Optimal kernel sizes for 4D image reconstruction using normalized convolution from sparse fast-rotating transesophageal 2D ultrasound images

A transesophageal echocardiography (TEE) micro-probe is suitable for monitoring long minimally invasive interventions in the heart, because it is well tolerated by patients. To visualize complex 3D structures of the beating heart, a 4D-image reconstruction derived from irregularly and sparsely sampled 2D images is needed. We previously showed that normalized convolution (NC) with optimized kernels performs better than nearest-neighbor or linear interpolation. In order to use NC for image reconstructions we need to be able to predict optimal kernel sizes. We therefore present an advanced optimization scheme, and estimate optimal NC kernel sizes for five different patient-data sets. From the optimization results we derive a model for estimating optimal NC kernel sizes. As ground truth (GT), we used five full-volume 4D TEE patient scans, acquired with the X7-2t matrix transducer. To simulate 2D data acquisition, the GT datasets were sliced at random rotation angles and at random normalized cardiac phases. Data sets containing 400, 600, 900, 1350, and 1800 2D images were created for all patients, producing a total of 25 data sets. A 2D Gaussian function was used as NC kernel, and optimal kernel sizes were obtained with a quasi-Newton optimizer. A power law model was fitted to the optimal kernels estimated. We conclude that optimal kernel sizes for NC can be successfully predicted by a model at the cost of a relatively small increase in the reconstruction error.