Accelerating 4D Hyperspectral Imaging through Physics-Informed Neural Representation and Adaptive Sampling

High-dimensional hyperspectral imaging (HSI) enables the visualization of ultrafast molecular dynamics and complex, heterogeneous spectra. However, applying this capability to resolve spatially varying vibrational couplings in two-dimensional infrared (2DIR) spectroscopy, a type of coherent multidimensional spectroscopy (CMDS), necessitates prohibitively long data acquisition, driven by dense Nyquist sampling requirements and the need for extensive signal accumulation. To address this challenge, we introduce a physics-informed neural representation approach that efficiently reconstructs dense spatially-resolved 2DIR hyperspectral images from sparse experimental measurements. In particular, we used a multilayer perceptron (MLP) to model the relationship between the sub-sampled 4D coordinates and their corresponding spectral intensities, and recover densely sampled 4D spectra from limited observations. The reconstruction results demonstrate that our method, using a fraction of the samples, faithfully recovers both oscillatory and non-oscillatory spectral dynamics in experimental measurement. Moreover, we develop a loss-aware adaptive sampling method to progressively introduce potentially informative samples for iterative data collection while conducting experiments. Experimental results show that the proposed approach achieves high-fidelity spectral recovery using only $1/32$ of the sampling budget, as opposed to exhaustive sampling, effectively reducing total experiment time by up to 32-fold. This framework offers a scalable solution for accelerating any experiments with hypercube data, including multidimensional spectroscopy and hyperspectral imaging, paving the way for rapid chemical imaging of transient biological and material systems.