Tensor Decomposition-Based Four-dimensional Background-Oriented Schlieren Tomography for High-Speed, High-Fidelity Flow Field Reconstruction

This work introduces an efficient reconstruction algorithm for time-resolved background-oriented Schlieren tomography (BOST) by leveraging tensor decomposition and neural networks. The proposed algorithm organizes data into a four-dimensional spatiotemporal tensor (X-Y-Z-T) and applies a decomposition strategy based on three component sets: (XY-ZT), (XZ-YT), and (YZ-XT). To enhance efficiency and accuracy, tensor decomposition is integrated with a lightweight neural network. Additionally, a specialized distortion correction model is designed to address light ray path distortions caused by inhomogeneous dynamic flow fields. This network iteratively corrects light ray displacements at the background plate, ensuring precise compensation for distortions. The framework employs an integrated optimization strategy, performing bilinear-interpolated ray tracing followed by back-propagation to update tensor factorization components and neural network parameters. Mixed-precision computations are utilized to accelerate convergence, with single-precision operations for the forward process and half-precision for back-propagation. Experimental results demonstrate that the proposed method significantly reduces memory usage and reconstruction time while improving accuracy. Notably, it achieves a processing time of 12.6 seconds per frame without pre-training, with potential for further acceleration. This work provides a novel and streamlined approach for time-resolved visualization of complex flow fields, offering promising applications in fluid dynamics and combustion physics.