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Image Reconstruction in Optical Interferometry: An Up-to-Date Overview

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Astronomy at High Angular Resolution

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 439))

Abstract

Optical interferometry is now routinely used to image stars and their environments with sub-milliarcsecond resolution. We present here a brief review of model-independent interferometric imaging, discussing the most recent advances in regularisation , optimisation algorithms , and imaging procedures with minimal formalism.

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References

  1. Baldwin, J., Beckett, M., Boysen, R.C., et al.: The first images from an optical aperture synthesis array: mapping of Capella with COAST at two epochs. A&A 306, L13 (1996)

    ADS  Google Scholar 

  2. Baron, F., Cotton, W.D., Lawson, P.R., et al.: The 2012 interferometric imaging beauty contest. Proc. SPIE 8445, 1 (2012)

    Google Scholar 

  3. Baron, F., Monnier, J., Young, J., Buscher, D.: New theoretical frameworks for interferometric imaging. In: Creech-Eakman, M.J., Guzik, J.A., Stencel, R.E. (eds.) Resolving the Future of Astronomy with Long-Baseline Interferometry. ASP Conference Series, vol. 487, p. 229. Astronomical Society of the Pacific, San Francisco (2014)

    Google Scholar 

  4. Baron, F., Monnier, J.D., Kiss, L.L., et al.: CHARA/MIRC observations of Two M supergiants in perseus OB1: temperature, bayesian modeling, and compressed sensing imaging. ApJ 785, 46 (2014)

    Article  ADS  Google Scholar 

  5. Baron, F., Monnier, J.D., Pedretti, E., et al.: Imaging the algol triple system in the H band with the CHARA interferometer. ApJ 752, 20 (2012)

    Article  ADS  Google Scholar 

  6. Baron, F., Young, J.S.: Image reconstruction at Cambridge University. Proc. SPIE 7013, 70133X (2008)

    Article  ADS  Google Scholar 

  7. Baron, F., Monnier, J., Kloppenborg, B.: A novel image reconstruction software for optical/infrared interferometry. Proc. SPIE 7734, 77342I (2010)

    Article  ADS  Google Scholar 

  8. Benisty, M., Renard, S., Natta, A., et al.: A low optical depth region in the inner disk of the Herbig Ae star HR 5999. A&A 531, A84 (2011)

    Article  ADS  Google Scholar 

  9. van den Berg, E., Friedlander, M.P.: Probing the Pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 31, 890 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Berger, J., Malbet, F., Baron, F., et al.: Imaging the heart of astrophysical objects with infrared interferometry. A&ARA 20, 53 (2012)

    Article  ADS  Google Scholar 

  11. Bhatnagar, S., Cornwell, T.J.: Scale sensitive deconvolution of interferometric images I. Adaptive Scale Pixel (ASP) decomposition. A&A 426, 747 (2004)

    Google Scholar 

  12. Blind, N., Boffin, H.M.J., Berger, J.P., et al.: An incisive look at the symbiotic star SS Leporis. A&A 536, A55 (2011)

    Article  ADS  Google Scholar 

  13. Bredies, K., Kunisch, K., Pock, T.: Total generalized variation. SIAM J. Imaging Sci. 3, 492 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Buscher, D.F.: Direct maximum-entropy image reconstruction from the bispectrum. In: Robertson, J.G., Tango, W.J. (eds.) IAU Symposium on Very High Angular Resolution Imaging, Sydney vol. 158, p. 91 (1994)

    Google Scholar 

  15. Cabrera, G.F., Casassus, S., Hitschfeld, N.: Bayesian image reconstruction based on Voronoi diagrams. ApJ 672, 1272 (2008)

    Article  ADS  Google Scholar 

  16. Candès, E., Romberg, J.: Sparsity and incoherence in compressive sampling. Inverse Probl. 23, 969 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Candès, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52, 489 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Carrillo, R.E., McEwen, J.D., Wiaux, Y.: Sparsity Averaging Reweighted Analysis (SARA): a novel algorithm for radio-interferometric imaging. MNRAS 426, 1223 (2012)

    Article  ADS  Google Scholar 

  19. Carrillo, R.E., McEwen, J.D., Wiaux, Y.: PURIFY: a new approach to radio-interferometric imaging. MNRAS 439, 3591 (2014)

    Article  ADS  Google Scholar 

  20. Chartrand, R., Staneva, V.: Restricted isometry properties and nonconvex compressive sensing. Inverse Probl. 24, 1 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  21. Che, X., Monnier, J.D., Zhao, M., Pedretti, E., Thureau, N., Mérand, A., ten Brummelaar, T., McAlister, H., Ridgway, S.T., Turner, N., Sturmann, J., Sturmann, L.: Colder and Hotter: Interferometric imaging of β Cassiopeiae and α Leonis. ApJ 732, 68 (2011)

    Article  ADS  Google Scholar 

  22. Chen, S., Donoho, D., Saunders, M.: Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20, 33 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  23. Cornwell, T.: Multiscale CLEAN deconvolution of radio synthesis images. IEEE Sel. Topics Signal Process. 2, 793 (2008)

    Article  ADS  Google Scholar 

  24. Cotton, W., Monnier, J., Baron, F., et al.: 2008 imaging beauty contest. Proc. SPIE 7013, 70131N (2008)

    Article  Google Scholar 

  25. Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc.: Ser. B 39, 1 (1977)

    Google Scholar 

  26. Donoho, D., Elad, M., Temlyakov, V.: Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inf. Theory 52, 6 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  27. Donoho, D., Johnstone, I., Hoch, J., Stern, A.: Maximum entropy and the nearly black object. J. R. Stat. Soc. Ser. B (Methodol.) 54, 41 (1992)

    Google Scholar 

  28. Gull, S.F.: Development in Maximum Entropy data analysis. In: Fougére, P.F. (ed.) Maximum Entropy and Bayesian Methods. vol. 5491, pp. 53–71. Kluwer Academic, Dordrecht (1990)

    Google Scholar 

  29. Hanbury Brown, R., Davis, J., Allen, L.R.: The angular diameters of 32 stars. MNRAS 167, 121 (1974)

    Article  ADS  Google Scholar 

  30. Haniff, C.A.: Least-squares Fourier phase estimation from the modulo 2pi bispectrum phase. J. Opt. Soc. Am. A 8, 134 (1991)

    Article  ADS  Google Scholar 

  31. Haniff, C.A., Mackay, C.D., Titterington, D.J., Sivia, D., Baldwin, J.E.: The first images from optical aperture synthesis. Nature 328, 694 (1987)

    Article  ADS  Google Scholar 

  32. Haubois, X., Perrin, G., Lacour, S., et al.: Imaging the spotty surface of Betelgeuse in the H band. A&A 508, 923 (2009)

    Article  ADS  Google Scholar 

  33. Hofmann, K.H., Weigelt, G., Schertl, D.: An image reconstruction method (IRBis) for optical/infrared interferometry. A&A 565, A48 (2014)

    Article  ADS  Google Scholar 

  34. Hofmann, K., Weigelt, G.: Iterative image reconstruction from the bispectrum. A&A 278, 328 (1993)

    ADS  Google Scholar 

  35. Ireland, M.J., Monnier, J.D., Thureau, N.: Monte-Carlo imaging for optical interferometry. Proc. SPIE 6268, 62681T (2006)

    Article  ADS  Google Scholar 

  36. Kloppenborg, B., Stencel, R., Monnier, J.D., et al.: Infrared images of the transiting disk in the ε Aurigae system. Nature 464, 870 (2010)

    Article  ADS  Google Scholar 

  37. Kluska, J., Malbet, F., Berger, J.P., et al.: SPARCO: a semi-parametric approach for image reconstruction of chromatic objects. Application to young stellar objects. A&A 564, A80 (2014)

    Google Scholar 

  38. Kraus, S., Hofmann, K.H., Menten, K.M., et al.: A hot compact dust disk around a massive young stellar object. Nature 466, 339 (2010)

    Article  ADS  Google Scholar 

  39. Labeyrie, A.: Interference fringes obtained on VEGA with two optical telescopes. ApJ 196, L71 (1975)

    Article  ADS  Google Scholar 

  40. Lannes, A.: Integer ambiguity resolution in phase closure imaging. J. Opt. Soc. Am. A 18, 1046 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  41. Lawson, P.R., Cotton, W.D., Hummel, C.A., et al.: 2006 interferometry imaging beauty contest. Proc. SPIE 6268 (2006)

    Google Scholar 

  42. Lawson, P.R., Cotton, W.D., Hummel, C.A., Monnier, J.D., Zhao, M., Young, J.S., Thorsteinsson, H., Meimon, S.C., Mugnier, L., Le Besnerais, G., Thiebaut, E., Tuthill, P.G.: The 2004 Optical/IR Interferometry Imaging Beauty Contest. BAAS 36, 1605 (2004)

    ADS  Google Scholar 

  43. Le Besnerais, G., Lacour, S., Mugnier, L.M., Thiebaut, E., Perrin, G., Meimon, S.: Advanced imaging methods for long-baseline optical interferometry. IEEE J. Sel. Top. Signal Process. 2, 767 (2008)

    Article  ADS  Google Scholar 

  44. Li, F., Cornwell, T.J., de Hoog, F.: The application of compressive sampling to radio astronomy. A&A 528, A31 (2011)

    Article  ADS  Google Scholar 

  45. Malbet, F., Cotton, W., Duvert, G., Lawson, P.: The 2010 interferometric imaging beauty contest. Proc. SPIE 7734, 12 (2010)

    Google Scholar 

  46. Meimon, S., Mugnier, L.M., Le Besnerais, G.: Convex approximation to the likelihood criterion for aperture synthesis imaging. J. Opt. Soc. Am. A 22, 2348 (2005)

    Article  ADS  Google Scholar 

  47. Meimon, S., Mugnier, L.M., Le Besnerais, G.: Self-calibration approach for optical long-baseline interferometry imaging. J. Opt. Soc. Am. A 26, 108 (2008)

    Article  ADS  Google Scholar 

  48. Millour, F., Meilland, A., Chesneau, O., Stee, P., Kanaan, S., Petrov, R., Mourard, D., Kraus, S.: Imaging the spinning gas and dust in the disc around the supergiant A[e] star HD 62623. A&A 526, A107 (2011)

    Article  ADS  Google Scholar 

  49. Millour, F., Petrov, R.G., Vannier, M., Kraus, S.: AMBER closure and differential phases: accuracy and calibration with a beam commutation. Proc. SPIE 7013, 1 (2008)

    Google Scholar 

  50. Monnier, J.D.: Astrophysics with closure phases. In: Perrin, G., Malbet, F. (eds.) EAS Publications Series, vol. 6, p. 213. EDP Sciences, Les Ulis (2003)

    Google Scholar 

  51. Monnier, J.D., Berger, J.P., Le Bouquin, J.B., et al.: The 2014 interferometric imaging beauty contest. Proc. SPIE 9146, 1 (2014)

    Google Scholar 

  52. Monnier, J.D., Berger, J., Millan-Gabet, R., et al.: Few skewed disks found in first closure-phase survey of Herbig Ae/Be stars. ApJ 647, 444 (2006)

    Article  ADS  Google Scholar 

  53. Monnier, J.D., Che, X., Zhao, M., Ekström, S., Maestro, V., Aufdenberg, J., Baron, F., Georgy, C., Kraus, S., McAlister, H., Pedretti, E., Ridgway, S., Sturmann, J., Sturmann, L., ten Brummelaar, T., Thureau, N., Turner, N., Tuthill, P.G.: Resolving Vega and the inclination controversy with CHARA/MIRC. ApJL 761, L3 (2012)

    Article  ADS  Google Scholar 

  54. Monnier, J.D., Zhao, M., Pedretti, E., Thureau, N., Ireland, M., Muirhead, P., Berger, J.P., Millan-Gabet, R., Van Belle, G., ten Brummelaar, T., McAlister, H., Ridgway, S., Turner, N., Sturmann, L., Sturmann, J., Berger, D.: Imaging the surface of Altair. Science 317, 342 (2007)

    Article  ADS  Google Scholar 

  55. Parks, J.R., White, R.J., Schaefer, G.H., Monnier, J.D., Henry, G.W., McAlister, H.A., ten Brummelaar, T.A.: Starspot Imaging with the CHARA Array. In: Creech-Eakman, M.J., Guzik, J.A., Stencel, R.E. (eds.) Resolving The Future Of Astronomy With Long-Baseline Interferometry. ASP Conference Series, vol. 487, p. 345. Astronomical Society of the Pacific, San Francisco (2014)

    Google Scholar 

  56. Pauls, T.A., Young, J.S., Cotton, W.D., Monnier, J.D.: A data exchange standard for optical (Visible/IR) Interferometry. PASP 117, 1255 (2005)

    Article  ADS  Google Scholar 

  57. Pearson, T.J., Readhead, A.C.S.: Image formation by self-calibration in radio astronomy. ARAA 22, 97 (1984)

    Article  ADS  Google Scholar 

  58. Rau, U., Cornwell, T.J.: A multi-scale multi-frequency deconvolution algorithm for synthesis imaging in radio interferometry. A&A 532, A71 (2011)

    Article  ADS  Google Scholar 

  59. Renard, S., Malbet, F., Benisty, M., Thiébaut, E., Berger, J.P.: Milli-arcsecond images of the Herbig Ae star HD 163296. A&A 519, A26 (2010)

    Article  ADS  Google Scholar 

  60. Renard, S., Thiébaut, E., Malbet, F.: Image reconstruction in optical interferometry: benchmarking the regularisation. A&A 533, A64 (2011)

    Article  ADS  Google Scholar 

  61. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D: Nonlinear Phenom. 60, 259 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  62. Schutz, A., Ferrari, A., Mary, D., Thiébaut, E., Soulez, F.: Large scale 3D image reconstruction in optical interferometry. ArXiv e-prints (2015)

    Google Scholar 

  63. Schutz, A., Ferrari, A., Mary, D., Soulez, F., Thiébaut, E., Vannier, M.: Painter: a spatiospectral image reconstruction algorithm for optical interferometry. J. Opt. Soc. Am. A 31, 2334 (2014)

    Article  ADS  Google Scholar 

  64. Schutz, A., Vannier, M., Mary, D., Ferrari, A., Millour, F., Romain, P.: Statistical characterization of polychromatic absolute and differential squared visibilities obtained from amber/vlti instrument. A&A 565, A88 (2014)

    Article  ADS  Google Scholar 

  65. Skilling, J.: Quantified maximum entropy. In: Fougére, P.F. (ed.) Maximum Entropy and Bayesian Methods, vol. 5491, pp. 341–350. Kluwer Academic, Dordrecht (1990)

    Chapter  Google Scholar 

  66. Starck, J.L., Bijaoui, A., Lopez, B., Perrier, C.: Image reconstruction by the wavelet transform applied to aperture synthesis. A&A 283, 349 (1994)

    ADS  Google Scholar 

  67. Starck, J.L., Fadili, J., Murtagh, F.: The undecimated wavelet decomposition and its reconstruction. IEEE Trans. Image Process. 16, 297 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  68. Strong, D., Chan, T.: Edge-preserving and scale-dependent properties of total variation regularisation. Inverse Probl. 19, S165 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  69. Tannirkulam, A., Monnier, J.D., Harries, T.J., Millan-Gabet, R., Zhu, Z., Pedretti, E., Ireland, M., Tuthill, P., ten Brummelaar, T., McAlister, H., Farrington, C., Goldfinger, P.J., Sturmann, J., Sturmann, L., Turner, N.: A Tale of Two Herbig Ae Stars, MWC 275 and AB Aurigae: comprehensive models for spectral energy distribution and interferometry. ApJ 689, 513 (2008)

    Article  ADS  Google Scholar 

  70. Taubman, D.S., Marcellin, M.W.: JPEG2000: image compression fundamentals, standards, and practice. Kluwer Academic, Boston (2002)

    Book  Google Scholar 

  71. Thiébaut, E.: Optimisation issues in blind deconvolution algorithms. Proc. SPIE 4847, 174 (2002)

    Article  ADS  Google Scholar 

  72. Thiébaut, E.: MIRA: an effective imaging algorithm for optical interferometry. Proc. SPIE 7013, 70131I (2008)

    Article  Google Scholar 

  73. Thiébaut, É.: Principles of Image Reconstruction in Interferometry. In: Mary, D., Theys, C., Aime, C. (eds.) EAS Publications Series, vol. 59, pp. 157–187. EDP Sciences, Les Ulis (2013)

    Google Scholar 

  74. Thiébaut, E., Giovannelli, J.F.: Image reconstruction in optical interferometry. IEEE Signal Proc. Mag. 27, 97 (2010)

    Article  ADS  Google Scholar 

  75. Thiébaut, É., Soulez, F., Denis, L.: Exploiting spatial sparsity for multiwavelength imaging in optical interferometry. J. Opt. Soc. Am. A 30, 160 (2013)

    Article  ADS  Google Scholar 

  76. Titterington, D.M.: General structure of regularisation procedures in image reconstruction. A&A 144, 381 (1985)

    ADS  MathSciNet  Google Scholar 

  77. Vannier, M., Mary, D., Millour, F., Petrov, R.G., Bourguignon, S., Theys, C.: Spectral regularisation and sparse representation bases for interferometric imaging. Proc. SPIE 7734, 2 (2010)

    Google Scholar 

  78. Wiaux, Y., Jacques, L., Puy, G., Scaife, A.M.M., Vandergheynst, P.: Compressed sensing imaging techniques for radio interferometry. MNRAS 395, 1733 (2009)

    Article  ADS  Google Scholar 

  79. Young, J.S., Baldwin, J.E., Boysen, R.C., Haniff, C.a., Lawson, P.R., Mackay, C.D., Pearson, D., Rogers, J., St.-Jacques, D., Warner, P.J., Wilson, D.M.A., Wilson, R.W.: New views of Betelgeuse: multi-wavelength surface imaging and implications for models of hotspot generation. MNRAS 315, 635 (2000)

    Google Scholar 

  80. Zhao, M., Gies, D., Monnier, J., Thureau, N., Pedretti, E., Baron, F., Merand, A., ten Brummelaar, T., McAlister, H., Ridgway, S., Others: First resolved images of the eclipsing and interacting binary β Lyrae. ApJL 684, L95 (2008)

    Article  ADS  Google Scholar 

  81. Zhao, M., Monnier, J.D., ten Brummelaar, T., Pedretti, E., Thureau, N.D.: Exoplanet studies with CHARA-MIRC. Proc. SPIE 7013, 1 (2008)

    Google Scholar 

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Acknowledgements

My work on image reconstruction is partially supported by NSF-AST 1445935.

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Baron, F. (2016). Image Reconstruction in Optical Interferometry: An Up-to-Date Overview. In: Boffin, H., Hussain, G., Berger, JP., Schmidtobreick, L. (eds) Astronomy at High Angular Resolution. Astrophysics and Space Science Library, vol 439. Springer, Cham. https://doi.org/10.1007/978-3-319-39739-9_5

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