Score-Based Diffusion Models for Photoacoustic Tomography Image Reconstruction

TL;DR

Problem addressed: limited-view PAT leads to ill-posed inverse problems requiring strong priors. Approach: a diffusion-prior framework with measurement-conditioning for any linear forward model, using a VP-SDE with $T=1$ and $x_T \sim \mathcal{N}(0,I)$ and a regularized update $x'_t = (\lambda A^T A + (1-\lambda) I)^{-1}((1-\lambda) x_t + \lambda A^T y_t)$. Key contributions: generalizes diffusion-based priors to PAT with a simple projection-like conditioning; demonstrates improved PSNR/SSIM over TV and competitive results to supervised baselines under SA, with careful analysis of uncertainty via sample variance; shows robustness to out-of-distribution breast images and cross-pattern generalization without retraining. Significance: provides flexible, unsupervised reconstruction with learned priors suitable for varying sensor geometries, enhancing applicability of PAT.

Abstract

Photoacoustic tomography (PAT) is a rapidly-evolving medical imaging modality that combines optical absorption contrast with ultrasound imaging depth. One challenge in PAT is image reconstruction with inadequate acoustic signals due to limited sensor coverage or due to the density of the transducer array. Such cases call for solving an ill-posed inverse reconstruction problem. In this work, we use score-based diffusion models to solve the inverse problem of reconstructing an image from limited PAT measurements. The proposed approach allows us to incorporate an expressive prior learned by a diffusion model on simulated vessel structures while still being robust to varying transducer sparsity conditions.

Figures (6)

• Figure 1: PAT measurement acquisition. A ring of ultrasound sensors (transducer array) surrounds the object to be imaged. The transducer array receives photoacoustic signals emitted in response to a laser pulse.
• Figure 2: Our conditional sampling process with a trained diffusion model. Given PAT measurements, sampling starts with an image of Gaussian noise, which is transformed over many steps into the reconstructed PAT image. Each step involves a measurement-conditioning update (blue arrow) followed by a denoising update (black arrow) that takes the image closer to the learned prior.
• Figure 3: Image reconstructions across meas. settings. Top two diagrams illustrate the limited-view and spatial-aliasing configurations, resp. (e.g., "LV74" refers to limited-view with $74\%$ transducers). PSNR is on the bottom left of each image. Our method's results include one sample and the avg. and std. dev. of 320 samples. The zoom-ins show high-fidelity details from our method that do not appear in baseline reconstructions. Overall, our method outperforms baselines in SA settings but may be prone to hallucination for LV (std. dev. maps show where hallucinations occur). Qualitatively, our samples tend to appear closer to the prior. The mean of our samples generally outperforms baselines.
• Figure 4: Average PSNR and SSIM on the 10-image test set for TV, SAU, and our diffusion-model approach. "Diffusion Average" computes the avg. PSNR or SSIM based on the empirical mean of 320 samples; "Diffusion Sample" computes the avg. PSNR or SSIM based on all samples for each measurement. Our samples beat both baselines for SA configurations and perform on par for LV, while our averaged reconstructions outperform baselines on nearly every configuration.
• Figure 5: Comparison of SAU performance on a new transducer pattern vs. our model and TV. Each model was tested on an LV50 image, but the SAU model used was trained on SA50 reconstructions. PSNRs show that SAU does not generalize across configurations. Zoom-in shows a GT feature that only our method was able to recover.