In laser-driven inertial confinement fusion (ICF) experiments, precise observation of dynamic wavefront changes is crucial for understanding fluid instabilities. The CUP-VISAR system, with its high spatiotemporal resolution, is widely used for this purpose. However, existing algorithms face challenges in processing CUP-VISAR data effectively due to high noise levels, particularly under low contrast-to-noise ratio (CNR), resulting in poor image reconstruction and inaccurate shock wave velocity measurements. To address these limitations, we propose a novel data reconstruction algorithm that combines tensor singular value thresholding (TSVT) and stripe phase mapping (SPM) to enhance noise suppression and feature extraction, improving velocity field accuracy under varying noise conditions.

The key innovation of this research is the integration of TSVT and SPM within a unified framework. TSVT transforms noisy data into the frequency domain, leveraging low-rank tensor properties to isolate essential signal components while filtering out noise using singular value decomposition (SVD). Following TSVT, SPM reconstructs phase data by treating deviations from sinusoidal interference patterns as noise, thereby enhancing stripe clarity for accurate velocity field estimation. Finally, total variation (TV) regularization smooths the data to reduce spatial and temporal artifacts. This multi-step approach effectively combines TSVT, SPM, and TV for robust noise suppression. The algorithm’s performance was validated on SG-III prototype data under varying CNR conditions, with comparisons to E-3DTV, ADMM-TV, and TVAL3 using metrics such as peak signal-to-noise ratio (PSNR), structural similarity index (SSIM) (Fig. 6), and relative velocity error.

The results indicate a significant enhancement in reconstruction quality achieved by the TSVT?SPM algorithm, particularly under low CNR conditions. Across the entire tested CNR range (4?10), the proposed algorithm consistently outperformed other methods in terms of both PSNR and SSIM. For instance, at a CNR of 6.56, the TSVT?SPM method achieved a PSNR of 29.15 dB and an SSIM of 0.94, compared to the 9.84 dB PSNR and 0.37 SSIM recorded by the E-3DTV algorithm (Table 2). This demonstrates a substantial improvement in reconstruction accuracy and image quality, demonstrating the robustness of the proposed approach. In addition to PSNR and SSIM comparisons, the relative velocity error between the reconstructed data and the original velocity field was analyzed. Even under challenging noise conditions, the TSVT?SPM algorithm exhibited a maximum relative velocity error of 6.11%, significantly lower than the errors produced by the other algorithms: 138.63% for E-3DTV, 130.98% for ADMM-TV, and 111.64% for TVAL3 (Fig. 12). These findings highlight the superior capability of the proposed method to accurately recover the velocity field despite substantial noise interference. Visual inspections of the reconstructed data further illustrate the strengths of the TSVT?SPM algorithm. As shown in Fig. 9, the proposed method delivers a markedly clearer and more precise representation of the dynamic 2D velocity fields, particularly in the 25th frame, where the stripes are well-defined, and noise is substantially reduced compared to other methods. Moreover, the temporal evolution of the stripes, depicted in Fig. 10, reveals that the algorithm effectively captures smooth transitions and subtle variations in the velocity field over time. In contrast, the E-3DTV and ADMM-TV methods exhibit severe artifacts and poor temporal resolution in noisy environments. The robustness of the TSVT?SPM algorithm is further validated by its performance across varying noise levels. In Table 2, we observe that as the CNR increases from 4 to 10, the proposed algorithm maintains consistent improvements in PSNR and SSIM, confirming its effectiveness across a wide range of noise intensities. This reliability across different experimental conditions underscores the algorithm’s adaptability without significant performance degradation. In addition, the low-rank structure extracted by TSVT enables efficient handling of large-scale datasets, a critical requirement for processing high-dimensional data in real-world ICF experiments.

The TSVT?SPM algorithm represents a significant breakthrough in CUP-VISAR data reconstruction by integrating tensor decomposition, phase mapping, and regularization techniques. This approach effectively addresses the challenges posed by noisy data in dynamic velocity field measurements. Experimental results demonstrate that the algorithm not only surpasses existing methods in reconstruction accuracy but also exhibits superior robustness under varying noise conditions. Its ability to deliver high-quality reconstructions, even at low CNRs, is particularly advantageous for inertial confinement fusion applications, where precision and reliability are paramount. With its effectiveness in noise suppression and feature preservation, the algorithm is well-suited for large-scale data processing. Its capability to handle high-dimensional data while maintaining consistent performance across different noise levels ensures its applicability in complex experimental environments.