Application: Image Deblurring for Optical Imaging

Chapter
Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)

Abstract

The problem of reconstruction of digital images from their blurred and noisy measurements is unarguably one of the central problems in imaging sciences. Despite its ill-posed nature, this problem can often be solved in a unique and stable manner, provided appropriate assumptions on the nature of the images to be discovered.

Keywords

Mean Square Error Point Spread Function Compressed Sensing Atmospheric Turbulence Adaptive Optic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    J. Primot, G. Rousset, J.C. Fontanella, Deconvolution from wave-front sensing: A new technique for compensating turbulence-degraded images. J. Opt. Soc. Am. 7, 1598–1608 (1990)CrossRefGoogle Scholar
  2. 2.
    M.C. Roggemann, B.M. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, 1996)Google Scholar
  3. 3.
    J. Yang, J. Wright, T.S. Huang, Y. Ma, Image super-resolution via sparse representation. IEEE Trans. Image Processing 19, 2861–2873 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    M. Elad, M. Aharon, Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Processing 17, 3736–3745 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    I.J. Mairal, G. Sapiro, M. Elad, Learning multiscale sparse representations for image and video restoration. Multiscale Modeling and Simulation 7, 214–241 (2008)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    R.T. Paul, Review of robust video watermarking techniques. IJCA Special Issue on Computational Science 3, 90–95 (2011)Google Scholar
  7. 7.
    G.D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE Optical Engineering Press, Bellingham, Washington, 2001)CrossRefGoogle Scholar
  8. 8.
    R.T. Paul, Blind deconvolution via cumulant extrema. IEEE Signal Processing Magazine 3, 24–42 (1996)Google Scholar
  9. 9.
    D. Kundur, D. Hatzinakos, Blind image deconvolution. IEEE Signal Processing Magazine 3, 43–64 (1996)CrossRefGoogle Scholar
  10. 10.
    J.K. Kauppinen, D.J. Moffatt, H.H. Mantsch, D.G. Cameron, Fourier self-deconvolution: A method for resolving intrinsically overlapped bands. Applied Spectroscopy 35, 271–276 (1981)CrossRefGoogle Scholar
  11. 11.
    S. Geman and D. Geman. Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans. Pattern Analysis and Machine Intelligence, PAMI-6:721–741, 1984Google Scholar
  12. 12.
    T. Poggio, V. Torre, C. Koch, Computational vision and regularization theory. Nature 317, 314–319 (1985)CrossRefGoogle Scholar
  13. 13.
    L.I. Rudin, S. Osher, E. Fatemi, Nonlinear total variation based noise removal algorithms. Phys. D 60, 259–268 (November 1992)MATHCrossRefGoogle Scholar
  14. 14.
    A. Chambolle, An algorithm for total variation minimization and applications. Journal of Mathematical Imaging and Vision 20, 89–97 (2004)MathSciNetCrossRefGoogle Scholar
  15. 15.
    T. Goldstein, S. Osher, The split Bregman method for \(l_1\)-regularized problems. SIAM J. Img. Sci. 2, 323–343 (2009)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    A. Marquina, Nonlinear inverse scale space methods for total variation blind deconvolution. SIAM J. Img. Sci. 2, 64–83 (2009)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    L. He, A. Marquina, S. Osher, Blind deconvolution using TV regularization and Bregman iteration. International Journal of Imaging Systems and Technology 15, 74–83 (2005)CrossRefGoogle Scholar
  18. 18.
    O. Michailovich, A. Tannenbaum, Blind deconvolution of medical ultrasound images: Parametric inverse filtering approach. IEEE Trans. Image Processing 16(12), 3005–3019 (December 2007)MathSciNetCrossRefGoogle Scholar
  19. 19.
    W.H. Richardson, Bayesian-based iterative method of image restoration. J. Opt. Soc. Am. A 62(1), 55–59 (1972)CrossRefGoogle Scholar
  20. 20.
    L.B. Lucy, An iterative technique for the rectification of observed distributions. Astron. J. 79(6), 745–754 (1974)CrossRefGoogle Scholar
  21. 21.
    P.A. Jansson, Deconvolution of Images and Spectra. Opt. Eng. 36, 3224 (1997)Google Scholar
  22. 22.
    M. J. Cullum. Adaptive Optics. European Southern, Observatory, 1996Google Scholar
  23. 23.
    D. Dayton, B. Pierson, B. Spielbusch, J. Gonglewski, Atmospheric structure function measurements with a Shack-Hartmann wave-front sensor. Journal of Mathematical Imaging and Vision 20, 89–97 (2004)MathSciNetCrossRefGoogle Scholar
  24. 24.
    R.G. Lane, M. Tallon, Wave-front reconstruction using a Shack Hartmann sensor. Applied Optics 31, 6902–6908 (1992)CrossRefGoogle Scholar
  25. 25.
    R. Irwan, R.G. Lane, Analysis of optimal centroid estimation applied to Shack-Hartmann sensing. Applied Optics 38(32), 6737–6743 (1999)CrossRefGoogle Scholar
  26. 26.
    Y. Eldar, P. Kuppinger, H. Bölcskei, Block-sparse signals: Uncertainty relations and efficient recovery. IEEE Trans. Signal Process 58(6), 3042–3054 (2010)MathSciNetCrossRefGoogle Scholar
  27. 27.
    D.L. Fried, Statistics of a geometric representation of wavefront distortion. J. Opt. Soc. Am. 55, 1427–1431 (1965)MathSciNetCrossRefGoogle Scholar
  28. 28.
    V. Stanković, L. Stanković, and S. Cheng. Compressive image sampling with side information. In Proceedings of the 16th IEEE International Conference on Image Processing, ICIP’09, pages 3001–3004, 2009Google Scholar
  29. 29.
    T.O. Salmon, L.N. Thibos, A. Bradley, Comparison of the eyes wave-front aberration measured psychophysically and with the ShackHartmann wave-front sensor. Journal of the Optical Society of America A 15, 2457–2465 (2007)CrossRefGoogle Scholar
  30. 30.
    O. Michailovich, A. Tannenbaum, A fast approximation of smooth functions from samples of partial derivatives with application to phase unwrapping. Signal Processing 88, 358–374 (2008)MATHCrossRefGoogle Scholar
  31. 31.
    M. Hosseini, O. Michailovich, Derivative compressive sampling with application to phase unwrapping (In Proceedings of EUSIPCO, Glasgow, UK, August, 2009)Google Scholar
  32. 32.
    I. Daubechies, Ten Lectures on Wavelets (SIAM, CBMS-NSF Reg. Conf. Series in Applied Math, 1992)MATHCrossRefGoogle Scholar
  33. 33.
    D. L. Donoho and Y. Tsaig. Fast solution of \(l_1\)-norm minimization problems when the solution may be sparse. Technical Report 2006–18, Stanford, 2006Google Scholar
  34. 34.
    S. Osher, M. Burger, D. Goldfarb, J. Xu, W. Yin, An iterative regularization method for total variation-based image restoration. Simul 4, 460–489 (2005)MathSciNetMATHGoogle Scholar
  35. 35.
    A. Savitzky, M.J.E. Golay, Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36, 1627–1639 (1964)CrossRefGoogle Scholar
  36. 36.
    A.N. Tikhonov, V.Y. Arsenin, Solutions of Ill-Posed Problem, vol. H (Winston, Washington, D.C., 1977)Google Scholar
  37. 37.
    Å. Björck, Numerical methods for least squares problems (SIAM, Philadelphia, 1996)MATHCrossRefGoogle Scholar
  38. 38.
    A. Beck, M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences 2, 183–202 (2009)MathSciNetMATHCrossRefGoogle Scholar
  39. 39.
    O. Michailovich, An iterative shrinkage approach to total-variation image restoration. IEEE Trans. Image Process 20(5), 1281–1299 (2011)MathSciNetCrossRefGoogle Scholar
  40. 40.
    J.D. Schmidt, Numerical Simulation of Optical Wave Propagation with Examples in MATLAB (SPIE, Washington, 2010)Google Scholar
  41. 41.
    I. Daubchies, M. Defrise, C.D. Mol, An iterative thresholding algorithm for linear inverse problems with sparsity constraint. Comm. Pure Appl. Math. 75, 1412–1457 (2009)Google Scholar
  42. 42.
    Z. Wang, A.C. Bovik, H.R. Sheikh, E.P. Simoncelli, Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Process 13(4), 600–612 (2004)CrossRefGoogle Scholar
  43. 43.
    Z. Wang, A.C. Bovik, Mean squared error: Love it or leave it? - A new look at signal fidelity measures. IEEE Signal Processing Magazine 26(1), 98–117 (2009)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2013

Authors and Affiliations

  1. 1.Singapore University of Technology and DesignSingaporeSingapore

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