Initial condition recovery in nonlinear damped viscous photoacoustic tomography using a convolutional neural network-guided gradient-free optimization framework

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.

Photoacoustic tomography (PAT) is an emerging imaging modality that combines the complementary strengths of optical contrast and ultrasonic resolution. A central task is image reconstruction, where measured acoustic signals are used to recover the initial pressure distribution. For ideal point-like or line-like detectors, several efficient and fast reconstruction algorithms exist, including Fourier methods, filtered backprojection, and time reversal. However, when applied to data acquired with finite-size detectors, these methods yield systematically blurred images. Although sharper images can be obtained by compensating for finite-detector effects, supervised learning approaches typically require ground-truth images that may not be available in practice. We propose a self-supervised reconstruction method based on Noisier2Inverse that addresses finite-size detector effects without requiring ground-truth data. Our approach operates directly on noisy measurements and learns to recover high-quality PAT images in a ground-truth-free manner. Its key components are: (i) PAT-specific modeling that recasts the problem as angular deblurring; (ii) a Noisier2Inverse formulation in the polar domain that leverages the known angular point-spread function; and (iii) a novel, statistically grounded early-stopping rule. In experiments, the proposed method consistently outperforms alternative approaches that do not use supervised data and achieves performance close to supervised benchmarks, while remaining practical for real acquisitions with finite-size detectors.

We study the deep image prior (DIP) framework applied to photoacoustic tomography (PAT) as an unsupervised reconstruction approach to mitigate limited-view artifacts and noise commonly encountered in experimental settings. Efficient implementation is achieved by employing recently published fast forward and adjoint algorithms for circular measurement geometries. Initialization via a fast inverse and total variation (TV) regularization are applied to further suppress noise and mitigate overfitting. For comparison, we compute a classical TV reconstruction. Our experiments comprise simulated PAT measurements under limited-view geometries and varying levels of added noise as well as experimental measurements together with using a digital twin for quality assessment. Our findings suggest that DIP framework provides an effective unsupervised strategy for robust PAT reconstruction even in the challenging case of a limited view geometry providing improvement in several quantitative measures over total variation reconstructions.