Fast Spline Interpolation using GPU Acceleration

Super-resolution imaging uses spatiotemporal filtering to separate moving blood from tissue, but the motion from, e.g., heartbeats and breathing reduces the effectiveness of these filters. Therefore, a motion correction is often performed to make the tissue stationary at a sub-pixel level through interpolation. However, the high-quality interpolation method cubic spline lacks an implementation for graphics processing units (GPUs), making it slow and impractical. The hypothesis is that motion correction can be performed at a 5000 Hz frame rate with GPU-accelerated spline interpolation, enabling this step in super-resolution imaging pipelines to run in real time. Spline interpolation was derived in 1D and then generalized to 2D. The system of equations for the necessary derivatives for spline interpolation was shown to be reducible to a convolution for large inputs within numerical precision, which could be parallelized on GPU. In-vivo data from a Sprague-Dawley rat kidney was acquired with a 10 MHz, 168-element GE L8-18iD linear array probe and a Verasonics Vantage 256 scanner. Motion was estimated using a transverse oscillation autocorrelation motion estimator, and then 2D motion correction was performed by resampling already-beamformed images with new pixel positions. An NVIDIA GeForce RTX 4090 GPU and Intel Xeon W-3223 CPU were used for processing, and the output was compared with that of MATLAB’s interp2. Motion correction was performed at the rate of 5013 images per second using the proposed GPU implementation, which was 668 times faster than MATLAB’s 2D spline interpolation, which lacks GPU support. Comparing the output to that of interp2 showed only insignificant numerical differences of less than -75 dB. Thus, GPU-accelerated motion correction for 2D imaging can be performed in real time using spline interpolation to benefit super-resolution and power Doppler imaging. The source code is made freely available online.