Optical Inversion and Spectral Unmixing of Spectroscopic Photoacoustic Images with Physics-Informed Neural Networks

Photoacoustic tomography (PAT) combines the optical absorption contrast of biological tissue with the spatial resolution of ultrasound, yet recovering the initial pressure distribution from sparse-view sensor measurements remains an ill-posed inverse problem. Iterative compressive-sensing solvers and unrolled deep networks both retain a dependence on the system matrix at inference, which leaves real-time clinical reconstruction computationally expensive. This paper proposes the Sensor Attention Network (SAN), a Transformer-based architecture that treats the full time series of each sensor as a token and maps raw measurements directly to the reconstructed image without invoking the system matrix at inference. For training and benchmarking, an analytical k-space H-matrix is constructed and validated against the k-Wave pseudo-spectral solver under matched geometry, achieving a mean per-sensor Pearson correlation of 0.919 +/- 0.049, with k-space apodization and Gaussian temporal damping acting synergistically to reduce the energy-normalized mismatch by 49%. Trained with a vessel-weighted loss on 488 augmented samples and evaluated on 46 held-out samples against ISTA, split-Bregman total variation (SBTV), and learned ISTA (LISTA), SAN attains the highest mean SSIM (0.522) and PSNR (22.09 dB) and the lowest NMSE (0.233). Paired t-tests and Wilcoxon signed-rank tests confirm the superiority of SAN over LISTA on PSNR, NMSE, and Pearson correlation at p < 1e-8, and over ISTA and SBTV on all fidelity metrics. By bypassing the H-matrix at inference, SAN reduces reconstruction time by at least an order of magnitude, supporting real-time PAT reconstruction.

In fluorescence microscopy, spectral unmixing aims to recover individual fluorophore concentrations from spectral images that capture mixed fluorophore emissions. Since classical methods operate pixel-wise and rely on least-squares fitting, their performance degrades with increasingly overlapping emission spectra and higher levels of noise, suggesting that a data-driven approach that can learn and utilize a structural prior might lead to improved results. Learning-based approaches for spectral imaging do exist, but they are either not optimized for microscopy data or are developed for very specific cases that are not applicable to fluorescence microscopy settings. To address this, we propose λSplit, a physics-informed deep generative model that learns a conditional distribution over concentration maps using a hierarchical Variational Autoencoder. A fully differentiable Spectral Mixer enforces consistency with the image formation process, while the learned structural priors enable state-of-the-art unmixing and implicit noise removal. We demonstrate λSplit on 3 real-world datasets that we synthetically cast into a total of 66 challenging spectral unmixing benchmarks. We compare our results against a total of 10 baseline methods, including classical methods and a range of learning-based methods. Our results consistently show competitive performance and improved robustness in high noise regimes, when spectra overlap considerably, or when the spectral dimensionality is lowered, making λSplit a new state-of-the-art for spectral unmixing of fluorescent microscopy data. Importantly, λSplit is compatible with spectral data produced by standard confocal microscopes, enabling immediate adoption without specialized hardware modifications.

The accurate recovery of constituent-level optical properties from integrating sphere measurements is a central analytical challenge in pharmaceutical analysis, food science, and biomedical diagnostics. Neural network autoencoders can extract spectrally resolved absorption and scattering coefficients for each constituent without prior knowledge, but their fully connected encoders bind learned features to absolute wavelength indices, causing accuracy loss under spectrometer calibration drift or hardware exchange. This work introduces the Bin Latent Transformer (BiLT)-Autoencoder, in which the dense encoder is replaced by a cross-attention scanner: 16 learnable probe vectors query a convolutional feature map, aggregating morphological spectral information independently of absolute wavelength position. A physics-constrained linear decoder with enforced absorption/scattering separation and a three-phase curriculum augmentation strategy complete the architecture. On a liquid phantom benchmark (intralipid and two ink absorbers; 496 samples), the model achieves $R^2 = 0.979$ and $0.975$ for $μ_a(λ)$ and $μ_s'(λ)$, respectively, on held-out test spectra, maintaining $R^2 > 0.90$ for $μ_a$ and $R^2 \approx 0.99$ for $μ_s'$ across the full tested shift range of $\pm 10$ spectral bands. The model generalises to a simulated spectrometer with a broader instrument line shape (${\approx}24$nm FWHM) without retraining, retaining $R^2 \approx 0.96$ and $0.974$ for the two channels. Attention map analysis reveals a physically interpretable two-component probe strategy: sparse anchor probes at absorption-edge wavelengths combined with a diffuse, SNR-driven ensemble at the high-transmittance long-wavelength region, which recruits additional probes dynamically under noise to provide implicit spectral averaging.