures and problems,” IEEE Trans. Acoust., Speech, Signal Process. 37, 2024–2036 (1989).
[CrossRef]

1985 (2)

J.-C. Fontanella, “Analyse de surface d’onde, déconvolution et optique active,” J. Mod. Opt. 16, 257–268 (1985).
[CrossRef]

C. M. Titterington, “General structure of regularization procedures in image reconstruction,” Astron. Astrophys. 144, 381–387 (1985).

1983 (1)

1976 (1)

Bakut, P. A.

P. A. Bakut, V. E. Kirakosyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wavefront reconstruction form a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994).
[CrossRef]

Bertsekas, D. P.

D. P. Bertsekas, Nonlinear Programming (Athena Scientific, Belmont, Mass., 1995).

Bouman, C.

C. Bouman, K. Sauer, “A generalized Gaussian image model for edge-preserving MAP estimation,” IEEE Trans. Image Process. 2, 296–310 (1993).
[CrossRef] [PubMed]

Brette, S.

S. Brette, J. Idier, “Optimized single site update algorithms for image deblurring,” in Proceedings of the Interna-tional Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1996), pp. 65–68.

Caulfield, H. J.

Conan, J.-M.

T. Fusco, J.-P. Véran, J.-M. Conan, L. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” Astron. Astrophys., Suppl. Ser. 134, 1–10 (1999).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, L. Mugnier, G. Rousset, “Efficient phase estimation for large-field-of-view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[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]

J.-M. Conan, T. Fusco, L. M. Mugnier, E. Kersalé, V. Michau, “Deconvolution of adaptive optics images with imprecise knowledge of the point spread function: results on astronomical objects,” in Astronomy with Adaptive Optics: Present Results and Future Programs, D. Bonaccini, ed., (European Southern Observatory, Garching, Germany, 1999), pp. 121–132.

L. M. Mugnier, J.-M. Conan, V. Michau, G. Rousset, “Imagerie travers la turbulence par déconvolution myope multi-trame,” in Seizième Colloque sur le Traitement du Signal et des Images, J.-M. Chassery, C. Jutten, eds. (Gretsi, Grenoble, France, 1997), pp. 567–570.

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

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation-through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[CrossRef]

Dainty, J. C.

P. A. Bakut, V. E. Kirakosyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wavefront reconstruction form a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994).
[CrossRef]

Dayton, D.

Dayton, D. C.

J. D. Gonglewski, D. G. Voelz, J. S. Fender, D. C. Dayton, B. K. Spielbusch, R. E. Pierson, “First astronomical application of postdetection turbulence compensation: images of α Aurigae, ν Ursae Majoris, and α Geminorum using self-referenced speckle holography,” Appl. Opt. 29, 4527–4529 (1990).
[CrossRef] [PubMed]

D. C. Dayton, S. C. Sandven, J. D. Gonglewski, “Expectation maximization approach to deconvolution from wavefront sensing,” in Image Reconstruction and Restoration II, T. J. Schulz, ed., Proc. SPIE3170, 16–24 (1997).
[CrossRef]

Demoment, G.

G. Demoment, “Image reconstruction and restoration: overview of common estimation structures and problems,” IEEE Trans. Acoust., Speech, Signal Process. 37, 2024–2036 (1989).
[CrossRef]

Devey, J.

Fender, J. S.

Fertin, G.

T. Marais, V. Michau, G. Fertin, J. Primot, J. C. Fontanella, “Deconvolution from wavefront sensing on a 4 m telescope,” in High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds., (European Southern Observatory, Garching, Germany, 1992), pp. 589–597.

Fienup, J. R.

Fontanella, J. C.

T. Marais, V. Michau, G. Fertin, J. Primot, J. C. Fontanella, “Deconvolution from wavefront sensing on a 4 m telescope,” in High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds., (European Southern Observatory, Garching, Germany, 1992), pp. 589–597.

Fontanella, J.-C.

J. Primot, G. Rousset, J.-C. Fontanella, “Deconvolution from wavefront sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598–1608 (1990).
[CrossRef]

J.-C. Fontanella, “Analyse de surface d’onde, déconvolution et optique active,” J. Mod. Opt. 16, 257–268 (1985).
[CrossRef]

J. Primot, G. Rousset, J.-C. Fontanella, “Image deconvolution from wavefront sensing: atmospheric turbulence simulation cell results,” in Very Large Telescopes and Their Instrumentation, Vol. II, M.-H. Ulrich, ed., (European Southern Observatory, Garching, Germany, 1988), pp. 683–692.

Ford, S. D.

S. D. Ford, B. M. Welsh, M. C. Roggemann, “Constrained least-squares estimation in deconvolution from wave-front sensing,” Opt. Commun. 151, 93–100 (1998).
[CrossRef]

Fusco, T.

T. Fusco, J.-P. Véran, J.-M. Conan, L. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” Astron. Astrophys., Suppl. Ser. 134, 1–10 (1999).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, L. Mugnier, G. Rousset, “Efficient phase estimation for large-field-of-view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation-through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[CrossRef]

J.-M. Conan, T. Fusco, L. M. Mugnier, E. Kersalé, V. Michau, “Deconvolution of adaptive optics images with imprecise knowledge of the point spread function: results on astronomical objects,” in Astronomy with Adaptive Optics: Present Results and Future Programs, D. Bonaccini, ed., (European Southern Observatory, Garching, Germany, 1999), pp. 121–132.

Gonglewski, J.

Gonglewski, J. D.

J. D. Gonglewski, D. G. Voelz, J. S. Fender, D. C. Dayton, B. K. Spielbusch, R. E. Pierson, “First astronomical application of postdetection turbulence compensation: images of α Aurigae, ν Ursae Majoris, and α Geminorum using self-referenced speckle holography,” Appl. Opt. 29, 4527–4529 (1990).
[CrossRef] [PubMed]

D. C. Dayton, S. C. Sandven, J. D. Gonglewski, “Expectation maximization approach to deconvolution from wavefront sensing,” in Image Reconstruction and Restoration II, T. J. Schulz, ed., Proc. SPIE3170, 16–24 (1997).
[CrossRef]

Green, P. J.

P. J. Green, “Bayesian reconstructions from emission tomography data using a modified EM Algorithm,” IEEE Trans. Med. Imaging 9, 84–93 (1990).
[CrossRef] [PubMed]

Hyde, C. A.

M. C. Roggemann, C. A. Hyde, B. M. Welsh, “Fourier phase spectrum estimation using deconvolution from wavefront sensing and bispectrum reconstruction,” in Adaptive Optics, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 133–135.

Idier, J.

S. Brette, J. Idier, “Optimized single site update algorithms for image deblurring,” in Proceedings of the Interna-tional Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1996), pp. 65–68.

Kaveh, M.

Y.-L. You, M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Processing 5, 416–428 (1996).
[CrossRef]

Kersalé, E.

J.-M. Conan, T. Fusco, L. M. Mugnier, E. Kersalé, V. Michau, “Deconvolution of adaptive optics images with imprecise knowledge of the point spread function: results on astronomical objects,” in Astronomy with Adaptive Optics: Present Results and Future Programs, D. Bonaccini, ed., (European Southern Observatory, Garching, Germany, 1999), pp. 121–132.

Kirakosyants, V. E.

P. A. Bakut, V. E. Kirakosyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wavefront reconstruction form a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994).
[CrossRef]

Loginov, V. A.

P. A. Bakut, V. E. Kirakosyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wavefront reconstruction form a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994).
[CrossRef]

Luenberger, D. G.

D. G. Luenberger, Introduction to Linear and Nonlinear Programming (Addison-Wesley, Reading, Mass., 1973).

Marais, T.

T. Marais, V. Michau, G. Fertin, J. Primot, J. C. Fontanella, “Deconvolution from wavefront sensing on a 4 m telescope,” in High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds., (European Southern Observatory, Garching, Germany, 1992), pp. 589–597.

Matson, C. L.

D. W. Tyler, C. L. Matson, “Speckle imaging detector optimization and comparison,” Opt. Eng. 32, 864–869 (1993).
[CrossRef]

Michau, V.

T. Fusco, J.-M. Conan, V. Michau, L. Mugnier, G. Rousset, “Efficient phase estimation for large-field-of-view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

T. Marais, V. Michau, G. Fertin, J. Primot, J. C. Fontanella, “Deconvolution from wavefront sensing on a 4 m telescope,” in High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds., (European Southern Observatory, Garching, Germany, 1992), pp. 589–597.

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation-through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[CrossRef]

J.-M. Conan, T. Fusco, L. M. Mugnier, E. Kersalé, V. Michau, “Deconvolution of adaptive optics images with imprecise knowledge of the point spread function: results on astronomical objects,” in Astronomy with Adaptive Optics: Present Results and Future Programs, D. Bonaccini, ed., (European Southern Observatory, Garching, Germany, 1999), pp. 121–132.

L. M. Mugnier, J.-M. Conan, V. Michau, G. Rousset, “Imagerie travers la turbulence par déconvolution myope multi-trame,” in Seizième Colloque sur le Traitement du Signal et des Images, J.-M. Chassery, C. Jutten, eds. (Gretsi, Grenoble, France, 1997), pp. 567–570.

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

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
[CrossRef]

Mugnier, L.

T. Fusco, J.-M. Conan, V. Michau, L. Mugnier, G. Rousset, “Efficient phase estimation for large-field-of-view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
[CrossRef]

T. Fusco, J.-P. Véran, J.-M. Conan, L. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” Astron. Astrophys., Suppl. Ser. 134, 1–10 (1999).
[CrossRef]

Mugnier, L. M.

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation-through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[CrossRef]

L. M. Mugnier, J.-M. Conan, V. Michau, G. Rousset, “Imagerie travers la turbulence par déconvolution myope multi-trame,” in Seizième Colloque sur le Traitement du Signal et des Images, J.-M. Chassery, C. Jutten, eds. (Gretsi, Grenoble, France, 1997), pp. 567–570.

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
[CrossRef]

J.-M. Conan, T. Fusco, L. M. Mugnier, E. Kersalé, V. Michau, “Deconvolution of adaptive optics images with imprecise knowledge of the point spread function: results on astronomical objects,” in Astronomy with Adaptive Optics: Present Results and Future Programs, D. Bonaccini, ed., (European Southern Observatory, Garching, Germany, 1999), pp. 121–132.

Noll, R. J.

Paxman, R. G.

Pierson, R. E.

Primot, J.

J. Primot, G. Rousset, J.-C. Fontanella, “Deconvolution from wavefront sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598–1608 (1990).
[CrossRef]

J. Primot, G. Rousset, J.-C. Fontanella, “Image deconvolution from wavefront sensing: atmospheric turbulence simulation cell results,” in Very Large Telescopes and Their Instrumentation, Vol. II, M.-H. Ulrich, ed., (European Southern Observatory, Garching, Germany, 1988), pp. 683–692.

T. Marais, V. Michau, G. Fertin, J. Primot, J. C. Fontanella, “Deconvolution from wavefront sensing on a 4 m telescope,” in High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds., (European Southern Observatory, Garching, Germany, 1992), pp. 589–597.

Rey, W. J.

W. J. Rey, Introduction to Robust and Quasi-Robust Statistical Methods (Springer-Verlag, Berlin, 1983).

Robert, C.

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
[CrossRef]

Roddier, F.

F. Roddier, “Passive versus active methods in optical interferometry,” in High-Resolution Imaging by Interferometry Part II, F. Merkle, ed., (European Southern Observatory, Garching, Germany, 1988), pp. 565–574.

Roddier, N.

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

Rogers, S.

Roggemann, M. C.

S. D. Ford, B. M. Welsh, M. C. Roggemann, “Constrained least-squares estimation in deconvolution from wave-front sensing,” Opt. Commun. 151, 93–100 (1998).
[CrossRef]

M. C. Roggemann, B. M. Welsh, J. Devey, “Biased estimators and object-spectrum estimation in the method of deconvolution from wave-front sensing,” Appl. Opt. 33, 5754–5763 (1994).
[CrossRef] [PubMed]

M. C. Roggemann, B. M. Welsh, “Signal to noise ratio for astronomical imaging by deconvolution from wave-front sensing,” Appl. Opt. 33, 5400–5414 (1994).
[CrossRef] [PubMed]

M. C. Roggemann, C. A. Hyde, B. M. Welsh, “Fourier phase spectrum estimation using deconvolution from wavefront sensing and bispectrum reconstruction,” in Adaptive Optics, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 133–135.

Rousset, G.

T. Fusco, J.-M. Conan, V. Michau, L. Mugnier, G. Rousset, “Efficient phase estimation for large-field-of-view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

J. Primot, G. Rousset, J.-C. Fontanella, “Deconvolution from wavefront sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1598–1608 (1990).
[CrossRef]

J. Primot, G. Rousset, J.-C. Fontanella, “Image deconvolution from wavefront sensing: atmospheric turbulence simulation cell results,” in Very Large Telescopes and Their Instrumentation, Vol. II, M.-H. Ulrich, ed., (European Southern Observatory, Garching, Germany, 1988), pp. 683–692.

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

L. M. Mugnier, J.-M. Conan, V. Michau, G. Rousset, “Imagerie travers la turbulence par déconvolution myope multi-trame,” in Seizième Colloque sur le Traitement du Signal et des Images, J.-M. Chassery, C. Jutten, eds. (Gretsi, Grenoble, France, 1997), pp. 567–570.

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation-through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[CrossRef]

Salem, S.

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
[CrossRef]

Sandven, S. C.

D. C. Dayton, S. C. Sandven, J. D. Gonglewski, “Expectation maximization approach to deconvolution from wavefront sensing,” in Image Reconstruction and Restoration II, T. J. Schulz, ed., Proc. SPIE3170, 16–24 (1997).
[CrossRef]

Sauer, K.

C. Bouman, K. Sauer, “A generalized Gaussian image model for edge-preserving MAP estimation,” IEEE Trans. Image Process. 2, 296–310 (1993).
[CrossRef] [PubMed]

Schulz, T. J.

T. J. Schulz, “Multiframe blind deconvolution of astronomical images,” J. Opt. Soc. Am. A 10, 1064–1073 (1993).
[CrossRef]

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992).
[CrossRef]

T. J. Schulz, “Estimation-theoretic approach to the deconvolution of atmospherically degraded images with wavefront sensor measurements,” in Digital Image Recovery and Synthesis II, P. S. Idell, ed., Proc. SPIE2029, 311–320 (1993).
[CrossRef]

Solomon, C. J.

P. A. Bakut, V. E. Kirakosyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wavefront reconstruction form a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994).
[CrossRef]

Spielbusch, B. K.

Thiébaut, E.

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

E. Thiébaut, “Speckle imaging with the bispectrum and without reference star,” in International Astronomical Union Symposium on Very High Angular Resolution Imaging, R. J. G. Robertson, W. J. Tango, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1994), Vol. 158, p. 209.

Titterington, C. M.

C. M. Titterington, “General structure of regularization procedures in image reconstruction,” Astron. Astrophys. 144, 381–387 (1985).

Tyler, D. W.

D. W. Tyler, C. L. Matson, “Speckle imaging detector optimization and comparison,” Opt. Eng. 32, 864–869 (1993).
[CrossRef]

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).

Véran, J.-P.

T. Fusco, J.-P. Véran, J.-M. Conan, L. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” Astron. Astrophys., Suppl. Ser. 134, 1–10 (1999).
[CrossRef]

Voelz, D. G.

VonNiederhausern, R. N.

Wallner, E. P.

Welsh, B. M.

S. D. Ford, B. M. Welsh, M. C. Roggemann, “Constrained least-squares estimation in deconvolution from wave-front sensing,” Opt. Commun. 151, 93–100 (1998).
[CrossRef]

M. C. Roggemann, B. M. Welsh, J. Devey, “Biased estimators and object-spectrum estimation in the method of deconvolution from wave-front sensing,” Appl. Opt. 33, 5754–5763 (1994).
[CrossRef] [PubMed]

M. C. Roggemann, B. M. Welsh, “Signal to noise ratio for astronomical imaging by deconvolution from wave-front sensing,” Appl. Opt. 33, 5400–5414 (1994).
[CrossRef] [PubMed]

B. M. Welsh, R. N. VonNiederhausern, “Performance analysis of the self-referenced speckle-holography image-reconstruction technique,” Appl. Opt. 32, 5071–5078 (1993).
[CrossRef] [PubMed]

M. C. Roggemann, C. A. Hyde, B. M. Welsh, “Fourier phase spectrum estimation using deconvolution from wavefront sensing and bispectrum reconstruction,” in Adaptive Optics, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 133–135.

Yaroslavsky, L. P.

You, Y.-L.

Y.-L. You, M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Processing 5, 416–428 (1996).
[CrossRef]

Appl. Opt. (7)

Astron. Astrophys. (1)

C. M. Titterington, “General structure of regularization procedures in image reconstruction,” Astron. Astrophys. 144, 381–387 (1985).

Astron. Astrophys., Suppl. Ser. (1)

T. Fusco, J.-P. Véran, J.-M. Conan, L. Mugnier, “Myopic deconvolution method for adaptive optics images of stellar fields,” Astron. Astrophys., Suppl. Ser. 134, 1–10 (1999).
[CrossRef]

IEEE Trans. Acoust., Speech, Signal Process. (1)

G. Demoment, “Image reconstruction and restoration: overview of common estimation structures and problems,” IEEE Trans. Acoust., Speech, Signal Process. 37, 2024–2036 (1989).
[CrossRef]

IEEE Trans. Image Process. (1)

C. Bouman, K. Sauer, “A generalized Gaussian image model for edge-preserving MAP estimation,” IEEE Trans. Image Process. 2, 296–310 (1993).
[CrossRef] [PubMed]

IEEE Trans. Image Processing (1)

Y.-L. You, M. Kaveh, “A regularization approach to joint blur identification and image restoration,” IEEE Trans. Image Processing 5, 416–428 (1996).
[CrossRef]

IEEE Trans. Med. Imaging (1)

P. J. Green, “Bayesian reconstructions from emission tomography data using a modified EM Algorithm,” IEEE Trans. Med. Imaging 9, 84–93 (1990).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

J.-C. Fontanella, “Analyse de surface d’onde, déconvolution et optique active,” J. Mod. Opt. 16, 257–268 (1985).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (4)

Opt. Commun. (2)

P. A. Bakut, V. E. Kirakosyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wavefront reconstruction form a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994).
[CrossRef]

S. D. Ford, B. M. Welsh, M. C. Roggemann, “Constrained least-squares estimation in deconvolution from wave-front sensing,” Opt. Commun. 151, 93–100 (1998).
[CrossRef]

Opt. Eng. (2)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29, 1174–1180 (1990).
[CrossRef]

D. W. Tyler, C. L. Matson, “Speckle imaging detector optimization and comparison,” Opt. Eng. 32, 864–869 (1993).
[CrossRef]

Opt. Lett. (1)

Other (18)

E. Thiébaut, “Speckle imaging with the bispectrum and without reference star,” in International Astronomical Union Symposium on Very High Angular Resolution Imaging, R. J. G. Robertson, W. J. Tango, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1994), Vol. 158, p. 209.

Groupe Problèmes Inverses, “GPAV: une grande oeuvre collective,” (Centre National de la Recherche Scientifique/Supélec/Université Paris-Sud, Paris, 1997).

D. P. Bertsekas, Nonlinear Programming (Athena Scientific, Belmont, Mass., 1995).

D. G. Luenberger, Introduction to Linear and Nonlinear Programming (Addison-Wesley, Reading, Mass., 1973).

J. Primot, G. Rousset, J.-C. Fontanella, “Image deconvolution from wavefront sensing: atmospheric turbulence simulation cell results,” in Very Large Telescopes and Their Instrumentation, Vol. II, M.-H. Ulrich, ed., (European Southern Observatory, Garching, Germany, 1988), pp. 683–692.

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

T. J. Schulz, “Estimation-theoretic approach to the deconvolution of atmospherically degraded images with wavefront sensor measurements,” in Digital Image Recovery and Synthesis II, P. S. Idell, ed., Proc. SPIE2029, 311–320 (1993).
[CrossRef]

L. M. Mugnier, J.-M. Conan, V. Michau, G. Rousset, “Imagerie travers la turbulence par déconvolution myope multi-trame,” in Seizième Colloque sur le Traitement du Signal et des Images, J.-M. Chassery, C. Jutten, eds. (Gretsi, Grenoble, France, 1997), pp. 567–570.

D. C. Dayton, S. C. Sandven, J. D. Gonglewski, “Expectation maximization approach to deconvolution from wavefront sensing,” in Image Reconstruction and Restoration II, T. J. Schulz, ed., Proc. SPIE3170, 16–24 (1997).
[CrossRef]

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation-through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[CrossRef]

W. J. Rey, Introduction to Robust and Quasi-Robust Statistical Methods (Springer-Verlag, Berlin, 1983).

S. Brette, J. Idier, “Optimized single site update algorithms for image deblurring,” in Proceedings of the Interna-tional Conference on Image Processing (IEEE Computer Society Press, Los Alamitos, Calif., 1996), pp. 65–68.

J.-M. Conan, T. Fusco, L. M. Mugnier, E. Kersalé, V. Michau, “Deconvolution of adaptive optics images with imprecise knowledge of the point spread function: results on astronomical objects,” in Astronomy with Adaptive Optics: Present Results and Future Programs, D. Bonaccini, ed., (European Southern Observatory, Garching, Germany, 1999), pp. 121–132.

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).

T. Marais, V. Michau, G. Fertin, J. Primot, J. C. Fontanella, “Deconvolution from wavefront sensing on a 4 m telescope,” in High-Resolution Imaging by Interferometry II, J. M. Beckers, F. Merkle, eds., (European Southern Observatory, Garching, Germany, 1992), pp. 589–597.

F. Roddier, “Passive versus active methods in optical interferometry,” in High-Resolution Imaging by Interferometry Part II, F. Merkle, ed., (European Southern Observatory, Garching, Germany, 1988), pp. 565–574.

M. C. Roggemann, C. A. Hyde, B. M. Welsh, “Fourier phase spectrum estimation using deconvolution from wavefront sensing and bispectrum reconstruction,” in Adaptive Optics, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 133–135.

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Figures (6)

Fig. 1
Fig. 1

Original object (SPOT satellite, left) one of the 100 turbulent PSF’s (D/r0=10, center) and corresponding noisy image (flux of 104 photons, right).

Fig. 2
Fig. 2

Restored object with conventional method (MAP wave-front estimation followed by a multiframe Wiener filter, left), to be compared with the restored object by myopic deconvolution (right). In both cases the same Gaussian prior is used for the object. The MSE is 0.48 photon (left) and 0.45 photon (right).

Fig. 3
Fig. 3

Restored object with conventional method (left): MAP wave-front estimation followed by a multiframe edge-preserving restoration. Restored object by myopic deconvolution (right). In both cases the same edge-preserving prior is used for the object, with an additional positivity constraint. The MSE is 0.45 photon (left) and 0.39 photon (right).

Fig. 4
Fig. 4

Comparison of the reconstructed phase errors, as a function the Zernike mode radial degree, for the conventional (MAP) and the myopic (join MAP) restoration schemes. The turbulent-phase variance is shown for comparison (dashed line).

Fig. 5
Fig. 5

Experimental short-exposure image of Capella taken on November 8, 1990 (left); corresponding long exposure (average of ten short exposures, right).

Fig. 6
Fig. 6

Restored object with conventional methods: MAP wave-front estimation followed by a multiframe Wiener filter (left); MAP wave-front estimation followed by a quadratic restoration with a positivity constraint (center), to be compared with the object restored by the myopic deconvolution (right), with use of the same quadratic regularization and the same positivity constraint.

Tables (1)

Tables Icon

Table 1 Block Diagram of the Algorithm Used for Myopic Deconvolution from Wave-Front Sensing

Equations (27)

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

it=oht+nt,1tM,
ht=|FT-1[P exp(jφt)]|2,
φt(r)=kϕtkZk(r),
it=oht+nt=Hto+nt,
st=Dϕt+nt,
ϕˆ=(DTD)-1DTs.
JMAPϕ=Js+Jϕ,
Js=12(s-Dϕ)TCn-1(s-Dϕ),
Jϕ=12ϕTCϕ-1ϕ.
ϕˆMAP=(DTCn-1D+Cϕ-1)-1DTCn-1s.
ϕˆMAP=CϕDT(DCϕDT+Cn)-1s.
p(o|{it}t=1M, {ϕt}t=1M)p({it}t=1M|o, {ϕt}t=1M)×p(o).
JMAPo(o)=t=1MJi(o; ϕt, it)+Jo(o),
Ji(o; ϕt, it)=-ln p(it|o, ϕt),
Jo(o)=-ln p(o).
Ji(o; ϕ, i)=12(ho-i)TCn-1(ho-i),
Ji(o; ϕ, i)=12σn2ho-i)2=12σm2l,m|[ho](l, m)-i(l, m)|2.
Jo(o)=μδ2l,mo(l, m)δ-ln1+o(l, m)δ,
p(o, {ϕt}t=1M|{it}t=1M, {st}t=1M)p({it}t=1M, {st}t=1M|o, {ϕt}t=1M)×p(o)×p({ϕt}t=1M)t=1Mp(it|o, ϕt)×p(o)×t=1Mp(st|ϕt)×t=1Mp(ϕt).
JMAP(o, {ϕt})=t=1MJi(o, ϕt; it)+Jo(o)+t=1MJs(ϕt; st)+t=1MJϕ(ϕt),
dJido=1σn2HtT(Hto-it)=1σn2FT-1(h˜t*(h˜to˜-i˜t)),
dJidht=1σn2FT-1(o˜*(h˜to˜-i˜t)).
dJidφt(l, m)=2AIP(l, m)exp[-jφt(l, m)]×FTdJidhtP exp(jφt)(l, m),
dJidϕtk=l,md Jidφt(l, m)Zk(l, m)=2Al,mZk(l, m)IP(l, m) exp[-jφt(l, m)]×FTdJidhtP exp(jφt)(l, m).
dJodo=μxTxo1+(xo)2+(yo)2/δ+yTyo1+(xo)2+(yo)2/δ,
dJsdϕt=1σn2DT(Dϕt-st).
dJϕdϕt=Cϕ-1ϕt.

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