Advertisement

Multiple Image Deblurring with High Dynamic-Range Poisson Data

  • Marco PratoEmail author
  • Andrea La Camera
  • Carmelo Arcidiacono
  • Patrizia Boccacci
  • Mario Bertero
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 36)

Abstract

An interesting problem arising in astronomical imaging is the reconstruction of an image with high dynamic range, for example a set of bright point sources superimposed to smooth structures. A few methods have been proposed for dealing with this problem and their performance is not always satisfactory. In this paper we propose a solution based on the representation, already proposed elsewhere, of the image as the sum of a pointwise component and a smooth one, with different regularization for the two components. Our approach is in the framework of Poisson data and to this purpose we need efficient deconvolution methods. Therefore, first we briefly describe the application of the Scaled Gradient Projection (SGP) method to the case of different regularization schemes and subsequently we propose how to apply these methods to the case of multiple image deconvolution of high-dynamic range images, with specific reference to the Fizeau interferometer LBTI of the Large Binocular Telescope (LBT). The efficacy of the proposed methods is illustrated both on simulated images and on real images, observed with LBTI, of the Jovian moon Io. The software is available at http://www.oasis.unimore.it/site/home/software.html.

Keywords

Deconvolution Numerical optimization Image reconstruction 

Notes

Acknowledgements

We thank Al Conrad, LBTO, for permission of using images of Io at M-band, observed with LBTI/LMIRcam [32, 45] during UT 2013 December 24 [21, 37]. Marco Prato is a member of the INdAM Research group GNCS, which is kindly acknowledged.

References

  1. 1.
    Anconelli, B., Bertero, M., Boccacci, P., Carbillet, M., Lantéri, H.: Reduction of boundary effects in multiple image deconvolution with an application to LBT LINC-NIRVANA. Astron. Astrophys. 448, 1217–1224 (2006)CrossRefGoogle Scholar
  2. 2.
    Bardsley, J.M., Goldes, J.: Regularization parameter selection methods for ill-posed poisson maximum likelihood estimation. Inverse Probl. 25, 095,005 (2009)Google Scholar
  3. 3.
    Barzilai, J., Borwein, J.M.: Two-point step size gradient methods. IMA J. Numer. Anal. 8(1), 141–148 (1988)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Benfenati, A., Ruggiero, V.: Inexact bregman iteration with an application to poisson data reconstruction. Inverse Probl. 29, 065,016 (2013)Google Scholar
  5. 5.
    Bertero, M., Boccacci, P.: Introduction to Inverse Problems in Imaging. IoP Publishing, Bristol (1998)CrossRefGoogle Scholar
  6. 6.
    Bertero, M., Boccacci, P.: A simple method for the reduction of boundary effects in the Richardson-Lucy approach to image deconvolution. Astron. Astrophys. 437, 369–374 (2005)CrossRefGoogle Scholar
  7. 7.
    Bertero, M., Boccacci, P., Desiderà, G., Vicidomini, G.: Image deblurring with Poisson data: from cells to galaxies. Inverse Probl. 25(12), 123,006 (2009)Google Scholar
  8. 8.
    Bertero, M., Boccacci, P., La Camera, A., Olivieri, C., Carbillet, M.: Imaging with LINC-NIRVANA, the Fizeau interferometer of the Large Binocular Telescope: state of the art and open problems. Inverse Probl. 27(11), 113,011 (2011)Google Scholar
  9. 9.
    Bertero, M., Boccacci, P., Talenti, G., Zanella, R., Zanni, L.: A discrepancy principle for Poisson data. Inverse Probl. 26(10), 10,500 (2010)Google Scholar
  10. 10.
    Bertsekas, D.: Nonlinear Programming. Athena Scientific, Belmont (1999)zbMATHGoogle Scholar
  11. 11.
    Bonettini, S., Landi, G., Loli Piccolomini, E., Zanni, L.: Scaling techniques for gradient projection-type methods in astronomical image deblurring. Int. J. Comput. Math. 90(1), 9–29 (2013)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Bonettini, S., Prato, M.: Nonnegative image reconstruction from sparse Fourier data: a new deconvolution algorithm. Inverse Probl. 26(9), 095,001 (2010)Google Scholar
  13. 13.
    Bonettini, S., Prato, M.: New convergence results for the scaled gradient projection method. Inverse Probl. 31(9), 095,008 (2015)Google Scholar
  14. 14.
    Bonettini, S., Ruggiero, V.: On the uniqueness of the solution of image reconstruction problems with Poisson data. In: Simos, T.E., Psihoyios, G., Tsitouras, C. (eds.), International Conference of Numerical Analysis and Applied Mathematics 2010, AIP Conference Proceedings, vol. 1281, pp. 1803–1806 (2010)Google Scholar
  15. 15.
    Bonettini, S., Ruggiero, V.: An alternating extragradient method for total variation-based image restoration. Inverse Problems 27, 095,001 (2011)Google Scholar
  16. 16.
    Bonettini, S., Zanella, R., Zanni, L.: A scaled gradient projection method for constrained image deblurring. Inverse Probl. 25(1), 015,002 (2009)Google Scholar
  17. 17.
    Byrne, C.L.: Iterative image reconstruction algorithms based on cross-entropy minimization. IEEE Trans. Image Proc. 2(1), 96–103 (1993)CrossRefGoogle Scholar
  18. 18.
    Carasso, A.S.: Linear and nonlinear image deblurring: a documented study. SIAM J. Numer. Anal. 36(6), 1659–1689 (1999)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Carbillet, M., La Camera, A., Deguignet, J., Prato, M., Bertero, M., Aristidi, E., Boccacci, P.: Strehl-constrained reconstruction of post-adaptive optics data and the Software Package AIRY, v. 6.1. In: Marchetti, E., Close, L.M., Véran, J.P. (eds.), Adaptive Optics Systems IV. Proceedings of SPIE, vol. 9148, p. 91484U (2014)Google Scholar
  20. 20.
    Charbonnier, P., Blanc-Féraud, L., Aubert, G., Barlaud, M.: Deterministic edge-preserving regularization in computed imaging. IEEE T. Image Process. 6, 298–311 (1997)CrossRefGoogle Scholar
  21. 21.
    Conrad, A., de Kleer, K., Leisenring, J., La Camera, A., Arcidiacono, C., Bertero, M., Boccacci, P., Defrère, D., de Pater, I., Hinz, P., Hofmann, K.H., Kürster, M., Rathbun, J., Schertl, D., Skemer, A., Skrutskie, M., Spencer, J., Veillet, C., Weigelt, G., Woodward, C.E.: Spatially Resolved M-Band Emission from Io’s Loki Patera-Fizeau Imaging at the 22.8m LBT. Astron. J. 149(5), 1–9 (2015)Google Scholar
  22. 22.
    Cornelio, A., Porta, F., Prato, M.: A convergent least-squares regularized blind deconvolution approach. Appl. Math. Comput. 259(12), 173–186 (2015)MathSciNetzbMATHGoogle Scholar
  23. 23.
    Correia, S., Carbillet, M., Boccacci, P., Bertero, M., Fini, L.: Restoration of interferometric images: I. the software package AIRY. Astron. Astrophys. 387, 733–743 (2002)Google Scholar
  24. 24.
    Csiszár, I.: Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems. Ann. Stat. 19(4), 2032–2066 (1991)MathSciNetCrossRefGoogle Scholar
  25. 25.
    De Mol, C., Defrise, M.: Inverse imaging with mixed penalties. In: Proceedings of the International Symposium on Electromagnetic Theory, pp. 798–800. Pisa, Italy (2004)Google Scholar
  26. 26.
    Engl, H.W., Hanke, M., Neubauer, A.: Regularization of Inverse Problems. Kluver Academic Publishers, Dordrecht (1996)CrossRefGoogle Scholar
  27. 27.
    Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6(6), 721–741 (1984)CrossRefGoogle Scholar
  28. 28.
    Giovannelli, J.F., Coulais, A.: Positive deconvolution for superimposed extended source and point sources. Astron. Astrophys. 439, 401–412 (2005)CrossRefGoogle Scholar
  29. 29.
    Herbst, T., Ragazzoni, R., Andersen, D., Boehnhardt, H., Bizenberger, P., Eckart, A., Gaessler, W., Rix, H.W., Rohloff, R.R., Salinari, P., Soci, R., Straubmeier, C., Xu, W.: LINC-NIRVANA: a fizeau beam combiner for the large binocular telescope. In: W.A. Traub (ed.), Interferometry for Optical Astronomy II. Proceedings of SPIE, vol. 4838, pp. 456–465 (2003)Google Scholar
  30. 30.
    Herbst, T.M., Santhakumari, K.K.R., Klettke, M., Arcidiacono, C., Bergomi, M., Bertram, T., Berwein, J., Bizenberger, P., Briegel, F., Farinato, J., Marafatto, L., Mathar, R., McGurk, R., Ragazzoni, R., Viotto, V.: Commissioning multi-conjugate adaptive optics with LINC-NIRVANA on LBT. In: Adaptive Optics Systems VI. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 10703, p. 107030B (2018).  https://doi.org/10.1117/12.2313421
  31. 31.
    Hill, J.M., Green, R.F., Slagle, J.H.: The large binocular telescope. In: Ground-based and Airborne Telescopes. Proceedings of SPIE, vol. 6267, p. 62670Y (2006)Google Scholar
  32. 32.
    Hinz, P., Bippert-Plymate, T., Breuninger, A., Connors, T., Duffy, B., Esposito, S., Hoffmann, W., Kim, J., Kraus, J., McMahon, T., Montoya, M., Nash, R., Durney, O., Solheid, E., Tozzi, A., Vaitheeswaran, V.: Status of the LBT interferometer. In: Optical and Infrared Interferometry. Proceedings of SPIE, vol. 7013, p. 701328 (2008)Google Scholar
  33. 33.
    Hom, E.F.Y., Marchis, F., Lee, T.K., Haase, S., Agard, D.A., Sedat, J.W.: Aida: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data. J. Opt. Soc. Am. A-24, 1580–1600 (1994)Google Scholar
  34. 34.
    Jefferies, S.M., Christou, J.C.: Restoration of astronomical images by iterative blind deconvolution. Astron. J. 415, 609–862 (1993)CrossRefGoogle Scholar
  35. 35.
    La Camera, A., Antonucci, S., Bertero, M., Boccacci, P., Lorenzetti, D., Nisini, B.: Image reconstruction for observations with a high dynamic range: LINC-NIRVANA simulations of a stellar jet. In: Delplancke, F., Rajagopal, F.J.K., Malbet, F. (eds.) Optical and Infrared Interferometry III. Proceedings of SPIE, vol. 8455, p. 84553D (2012)Google Scholar
  36. 36.
    Lantéri, H., Roche, M., Aime, C.: Penalized maximum likelihood image restoration with positivity constraints: multiplicative algorithms. Inverse Probl. 18(5), 1397–1419 (2002)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Leisenring, J.M., Hinz, P.M., Skrutskie, M.F., Skemer, A., Woodward, C.E., Veillet, C., Arcidiacono, C., Bailey, V., Bertero, M., Boccacci, P., Conrad, A., de Kleer, K., de Pater, I., Defrère, D., Hill, J., Hofmann, K.H., Kaltenegger, L., La Camera, A., Nelson, M.J., Schertl, D., Spencer, J., Weigelt, G., Wilson, J.C.: Fizeau interferometric imaging of Io volcanism with LBTI/LMIRcam. In: Optical and Infrared Interferometry IV. Proceedings of SPIE, vol. 9146, p. 91462S (2014)Google Scholar
  38. 38.
    Mugnier, L.M., Fusco, T., Conan, J.M.: Mistral: a myopic edge-preserving image restoration method, with application to astronomical adaptive-optics-corrected long-exposure images. J. Opt. Soc. Am. A-21(4), 1841–1854 (2004)Google Scholar
  39. 39.
    Porta, F., Prato, M., Zanni, L.: A new steplength selection for scaled gradient methods with application to image deblurring. J. Sci. Comput. 65(3), 895–919 (2015)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Porta, F., Zanella, R., Zanghirati, G., Zanni, L.: Limited-memory scaled gradient projection methods for real-time image deconvolution in microscopy. Commun. Nonlinear Sci. Numer. Simul. 21(1–3), 112–127 (2015)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Prato, M., Cavicchioli, R., Zanni, L., Boccacci, P., Bertero, M.: Efficient deconvolution methods for astronomical imaging: algorithms and IDL-GPU codes. Astron. Astrophys. 539, A133 (2012)CrossRefGoogle Scholar
  42. 42.
    Prato, M., La Camera, A., Bonettini, S., Bertero, M.: A convergent blind deconvolution method for post-adaptive-optics astronomical imaging. Inverse Probl. 29(6), 065,017 (2013)Google Scholar
  43. 43.
    Prato, M., La Camera, A., Bonettini, S., Rebegoldi, S., Bertero, M., Boccacci, P.: A blind deconvolution method for ground based telescopes and fizeau interferometers. New Astron. 40, 1–13 (2015)CrossRefGoogle Scholar
  44. 44.
    Skilling, J., Bryan, R.K.: Maximum entropy image reconstruction: general algorithm. Mon. Not. R. Astr. Soc. 211, 111–124 (1984)CrossRefGoogle Scholar
  45. 45.
    Skrutskie, M.F., Jones, T., Hinz, P., Garnavich, P., Wilson, J., Nelson, M., Solheid, E., Durney, O., Hoffmann, W.F., Vaitheeswaran, V., McMahon, T., Leisenring, J., Wong, A., Garnavic, P., Wilson, J., Nelson, M., Sollheid, E., Durney, O., Hoffmann, W.F., Vaitheeswaran, V., McMahon, T., Leisenring, J., Wong, A.: The Large Binocular Telescope mid-infrared camera (LMIRcam): final design and status. In: McLean, I.S., Ramsay, S.K., Takami, H. (eds.) Ground-based and Airborne Instrumentation for Astronomy III. Proceedings of SPIE, vol. 7735, p. 77353H (2010).  https://doi.org/10.1117/12.857615. http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=750817
  46. 46.
    Snyder, D.L., Hammoud, A.M., White, R.L.: Image recovery from data acquired with a charge-coupled-device camera. J. Opt. Soc. Am. A 10(5), 1014–1023 (1994)CrossRefGoogle Scholar
  47. 47.
    Snyder, D.L., Helstrom, C.W., Lanterman, A.D., Faisal, M., White, R.L.: Compensation for readout noise in CCD images. J. Opt. Soc. Am. A 12(2), 272–283 (1995)CrossRefGoogle Scholar
  48. 48.
    Titterington, D.: On the iterative image space reconstruction algorithm for ECT. IEEE Trans. Med. Imaging 6(1), 52–56 (1987)CrossRefGoogle Scholar
  49. 49.
    Vio, R., Bardsley, J., Wamsteher, W.: Least-squares methods with poissonian noise: analysis and comparison with the richardson-lucy algorithm. Astron. Astrophys. 436(2), 741–755 (2005)CrossRefGoogle Scholar
  50. 50.
    Zanella, R., Boccacci, P., Zanni, L., Bertero, M.: Efficient gradient projection methods for edge-preserving removal of Poisson noise. Inverse Probl. 25(4), 045,010 (2009)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Marco Prato
    • 1
    Email author
  • Andrea La Camera
    • 2
  • Carmelo Arcidiacono
    • 3
  • Patrizia Boccacci
    • 2
  • Mario Bertero
    • 2
  1. 1.Dipartimento di Scienze Fisiche, Informatiche e MatematicheUniversità di Modena e Reggio EmiliaModenaItaly
  2. 2.Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi (DIBRIS)Università di GenovaGenovaItaly
  3. 3.Osservatorio Astronomico di PadovaIstituto Nazionale di AstrofisicaPadovaItaly

Personalised recommendations