Nonconvex Constrained Minimisation for 3D Left Ventricular Shape Recovery Using 2D Echocardiography Data

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.