A state-space model-based three-dimensional flow reconstruction method for accurate tomographic particle image velocimetry measurements

High accuracy and high resolution are essential for tomographic particle image velocimetry (Tomo-PIV) measurements, particularly in complex flows like turbulence. However, the widely used cross-correlation-based methods are limited by their correlation window sizes. Although some recently developed optical flow-based methods have shown significant improvements, they are still limited by low particle densities and particle volume reconstruction errors. To solve these problems, in this study, a novel three-dimensional (3D) flow field reconstruction method is proposed for postprocessing optical flow velocity measurements to obtain high spatial accuracy and resolution in Tomo-PIV measurements. First, a 3D global feature extraction module based on volumetric adaptive Mamba blocks is introduced to capture long-range dependencies within the flow field. Second, a local feature extraction module based on the wavelet transform and large kernel convolution is proposed to capture the local high-frequency components in the flow field. The newly proposed 3D flow field reconstruction method fully captures flow field features, combining global and local features with low- and high-frequency features to reconstruct the 3D flow field structure with high accuracy. Additionally, to improve the performance achieved in experimental applications, a synthetic 3D flow field training dataset generation framework is proposed to simulate real Tomo-PIV measurement conditions. The framework incorporates key factors that influence the accuracy of optical flow estimation, including particle volume reconstruction errors and limited particle densities. Evaluation on both direct numerical simulation data and experimental Tomo-PIV data demonstrates the substantial advantages of the proposed method over existing 3D flow field reconstruction methods.