Advertisement

Abstract

Regularization is an well-known technique for obtaining stable solution of ill-posed inverse problems. In this paper we establish a key relationship among the regularization methods with edge-preserving noise filtering method which leads to an efficient adaptive regularization methods. We show experimentally the efficiency and superiority of the proposed regularization methods for some inverse problems, e.g. deblurring and super-resolution (SR) image reconstruction.

Keywords

Inverse Problem Regularization Method Regularization Term Geodesic Distance Super Resolution 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chang, S.G., Yu, B., Vetterli, M.: Adaptive wavelet thresholding for image denoising and compression. IEEE Trans. Image Process. 9, 1532–1546 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. of Imaging Sciences 2, 183–202 (2006)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)zbMATHCrossRefGoogle Scholar
  4. 4.
    Purkait, P., Chanda, B.: Super resolution image reconstruction through bregman iteration using morphologic regularization. IEEE Transactions on Image Processing 21, 4029–4039 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Widrow, B., Stearns, S.: Adaptive signal processing, vol. 491, p. 1. Prentice-Hall, Inc., Englewood Cliffs (1985)zbMATHGoogle Scholar
  6. 6.
    Zhang, X., Lam, E.Y., Wu, E.X., Wong, K.K.: Application of tikhonov regularization to super-resolution reconstruction of brain mri image. Medical Imaging and Informatics 49, 51–56 (2008)CrossRefGoogle Scholar
  7. 7.
    Hansen, P.C., Nagy, J.G., OLeary, D.P.: Deblurring images. Fundamentals of Algorithms, vol. 3, pp. 291–294. Society for Industrial and Applied Mathematics (SIAM) (2006)Google Scholar
  8. 8.
    Farsiu, S., Robinson, M.D., Elad, M., Milanfar, P.: Fast and robust multiframe super-resolution. IEEE Transactions on Image Processing 13, 1327–1344 (2004)CrossRefGoogle Scholar
  9. 9.
    Chan, T.F., Wong, C.K.T.: Multichannel image deconvolution by total variation regularization. In: Proceedings of SPIE, San Diego, CA, USA, pp. 358–366 (1997)Google Scholar
  10. 10.
    Li, X., Hu, Y., Gao, X., Tao, D., Ning, B.: A multi-frame image super-resolution method. Signal Processing 90, 405–414 (2010)zbMATHCrossRefGoogle Scholar
  11. 11.
    Nguyen, N., Milanfar, P., Golub, G.: Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement. IEEE Transactions on Image Processing 10, 1299–1308 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Nguyen, N., Milanfar, P., Golub, G.H.: A computationally efficient image super resolution algorithm. IEEE Transaction on Image Processing 10, 573–583 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Elad, M., Feuer, A.: Restoration of a single super-resolution image from several blurred, noisy, and under-sampled measured images. IEEE Transactions on Image Processing 6, 1646–1658 (1997)CrossRefGoogle Scholar
  14. 14.
    Elad, M.: On the bilateral filter and ways to improve it. IEEE Transaction on Image Processing 11, 1141–1151 (2002)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: IEEE International Conference on Computer Vision, New Delhi, India, pp. 836–846 (1998)Google Scholar
  16. 16.
    Lerallut, R., Decencière, E., Meyer, F.: Image filtering using morphological amoebas. Image and Vision Computing 25, 395–404 (2007)Google Scholar
  17. 17.
    Cheng, F., Venetsanopoulos, A.: Adaptive morphological operators, fast algorithms and their applications. Pattern Recognition 33, 917–933 (2000)CrossRefGoogle Scholar
  18. 18.
    Soille, P.: Generalized geodesy via geodesic time. Pattern Recognition Letters 15, 1235–1240 (1994)CrossRefGoogle Scholar
  19. 19.
    Debayle, J., Pinoli, J.C.: General adaptive neighborhood image processing. J. Math. Imaging Vis. 25, 267–284 (2006)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Borgefors, G.: Distance transformations in digital images. Comput. Vision Graph. Image Process. 34, 344–371 (1986)CrossRefGoogle Scholar
  21. 21.
    Sethian, J.A.: Fast marching methods. SIAM Review 41, 199–235 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Toivanen, J.P.: New geodosic distance transforms for gray-scale images. Pattern Recognition Letters 17, 437–450 (1996)CrossRefGoogle Scholar
  23. 23.
    Yatziv, L., Bartesaghi, A., Sapiro, G.: O(n) implementation of the fast marching algorithm. Journal of Computational Physics 212, 393–399 (2006)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Pulak Purkait
    • 1
  • Bhabatosh Chanda
    • 1
  1. 1.ECSUIndian Statistical InstituteIndia

Personalised recommendations