Volume 12, Issue 1
Nonconvex Constrained Minimisation for 3D Left Ventricular Shape Recovery Using 2D Echocardiography Data

Chi Young Ahn & Sangwoon Yun

East Asian J. Appl. Math., 12 (2022), pp. 111-124.

Published online: 2021-10

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  • Abstract

A mathematical model in the form of a nonconvex constrained minimisation problem, aimed to determine the 3D position of LV contours using 2D echocardiography data for the entire cardiac cycle is proposed. It can be considered as a quadratically constrained quadratic program in terms of one of four variables with the others fixed. The model is solved by a proximal block coordinate descent method with cyclic order and the convergence of the algorithm is proved by using the Kurdyka-Lojasiewicz property. The model does not require unsuitable assumptions in practical environments and numerical experiments show its suitability in working with real echocardiography data.

  • Keywords

Nonconvex constrained minimisation, quadratically constrained quadratic program, echocardiography, left ventricle, 3D reconstruction.

  • AMS Subject Headings

49M27, 68U10, 90C20, 90C26, 92C50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-111, author = {Ahn , Chi Young and Yun , Sangwoon}, title = {Nonconvex Constrained Minimisation for 3D Left Ventricular Shape Recovery Using 2D Echocardiography Data}, journal = {East Asian Journal on Applied Mathematics}, year = {2021}, volume = {12}, number = {1}, pages = {111--124}, abstract = {

A mathematical model in the form of a nonconvex constrained minimisation problem, aimed to determine the 3D position of LV contours using 2D echocardiography data for the entire cardiac cycle is proposed. It can be considered as a quadratically constrained quadratic program in terms of one of four variables with the others fixed. The model is solved by a proximal block coordinate descent method with cyclic order and the convergence of the algorithm is proved by using the Kurdyka-Lojasiewicz property. The model does not require unsuitable assumptions in practical environments and numerical experiments show its suitability in working with real echocardiography data.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.120321.220721}, url = {http://global-sci.org/intro/article_detail/eajam/19923.html} }
TY - JOUR T1 - Nonconvex Constrained Minimisation for 3D Left Ventricular Shape Recovery Using 2D Echocardiography Data AU - Ahn , Chi Young AU - Yun , Sangwoon JO - East Asian Journal on Applied Mathematics VL - 1 SP - 111 EP - 124 PY - 2021 DA - 2021/10 SN - 12 DO - http://doi.org/10.4208/eajam.120321.220721 UR - https://global-sci.org/intro/article_detail/eajam/19923.html KW - Nonconvex constrained minimisation, quadratically constrained quadratic program, echocardiography, left ventricle, 3D reconstruction. AB -

A mathematical model in the form of a nonconvex constrained minimisation problem, aimed to determine the 3D position of LV contours using 2D echocardiography data for the entire cardiac cycle is proposed. It can be considered as a quadratically constrained quadratic program in terms of one of four variables with the others fixed. The model is solved by a proximal block coordinate descent method with cyclic order and the convergence of the algorithm is proved by using the Kurdyka-Lojasiewicz property. The model does not require unsuitable assumptions in practical environments and numerical experiments show its suitability in working with real echocardiography data.

Chi Young Ahn & Sangwoon Yun. (2021). Nonconvex Constrained Minimisation for 3D Left Ventricular Shape Recovery Using 2D Echocardiography Data. East Asian Journal on Applied Mathematics. 12 (1). 111-124. doi:10.4208/eajam.120321.220721
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