Design and optimization of 3D VSHARP® scatter correction for industrial CBCT using the Linear Boltzmann Transport Equation

We have developed VSHARP®, a suite of scatter correction solutions that have been incorporated into the commercially available cone-beam software development toolkit, CST (Varex Imaging, Salt Lake City, UT) enabling scatter correction to be applied as part of an entire CBCT reconstruction pipeline. The suite includes 2D VSHARP®, a deconvolution correction using asymmetric Gaussian kernels, 2D VSHARP-ML, a U-NET machine-learning correction, and 3D VSHARP®, a correction using a rapid finite-element Linear Boltzmann Transport Equation (LBTE) solver to estimate scatter in a manner similar to traditional stochastic Monte Carlo (MC) simulations. Of the three corrections, 3D VSHARP is the most accurate and flexible since it can be readily applied to arbitrary scanner geometries, protocols, and scan parts while the 2D VSHARP models may need to be regenerated for each configuration. On the other hand, 3D VSHARP is inherently slower since a minimum of two reconstruction passes are needed and the LBTE solver, while much faster than traditional MC, is still computationally intensive. The goal of this work was to minimize LBTE run times for (typically large) industrial datasets by optimizing parameter settings, particularly the choice of the sampling grid dimensions. This was achieved by applying a multi-objective genetic algorithm to find the Pareto front characterizing the tradeoff between speed and accuracy and identifying key operating points on the curve. Testing with 720 frames of 3720x3720 projection data to make a reconstruction volume of size 500x500x600, we found that excellent image quality can be obtained by using a coarse scatter grid size of 27x27x32 volume and 44x44 detector and a primary grid size of 246x246 x295 volume and 295x295 detector, both over 42 frames for a grand total of 21 seconds LBTE computation time. We show the Pareto characterization, as well as demonstrations of 3D VSHARP image quality with significantly reduced scatter-induced artifacts such as streaking and shading.