Nonconvex Constrained Minimisation for 3D Left Ventricular Shape Recovery Using 2D Echocardiography Data
Year: 2022
Author: Chi Young Ahn, Sangwoon Yun
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.120321.220721
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 1 : pp. 111–124
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Nonconvex constrained minimisation quadratically constrained quadratic program echocardiography left ventricle 3D reconstruction.