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 - <p style="text-align: justify;">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.</p>