Spatiotemporal interpolation by normalized convolution for 4D transesophageal echocardiography

For interventional monitoring, we aim at 4D ultrasound reconstructions of structures in the beating heart from 2D transesophageal echo images by fast scan plane rotation, unsynchronized to the heart rate. For such sparsely and irregularly sampled 2D images, a special spatiotemporal interpolation approach is desired. We have previously shown the potential of spatiotemporal interpolation by normalized convolution (NC). In this work we optimized NC for our application and compared it to nearest neighbor interpolation (NN) and to temporal binning followed by linear spatial interpolation (LTB). The test datasets consisted of 600, 1350, and 1800 2D images and were derived by slicing a 4D echocardiography data sets at random rotation angle (θ, range: 0-180°) and random normalized cardiac phase (τ, range: 0-1). A Gaussian kernel was used for NC and optimal kernel sizes (σ_τ and σ_θ) 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 σ_θ=3.24°/ σ_τ=0.048, σ_θ=2.34°/σ_τ=0.026, and σ_θ=1.89°/σ_τ=0.023 for 600, 1350, and 1800 input images, respectively. The minimum RMSE for NC was 13.8, 10.4, and 9.4 for 600, 1350, and 1800 input images, respectively. The NN/LTB reconstruction had an RMSE of 17.8/16.4, 13.9/15.1, and 12.0/14.7 for 600, 1350, and 1800 2D input images, respectively. We showed that NC outperforms NN and LTB. For a small number of input images the advantage of NC is more pronounced.