Contrast enhanced tomographic reconstruction of vascular blood flow with first order and second order adjoint methods

References

[1] R. A. Adams, Sobolev Spaces, Pure Appl. Math. 65, Academic Press, New York, 1975. Suche in Google Scholar

[2] A. Borzì, K. Ito and K. Kunisch, An optimal control approach to optical flow computation, Internat. J. Numer. Methods Fluids 40 (2002), no. 1–2, 231–240. 10.1002/fld.273Suche in Google Scholar

[3] H. Choi, Suboptimal control of turbulent flow using control theory, Proceedings of the International Symposium on Mathematical Modelling of Turbulent Flows, Tokyo (1995). Suche in Google Scholar

[4] M. Choulli, Une introduction aux problèmes inverses elliptiques et paraboliques, Math. Appl. (Berlin) 65, Springer, Berlin, 2009. 10.1007/978-3-642-02460-3Suche in Google Scholar

[5] Y. H. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim. 10 (1999), no. 1, 177–182. 10.1137/S1052623497318992Suche in Google Scholar

[6] P. Deuflhard, Newton Methods for Nonlinear Problems, Springer Ser. Comput. Math. 35, Springer, Berlin, 2004. Suche in Google Scholar

[7] L. C. Evans, Partial Differential Equations, Grad. Stud. Math. 19, American Mathematical Society, Providence, 1998. Suche in Google Scholar

[8] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, 1964. Suche in Google Scholar

[9] J. C. Gilbert and J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Optim. 2 (1992), no. 1, 21–42. 10.1137/0802003Suche in Google Scholar

[10] R. Herzog and K. Kunisch, Algorithms for PDE-constrained optimization, GAMM-Mitt. 33 (2010), no. 2, 163–176. 10.1002/gamm.201010013Suche in Google Scholar

[11] M. Hinze and K. Kunisch, Second order methods for optimal control of time-dependent fluid flow, SIAM J. Control Optim. 40 (2001), no. 3, 925–946. 10.1137/S0363012999361810Suche in Google Scholar

[12] S. Kindermann and A. Leitão, On regularization methods for inverse problems of dynamic type, Numer. Funct. Anal. Optim. 27 (2006), no. 2, 139–160. 10.1080/01630560600569973Suche in Google Scholar

[13] J. G. Korporaal, M. R. Benz, S. T. Schindera, T. G. Flohr and B. Schmidt, Contrast gradient-based blood velocimetry with computed tomography, Invest. Radiol. 51 (2016), 1–9. 10.1097/RLI.0000000000000202Suche in Google Scholar PubMed

[14] O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural’ceva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monogr. 23, American Mathematical Society, Providence, 1968. 10.1090/mmono/023Suche in Google Scholar

[15] A. Lipponen, A. Seppänen and J. P. Kaipio, Reduced-order estimation of nonstationary flows with electrical impedance tomography, Inverse Problems 26 (2010), no. 7, Article ID 074010. 10.1088/0266-5611/26/7/074010Suche in Google Scholar

[16] K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, Cambridge, 1994. Suche in Google Scholar

[17] C. Mory, V. Auvray, B. Zhang, M. Grass, D. Schafer, S. J. Chen, J. D. Carrol, S. Rit, F. Peyrin, P. Douek and L. Boussel, Cardiac C-arm computed tomography using a 3d+time ROI reconstruction method with spatial and temporal regularization, Med. Phys. 41 (2014), Article ID 021903. 10.1118/1.4860215Suche in Google Scholar PubMed

[18] F. Natterer, The Mathematics of Computerized Tomography, B. G. Teubner, Stuttgart, 1986. 10.1007/978-3-663-01409-6Suche in Google Scholar

[19] J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed., Springer Ser. Oper. Res. Financ. Eng., Springer, New York, 2006. Suche in Google Scholar

[20] S. Prevrhal, C. H. Forsythe, R. J. Harnish, M. Saeed and B. M. Yeh, CT angiographic measurement of vascular blood fowl velocity by using projection data, Radiology 261 (2011), 923–929. 10.1148/radiol.11110617Suche in Google Scholar PubMed

[21] T. Roubíček, Nonlinear Partial Differential Equations with Applications, 2nd ed., Internat. Ser. Numer. Math. 153, Birkhäuser/Springer, Basel, 2013. 10.1007/978-3-0348-0513-1Suche in Google Scholar

[22] U. Schmitt, A. K. Louis, C. Wolters and M. Vauhkonen, Efficient algorithms for the regularization of dynamic inverse problems. I: Theory, Inverse Problems 18 (2002), 645–658. 10.1088/0266-5611/18/3/308Suche in Google Scholar

[23] U. Schmitt, A. K. Louis, C. Wolters and M. Vauhkonen, Efficient algorithms for the regularization of dynamic inverse problems. II: Applications, Inverse Problems 18 (2002), no. 3, 659–676. 10.1088/0266-5611/18/3/309Suche in Google Scholar

[24] A. Seppänen, M. Vauhkonen, P. J. Vauhkonen, E. Somersalo and J. P. Kaipio, State estimation with fluid dynamical evolution models in process tomography—an application to impedance tomography, Inverse Problems 17 (2001), no. 3, 467–483. 10.1088/0266-5611/17/3/307Suche in Google Scholar

[25] A. Seppänen, A. Voutilainen and J. P. Kaipio, State estimation in process tomography—reconstruction of velocity fields using EIT, Inverse Problems 25 (2009), no. 8, Article ID 085009. 10.1088/0266-5611/25/8/085009Suche in Google Scholar

[26] B. Sixou, L. Boussel and M. Sigovan, Contrast enhanced computerized tomography measurement of vascular blood flow, J. Phys. Conf. Ser. 756 (2016), Article ID 012003. 10.1088/1742-6596/756/1/012003Suche in Google Scholar

[27] B. Sixou, L. Boussel and M. Sigovan, Vascular blood flow reconstruction with contrast-enhanced computerized tomography, Inverse Probl. Sci. Eng. 26 (2018), no. 6, 855–876. 10.1080/17415977.2017.1361421Suche in Google Scholar

[28] G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd ed., Oxford Appl. Math. Comp. Sci. Ser., Oxford University Press, New York, 1985. Suche in Google Scholar

[29] A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov and A. G. Yagola, Numerical Methods for the Solution of Ill-posed Problems, Math. Appl. 328, Kluwer Academic, Dordrecht, 1995. 10.1007/978-94-015-8480-7Suche in Google Scholar

[30] Y. Wang, A. G. Yagola and C. Yang, Optimization and Regularization for Computational Inverse Problems and Applications, Springer, New York, 2010. 10.1007/978-3-642-13742-6Suche in Google Scholar

[31] E. Zeidler, Applied Functional Analysis, Appl. Math. Sci. 109, Springer, New York, 1995. 10.1007/978-1-4612-0815-0Suche in Google Scholar