G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential 770 Equations and the Calculus of Variations, vol.147, 2002.

W. Bai and M. Brady, Regularized B-spline deformable registration for respiratory motion correction 773 in PET images, Phys. Med. Biol, vol.54, pp.2719-2736, 2009.

W. Bai and M. Brady, Motion correction and attenuation correction for respiratory gated PET images, IEEE Trans. Med. Imaging, vol.775, pp.351-365, 2011.

H. H. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert 777 Spaces, 2017.

F. M. Beg, M. I. Miller, A. Trouvé, and L. Younes, Computing large deformation metric mappings 779 via geodesic flow of diffeomorphisms, International Journal of Computer Vision, vol.61, p.157, 2005.

R. Bhagalia, J. Pack, S. Miller, and M. Iatrou, Nonrigid registration-based coronary artery motion 782 correction for cardiac computed tomography, Med. Phys, vol.39, pp.4245-4254, 2012.

M. Blume, N. Navab, and M. Rafecas, Joint image and motion reconstruction for PET using a 784 B-spline motion model, Phys. Med. Biol, vol.57, pp.8249-8270, 2012.

M. Brehm, P. Paysan, M. Oelhafen, and M. Kachelriess, Artifact-resistant motion estimation 786 with a patient-specific artifact model for motion-compensated cone-beam CT, Med. Phys, vol.40, pp.787-101913, 2013.

M. Brehm, P. Paysan, M. Oelhafen, P. Kunz, and M. Kachelriess, Self-adapting cyclic registration 789 for motion-compensated cone-beam CT in image-guided radiation therapy, Med. Phys, vol.39, pp.790-7603, 2012.

M. Brehm, S. Sawall, J. Maier, S. Sauppe, and M. Kachelriess, Cardiorespiratory motion-792 compensated micro-CT image reconstruction using an artifact model-based motion estimation, Med. 793 Phys, vol.42, pp.1948-1958, 2015.

M. Bruveris and D. D. Holm, Geometry of image registration: The diffeomorphism group and momen-795 tum maps, Geometry, Mechanics, and Dynamics: The Legacy of Jerry Marsden

G. Holm, T. Patrick, and . Ratiu, of Fields Institute Communications, vol.73, pp.19-56, 2015.

M. Bruveris and F. Vialard, On completeness of groups of diffeomorphisms, J. Eur. Math. Soc, vol.799, pp.1507-1544, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01102814

M. Burger, H. Dirks, and C. Schönlieb, A Variational Model for Joint Motion Estimation and Image 801 Reconstruction, SIAM Journal on Imaging Sciences, vol.11, pp.94-128, 2018.

M. Burger, J. Modersitzki, and L. Ruthotto, A Hyperelastic Regularization Energy for Image 803 Registration, SIAM J. Sci. Comput, vol.35, pp.132-148, 2013.

F. Büther, M. Dawood, L. Stegger, F. Wübbeling, M. Schäfers et al.,

. Schäfers, List mode-driven cardiac and respiratory gating in PET, J. Nucl. Med, vol.50, p.681, 2009.

B. Chen, Z. Zhang, E. Y. Sidky, D. Xia, and X. Pan, Image reconstruction and scan configurations 808 enabled by optimization-based algorithms in multispectral CT, Phys. Med. Biol, vol.62, p.8793, 2017.

C. Chen and O. Öktem, Indirect Image Registration with Large Diffeomorphic Deformations, SIAM 811 Journal on Imaging Sciences, vol.11, pp.575-617, 2018.

C. Chen and G. Xu, Gradient-flow-based semi-implicit finite-element method and its convergence analysis 813 for image reconstruction, Inverse Problems, vol.28, p.35006, 2012.

C. Chen and G. Xu, The Linearized Split Bregman Iterative Algorithm and Its Convergence Analysis 815 for Robust Tomographic Image Reconstruction, UCLA CAM Reports, p.816, 2013.

C. Chen and G. Xu, A new linearized split Bregman iterative algorithm for image reconstruction in 817 sparse-view X-ray computed tomography, Comput. Math. Appl, vol.71, pp.1537-1559, 2016.

K. Chen and D. A. Lorenz, Image sequence interpolation using optimal control, Journal of Mathemat-819 ical Imaging and Vision, vol.41, pp.222-238, 2011.

M. Dawood, F. Büther, X. Jiang, and K. P. Schäfers, Respiratory motion correction in 3-D PET 821 data with advanced optical flow algorithms, IEEE Trans. Med. Imaging, vol.27, pp.1164-1175, 2008.

M. Dawood, F. Büther, N. Lang, O. Schober, and K. P. Schäfers, Respiratory gating in positron 823 emission tomography: a quantitative comparison of different gating schemes, Med. Phys, vol.34, pp.824-3067, 2007.

M. Dawood, N. Lang, X. Jiang, and K. P. Schäfers, Lung motion correction on respiratory gated 826 3-d PET/CT images, IEEE Trans. Med. Imaging, vol.25, pp.1164-1175, 2006.

M. Dawood, L. Stegger, X. Jiang, O. Schober, M. Schäfers et al., Optimal 828 number of respiratory gates in positron emission tomography: a cardiac patient study, Med. Phys, vol.36, pp.1775-1784, 2009.

P. Dupuis, U. Grenander, and M. Miller, Variational Problems on Flows of Diffeomorphisms for 831 Imaging Matching, vol.56, pp.587-600, 1998.

W. V. Elmpt, J. Hamill, J. Jones, D. De-ruysscher, P. Lambin et al., Optimal gating 833 compared to 3D and 4D PET reconstruction for characterization of lung tumors, Eur. J. Nucl. Med

, Mol. Imaging, vol.38, pp.843-855, 2011.

H. Gao, J. Cai, Z. Shen, and H. Zhao, Robust principal component analysis-based four-dimensional 836 computed tomography, Phys. Med. Biol, vol.56, pp.3181-3198, 2011.

F. Gigengack, X. Jiang, M. Dawood, and K. Schäfers, Motion Correction in Thoracic Position 838 Emission Tomography, Springer Briefs in Electrical and Computer Engineering, p.839, 2015.

F. Gigengack, L. Ruthotto, M. Burger, C. H. Wolters, X. Jiang et al., Motion 840 correction in dual gated cardiac PET using mass-preserving image registration, IEEE Trans. Med. 841 Imaging, pp.698-712, 2012.

U. Grenander and M. Miller, Pattern Theory. From Representation to Inference, 2007.

W. Grootjans, L. De-geus-oei, A. P. Meeuwis, S. Charlotte, M. Gotthardt et al., Amplitude-based optimal respiratory gating in positron emission tomography in pa-846 tients with primary lung cancer, Eur. Radio, vol.24, pp.3242-3250, 2014.

J. Hinkle, M. Szegedi, B. Wang, B. Salter, and S. Joshi, 4D CT image reconstruction with diffeo-848 morphic motion model, Medical Image Analysis, vol.16, pp.1307-1316, 2012.

X. Jia, Y. Lou, B. Dong, Z. Tian, and S. Jiang, 4D computed tomography reconstruction from few-850 projection data via temporal non-local regularization, Medical Image Computing and Computer, p.851

, Lecture Notes in Computer Science, vol.6361, pp.143-150, 2010.

N. Lang, M. Dawood, F. Büther, O. Schober, M. Schäfers et al., Organ move-854 ment reduction in PET/CT using dual-gated list-mode acquisition, Med. Phys, vol.16, pp.93-100, 2006.

J. Liu, X. Zhang, H. Zhao, Y. Gao, D. Thomas et al., 5D respiratory motion model 856 based image reconstruction algorithm for 4D cone-beam computed tomography, Inverse Problems, p.115007, 2015.

G. Lucignani, Respiratory and cardiac motion correction with 4D PET imaging: shooting at moving 859 targets, Eur. J. Nucl. Med. Mol. Imaging, vol.36, pp.315-319, 2009.

M. I. Miller, A. Trouvé, and L. Younes, On the metrics and Euler-Lagrange equations of computa-861 tional anatomy, Annual Reviews of Biomedical Engineering, vol.4, pp.375-405, 2002.

M. I. Miller, A. Trouvé, and L. Younes, Geodesic shooting for computational anatomy, Journal of 863 Mathematical Imaging and Vision, vol.24, pp.209-228, 2006.

M. I. Miller, A. Trouvé, and L. Younes, Hamiltonian systems and optimal control in computational 865 anatomy: 100 years since D'arcy Thompson, Annual Review of Biomedical Engineering, vol.17, pp.866-447, 2015.

F. Natterer, The Mathematics of Computerized Tomography, vol.32, p.868, 2001.

H. Nien and J. A. Fessler, Fast X-ray CT image reconstruction using a linearized augmented La-870 grangian method with ordered subsets, IEEE Trans. Med. Imag, vol.34, pp.388-399, 2015.

O. Öktem, C. Chen, N. O. Domaniç, P. Ravikumar, and C. Bajaj, Shape based image reconstruction 872 using linearised deformations, Inverse Problems, p.35004, 2017.

L. Ritschl, S. Sawall, M. Knaup, A. Hess, and M. Kachelriess, Iterative 4D cardiac micro-CT 874 image reconstruction using an adaptive spatio-temporal sparsity prior, Phys. Med. Biol, vol.57, pp.875-1517, 2012.

L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys, vol.877, pp.259-268, 1992.

O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier, and F. Lenzen, Variational Methods in 879 Imaging, vol.167, 2009.

H. Schumacher, J. Modersitzki, and B. Fischer, Combined reconstruction and motion correction in 881 SPECT imaging, IEEE Trans. Nucl. Sci, vol.56, pp.73-80, 2009.

A. J. Schwarz and M. O. Leach, Implications of respiratory motion for the quantification of 2D MR 883 spectroscopic imaging data in the abdomen, Phys. Med. Biol, vol.45, pp.2105-2116, 2000.

E. Sidky, J. Jørgensen, and X. Pan, Convex optimization problem prototyping for image reconstruction 885 in computed tomography with the Chambolle-Pock algorithm, Physics in medicine and biology, vol.57, p.3065, 2012.

E. Sidky, C. Kao, and X. Pan, Accurate image reconstruction from few-views and limited-angle data 888 in divergent-beam CT, Journal of X-ray Science and Technology, vol.14, pp.119-139, 2006.

K. Taguchi and H. Kudo, Motion Compensated Fan-Beam Reconstruction for Nonrigid Transformation, IEEE Trans. Med. Imaging, vol.890, pp.907-917, 2008.

Q. Tang, J. Cammin, S. Srivastava, and K. Taguchi, A fully four-dimensional, iterative motion 892 estimation and compensation method for cardiac CT, Med. Phys, vol.39, pp.4291-4305, 2012.

D. Thompson, On Growth and Form, 1945.

A. Trouvé, Diffeomorphisms Groups and Pattern Matching in Imaging Analysis, International Journal 895 of Computer Vision, vol.28, pp.213-221, 1998.

A. Trouvé and L. Younes, Shape spaces, Handbook of Mathematical Methods in Imaging, S. Otmar, pp.1759-1817, 2015.

A. Van-der-gucht, B. Serrano, F. Hugonnet, B. Paulmier, N. Garnier et al., 899 Impact of a new respiratory amplitude-based gating technique in evaluation of upper abdominal PET 900 lesions, Eur. J. Radiol, vol.83, pp.509-515, 2014.

F. Vialard, L. Risser, D. Rueckert, and C. J. Cotter, Diffeomorphic 3D image registration via 902 geodesic shooting using an efficient adjoint calculation, International Journal of Computer Vision, vol.97, pp.229-241, 2012.

Y. Wang, E. Vidan, and G. W. Bergman, Cardiac motion of coronary arteries: variability in the rest 905 period and implications for coronary MR angiography, vol.213, pp.751-758, 1999.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, Image quality assessment: From error 907 visibility to structural similarity, IEEE Trans. Image Process, vol.13, pp.600-612, 2004.

L. Younes, Shapes and Diffeomorphisms, vol.171, 2010.