°For electrophysiology intervention monitoring, we intend to reconstruct 4D ultrasound (US) of structures in
the beating heart from 2D transesophageal US by scanplane rotation. The image acquisition is continuous but
unsynchronized to the heart rate, which results in a sparsely and irregularly sampled dataset and a spatiotemporal
interpolation method is desired. Previously, we showed the potential of normalized convolution (NC) for
interpolating such datasets.
We explored 4D interpolation by 3 different methods: NC, nearest neighbor (NN), and temporal binning
followed by linear interpolation (LTB). The test datasets were derived by slicing three 4D echocardiography
datasets at random rotation angles (θ, range: 0-180) and random normalized cardiac phase (τ, range: 0-1).
Four different distributions of rotated 2D images with 600, 900, 1350, and 1800 2D input images were created
from all TEE sets. A 2D Gaussian kernel was used for NC and optimal kernel sizes (σθ and στ) were found by
performing an exhaustive search. The RMS gray value error (RMSE) of the reconstructed images was computed
for all interpolation methods. The estimated optimal kernels were in the range of σθ = 3.24 - 3.69°/ στ = 0.045 - 0.048, σθ = 2.79°/ στ =
0.031 - 0.038, σθ = 2.34°/ στ = 0.023 - 0.026, and σθ = 1.89°/ στ = 0.021 - 0.023 for 600, 900, 1350, and 1800
input images respectively.
We showed that NC outperforms NN and LTB. For a small number of input images the advantage of NC is