Display options
Cite
Mang A, Biros G. A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION. SIAM J Sci Comput. 2017;39(6):B1064-B1101doi: 10.1137/16M1070475.
Mang, A., & Biros, G. (2017). A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION. SIAM journal on scientific computing : a publication of the Society for Industrial and Applied Mathematics, 39(6), B1064-B1101. https://doi.org/10.1137/16M1070475
Mang, Andreas, and Biros, George. "A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION." SIAM journal on scientific computing : a publication of the Society for Industrial and Applied Mathematics vol. 39,6 (2017): B1064-B1101. doi: https://doi.org/10.1137/16M1070475
Mang A, Biros G. A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION. SIAM J Sci Comput. 2017;39(6):B1064-B1101. doi: 10.1137/16M1070475. Epub 2017 Nov 21. PMID: 29255342; PMCID: PMC5731678.
Copy Download .nbib Format: NLM
Share it on

SIAM J Sci Comput. 2017;39(6):B1064-B1101. doi: 10.1137/16M1070475. Epub 2017 Nov 21.

A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.

SIAM journal on scientific computing : a publication of the Society for Industrial and Applied Mathematics

Andreas Mang, George Biros

Affiliations

  1. The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas, 78712-0027, US.

PMID: 29255342 PMCID: PMC5731678 DOI: 10.1137/16M1070475

Abstract

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20

Keywords: 35Q93; 49J20; 65F08; 65K10; 68U10; 76D55; KKT preconditioners; Krylov method; Newton; PDE constrained optimization; constrained diffeomorphic image registration; optimal control; semi-Lagrangian formulation; stationary velocity field registration

References

  1. Neuroimage. 2009 Mar;45(1 Suppl):S61-72 - PubMed
  2. Neuroimage. 2011 Apr 1;55(3):954-67 - PubMed
  3. J Math Biol. 2016 Jan;72 (1-2):409-33 - PubMed
  4. IEEE Trans Med Imaging. 2008 Feb;27(2):271-81 - PubMed
  5. IEEE Trans Med Imaging. 2005 Sep;24(9):1216-30 - PubMed
  6. Neuroimage. 2007 Oct 15;38(1):95-113 - PubMed
  7. IEEE Trans Med Imaging. 2013 Jul;32(7):1153-90 - PubMed
  8. Med Image Anal. 2008 Feb;12(1):26-41 - PubMed
  9. Med Phys. 2012 Jul;39(7):4444-59 - PubMed
  10. SIAM J Imaging Sci. 2015;8(2):1030-1069 - PubMed
  11. SIAM J Imaging Sci. 2016;9(3):1154-1194 - PubMed
  12. Phys Med Biol. 2014 Oct 21;59(20):6085-115 - PubMed
  13. Med Image Comput Comput Assist Interv. 2008;11(Pt 1):754-61 - PubMed

Publication Types

Grant support