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      A Semi-Lagrangian Two-Level Preconditioned Newton--Krylov Solver for Constrained Diffeomorphic Image Registration

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      SIAM Journal on Scientific Computing

      Society for Industrial & Applied Mathematics (SIAM)

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          Abstract

          <p class="first" id="P1">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. </p><p id="P2">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. </p><p id="P3">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 <i>×</i> speedup for a two dimensional, real world multi-subject medical image registration problem. </p>

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          Most cited references 44

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          Methods of conjugate gradients for solving linear systems

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            Ordinary differential equations, transport theory and Sobolev spaces

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              Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms

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                Author and article information

                Journal
                SIAM Journal on Scientific Computing
                SIAM J. Sci. Comput.
                Society for Industrial & Applied Mathematics (SIAM)
                1064-8275
                1095-7197
                January 2017
                January 2017
                : 39
                : 6
                : B1064-B1101
                Article
                10.1137/16M1070475
                5731678
                29255342
                © 2017
                Product

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