Advertisement

Registration of Noisy Images via Maximum A-Posteriori Estimation

  • Sebastian Suhr
  • Daniel Tenbrinck
  • Martin Burger
  • Jan Modersitzki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8545)

Abstract

Biomedical image registration faces challenging problems induced by the image acquisition process of the involved modality. A common problem is the omnipresence of noise perturbations. A low signal-to-noise ratio – like in modern dynamic imaging with short acquisition times – may lead to failure or artifacts in standard image registration techniques. A common approach to deal with noise in registration is image presmoothing, which may however result in bias or loss of information. A more reasonable alternative is to directly incorporate statistical noise models into image registration. In this work we present a general framework for registration of noise perturbed images based on maximum a-posteriori estimation. This leads to variational registration inference problems with data fidelities adapted to the noise characteristics, and yields a significant improvement in robustness under noise impact and parameter choices. Using synthetic data and a popular software phantom we compare the proposed model to conventional methods recently used in biomedical imaging and discuss its potential advantages.

Keywords

Image Registration Noise Model Noisy Image Jacobian Determinant Additive Gaussian Noise 
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.
    Allassonnière, S., Amit, Y., Trouvé, A.: Towards a coherent statistical framework for dense deformable template estimation. Journal of the Royal Statistical Society 69, 3–29 (2007)Google Scholar
  2. 2.
    Burger, M., Modersitzki, J., Ruthotto, L.: A hyperelastic regularization energy for image registration. SIAM Journal on Scientific Computing 35(1), B132–B148 (2013)Google Scholar
  3. 3.
    Cademartiri, F., et al.: Influence of increasing convolution kernel filtering on plaque imaging with multislice CT using an ex-vivo model of coronary angiography. La Radiologia Medica 110(3), 234–240 (2005)Google Scholar
  4. 4.
    Chan, T.F., Shen, J.: Image processing and analysis: variational, PDE, wavelet, and stochastic methods. SIAM (2005)Google Scholar
  5. 5.
    Dawood, M., et al.: A mass conservation-based optical flow method for cardiac motion correction in 3D-PET. Medical Physics 40(1), 012505 (2013)Google Scholar
  6. 6.
    Fremlin, D.H.: Measure theory: broad foundations, vol. 2. Torres Fremlin (2001)Google Scholar
  7. 7.
    Frick, K., Marnitz, P., Munk, A.: Statistical multiresolution Dantzig estimation in imaging: fundamental concepts and algorithmic framework. Journal of Statistical Mechanics: Theory and Experiment 6, 231–268 (2012)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. Journal of Applied Statistics 20, 25–62 (1993)CrossRefGoogle Scholar
  9. 9.
    Hintermüller, M., Stadler, G.: A primal-dual algorithm for TV-based inf-convolution-type image restoration. SIAM Journal on Scientific Computing 28(1), 1–23 (2006)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Mair, B.A., Gilland, D.R., Sung, J.: Estimation of images and nonrigid deformations in gated emission CT. IEEE Transactions on Medical Imaging 25(9), 1130–1144 (2006)CrossRefGoogle Scholar
  11. 11.
    Modersitzki, J.: FAIR: Flexible Algorithms for Image Registration. SIAM (2009)Google Scholar
  12. 12.
    Nicolau, S., Pennec, X., Soler, L., Ayache, N.: Evaluation of a new 3D/2D registration criterion for liver radio-frequencies guided by augmented reality. In: Ayache, N., Delingette, H. (eds.) IS4TM 2003. LNCS, vol. 2673, pp. 270–283. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Paquin, D.C., Levy, D., Xing, L.: Multiscale deformable registration of noisy medical images. Mathematical Biosciences and Engineering 5(1), 125–144 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Roche, A., Malandain, G., Ayache, N.: Unifying maximum likelihood approaches in medical image registration. International Journal of Imaging Systems and Technology 11, 71–80 (1999)CrossRefGoogle Scholar
  15. 15.
    Segars, W.P., et al.: 4D XCAT phantom for multimodality imaging research. Medical Physics 37, 4902–4915 (2010)CrossRefGoogle Scholar
  16. 16.
    Sermesant, M., et al.: Deformable biomechanical models: application to 4D cardiac image analysis. Medical Image Analysis 7, 475–488 (2003)CrossRefGoogle Scholar
  17. 17.
    Simpson, I.J.A., et al.: Probabilistic inference of regularisation in non-rigid registration. NeuroImage 59, 2438–2451 (2012)CrossRefGoogle Scholar
  18. 18.
    Vardi, Y., Shepp, L.A., Kaufman, L.: A statistical model for positron emission tomography. Journal of the American Statistical Association 80, 8–20 (1985)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sebastian Suhr
    • 1
    • 4
  • Daniel Tenbrinck
    • 2
  • Martin Burger
    • 1
    • 3
  • Jan Modersitzki
    • 4
  1. 1.Institute for Computational and Applied MathematicsUniversity of MünsterMünsterGermany
  2. 2.GREYC, UMR 6072 CNRSÉcole Nationale Supérieure d’Ingénieurs de CaenCaenFrance
  3. 3.Cells in Motion (CiM) Cluster of ExcellenceUniversity of MünsterMünsterGermany
  4. 4.Institute of Mathematics and Image ComputingUniversity of LübeckLübeckGermany

Personalised recommendations