An evaluation framework for sparse 4D (3D + time) imaging reconstruction via bootstrapped cross-validation

Four-dimensional (4D; 3D + time) microscopic imaging has emerged as a powerful technique for investigating dynamic phenomena in complex systems, enabling direct visualisation of structural evolution in space and time. However, when pushing the limits of spatiotemporal resolution, most time-resolved imaging techniques yield inherently sparse 4D datasets. While deep learning-based reconstruction methods have shown promise in reconstructing 4D from sparse spatiotemporal measurements, a practical approach for evaluating their performance in the absence of a 4D reference has, to the best of our knowledge, been lacking. Here, we present a bootstrapped cross-validation framework that estimates reconstruction performance by quantifying correlations between reconstructions generated from independently sampled subsets of the acquired data, as inspired by the 3D validation strategy in cryo-electron microscopy, where reconstructions from split datasets are compared to assess resolutions. This enables both qualitative and quantitative assessment in the absence of ground truth. We investigate two representative scenarios with sparse and ultra-sparse X-ray datasets and validate this approach using 4D-ONIX, a 4D deep-learning reconstruction method, on simulated water droplet collision experiments. The proposed approach provides a reference-free framework for performance estimation and support for better-informed experimental strategies across a wide range of ultrafast imaging applications.