GS-DOT: Gaussian splatting-based image reconstruction for diffuse optical tomography

Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems, enabling high-quality reconstructions in inverse problems by leveraging expressive prior distributions learned from empirical data. Despite their strong empirical performance and growing interest within the machine learning community, their behaviour in realistic, severely ill-posed inverse problems with experimental measurement data remains under-explored. Diffuse optical tomography (DOT) is an inverse boundary value problem that uses boundary measurements of near-infrared light to recover spatially varying absorption and scattering parameters in biological tissue. The problem is highly ill-posed and particularly sensitive to both measurement noise and modelling errors. We introduce a regularization strategy by constructing a mixed score consisting of a learned component and a model-based component. We show that the resulting mixed score approximates the score of a corresponding mixture distribution locally and in the small diffusion-time regime, providing a theoretical justification for the approach. We compare four approaches for difference imaging in DOT: a classical model-based method, an approximate score-based diffusion method (DPS), an exact posterior sampling method (UCoS) and a novel, regularized version of UCoS. We show that both the model-based approach and approximate diffusion-based sampling degrade significantly in the presence of limited-view geometry and real experimental data, whereas UCoS yields more accurate reconstructions.

2D Gaussian Splatting is an attractive direction for image representation due to its explicit formulation, fast rasterization, and favorable decoding efficiency. The representation quality of this paradigm depends on the proper allocation of Gaussian capacity to the demanding regions. However, existing methods fail to allocate Gaussian capacity efficiently during optimization: under-reconstructed content is often refined in a fragmented pixel-wise manner, while neighboring optimized Gaussians with similar attributes are redundantly retained. This inefficiency motivates the need for a density control framework that jointly addresses insufficient allocation in under-reconstructed regions and redundant allocation in over-reconstructed regions. Our key insight is that this framework should exploit two complementary forms of locality: the local continuity of reconstruction errors in image space for improved Gaussian allocation, and the local similarity of neighboring Gaussians in Gaussian space for redundant elimination. Based on this insight, we propose Locality-Aware Density Control (LocoADC), a plug-and-play framework that improves Gaussian capacity utilization through Region-wise Gaussian Densification (RGD) and Similarity-Driven Gaussian Merging (SDGM) strategies, together with a local color consistency constraint for more reliable merging. Extensive experiments on diverse datasets show that LocoADC consistently improves multiple baselines by enabling more effective local Gaussian allocation, including a 2.93 dB PSNR gain over GI on the CLIC dataset under the same 30k Gaussian budget. Code is available at: \textit{https://github.com/ChenJiaCong-1005/LocoADC}.

The inverse problem of reconstructing optical properties, specifically absorption and scattering coefficients, in layered biological media from time-domain reflectance measurements remains a significant challenge for traditional analytical models. Inverse solvers based on the diffusion equation often struggle with structural heterogeneity, frequently yielding poor accuracy for superficial absorption and deep-layers scattering. In this work, we propose a machine learning framework as an alternative approach to reconstruct the optical properties of a bilayered medium, benchmarking its efficiency and accuracy against model-based algorithms. To overcome the intrinsic approximations of diffusion theory and inverse reconstruction, we generated a robust synthetic dataset of forward DTOF using exact Monte Carlo simulations at multiple source-detector distances. A machine learning pipeline was then trained on this dataset and validated against state-of-the-art model-based reconstruction methods. Besides the significant reconstruction speed-up, the machine learning approach achieves higher accuracy than model-based inverse solvers, further providing an estimate of the parameter space dimensionality without requiring any a priori information about the number of layers in the investigated geometry. Further enhancements in the reconstruction accuracy can be expected in future extensions of this work, by training the pipeline over multiple DTOF curves from the same medium, in a joint multi-distance reconstruction approach.