Pano: PACT Imaging Neural Operator

• The paper introduces Pano, a physics-aware neural operator that learns the inverse mapping in PACT by integrating data fidelity with Helmholtz-based physical loss.
• It employs spherical discrete-continuous convolutions to preserve geodesic features from curved sensor arrays, ensuring resolution-independent and artifact-minimized reconstructions.
• Pano achieves rapid, high-quality 3D volumetric imaging with reduced hardware demands, demonstrating superior PSNR, SSIM, and artifact suppression compared to traditional methods.

Pano (PACT Imaging Neural Operator) is an end-to-end, physics-aware neural operator architecture developed for three-dimensional photoacoustic computed tomography (PACT). Pano directly learns the mapping from photoacoustic sensor measurements to volumetric reconstructions while embedding physical constraints, enabling robust high-fidelity imaging under sparse sampling and varying sensor configurations. The architecture combines spherical discrete-continuous convolutions, Helmholtz equation constraints, and neural operator frameworks to accelerate 3D PACT imaging and substantially reduces hardware requirements, positioning it for effective deployment in both preclinical and clinical applications (Wang et al., 11 Sep 2025).

1. Physics-Aware Inverse Mapping in PACT

Pano is designed to address the ill-posed inverse problem in PACT, where the objective is to recover the initial pressure distribution within tissue from externally measured acoustic signals. Unlike conventional analytical and iterative reconstruction algorithms (e.g., universal back-projection, time reversal, or filtered back projection), which invert the photoacoustic forward model through explicit solver methods, Pano is trained to learn the entire inverse operator in an end-to-end manner. This approach enables the model to incorporate both physics-informed constraints and empirical data priors, thereby enhancing its robustness in sparse-data regimes and providing resolution-independence across acquisition hardware configurations (Wang et al., 11 Sep 2025, Wang et al., 5 Nov 2024).

The inversion process within Pano incorporates physical plausibility through loss terms grounded in the Helmholtz equation, ensuring consistency between the reconstructed images and acoustic wave propagation physics. Specifically, the loss function includes both a data fidelity term and a physics loss: $$\mathcal{L}(\Theta) = \lambda_{\text{data}} \|\hat{P} - P\|_1 + \lambda_{\text{phys}} \|A \hat{P} - \Psi\|_2^2$$ where $\hat{P}$ is the neural reconstruction, $P$ is the ground-truth, $A$ is the forward physical operator that implements the Helmholtz equation, and $\Psi$ is the measured photoacoustic wavefield.

2. Spherical DISCO and Sensor Geometry Preservation

A distinguishing feature of Pano is its use of spherical discrete-continuous convolution (DISCO) blocks to process the measured photoacoustic signals. Traditional planar convolutions are suboptimal for hemispherical sensor arrays as they distort geodesic distances and spatial relations inherent to curved acquisition geometries. DISCO operates natively on functions defined on a spherical domain, ensuring geodesic local features are preserved. The spherical convolution is formulated as: $(k \star f)(v) = \int_D \kappa(u - v) f(u)\,du$ which is approximated discretely as: $$(k \star f)(v_i) \approx \sum_j \kappa(u_j - v_i) f(u_j) q_j$$ where $u_j$ are sampling points with quadrature weights $q_j$, and $\kappa$ is a kernel parameterized using learnable basis functions, such as piecewise linear, wavelet, or Zernike polynomials. This approach allows resolution-agnostic processing of input data and avoids artifacts induced by projecting curved geometries onto Cartesian grids (Wang et al., 11 Sep 2025).

3. Neural Operator Frameworks and Implicit Representations

Pano leverages advances in neural operator theory and implicit neural representations to bridge discrete sensor measurements and continuous image domains. Neural operators, such as those realized via Fourier Neural Operator (FNO) layers, aggregate multi-frequency information and enable coordinate transformation between spherical and Cartesian domains.

Recent research in implicit neural representations (INR) for PACT reconstructs the initial pressure as a continuous function using multilayer perceptrons (MLPs), mapping $(\mathbf{x}, \mathbf{y}) \to H$ where $H$ denotes the local initial pressure. The function is optimized by minimizing discrepancies between the predicted and measured signals through a self-supervised training protocol. The INR approach has demonstrated superior performance over both UBP and discrete model-based reconstructions, achieving higher SSIM and PSNR, improved SNR and CNR, and enhanced artifact suppression in sparse-view settings (Yao et al., 4 Sep 2024).

The integration of adjoint forward models—such as those based on the elastic wave equation with full shear modulus modeling—provides accurate physics-driven gradients for iterative neural optimization, further improving reconstruction quality, especially in scenarios involving strong aberrators like the skull (Mitsuhashi et al., 2017).

4. Artifact Suppression and Sparse Data Robustness

Deep learning strategies embedded in Pano encompass multiple processing pathways to address artifacts due to limited-angle acquisitions, sparse detector arrays, and measurement noise. These include neighborhood attention mechanisms, hybrid architectures combining direct and post-processing modules, and physics-informed regularization.

For dynamic and multi-frame PACT imaging, low-rank signal processing techniques (e.g., Karhunen–Loève transform) can be employed to denoise the data and reduce the inversion problem’s effective dimensionality by concentrating signal energy in principal components. Low-rank representations and spatial-temporal iterative reconstruction (STIR) schemes have demonstrated improved image quality and computational efficiency relative to frame-by-frame conventional methods (Poudel et al., 2019).

State-of-the-art deep networks, such as Res-Unet or hybrid FD-UNet/Y-Net architectures, also provide robust direct reconstructions and artifact removal through learned mappings and residual connections. These methods are especially valuable when conventional algorithms fail in ill-posed or artifact-prone conditions (Wang et al., 5 Nov 2024).

5. Performance, Scalability, and Hardware Implications

Published evaluations of Pano demonstrate high-quality 3D volumetric reconstruction under uniform subsampling accelerations ranging from $6\times$ to $20\times$, with reported gains in cosine similarity and PSNR of up to $37\%$ over universal back-projection, along with consistently lower normalized mean square error (NMSE). Pano maintains coherent vessel topology and low-noise reconstructions even at drastic transducer count reductions and restricted angular coverage, outperforming both traditional and reconstruction–then–denoising baselines under equivalent acquisition conditions (Wang et al., 11 Sep 2025, Yao et al., 4 Sep 2024).

A plausible implication is broader clinical translation: reduced hardware requirements (fewer transducers, compact array designs) and fast inference times (0.11 seconds for $256^3$ volumes on RTX 4090 GPU) enable real-time volumetric imaging and interactive visualization in resource-constrained environments.

6. Validation, Limitations, and Future Directions

Validation studies combining simulations and phantom experiments confirm the reliability of Pano’s learned inverse mappings. Physical models, such as FDTD-based forward–adjoint operator pairs, are rigorously tested against analytic pressure profiles and inner-product adjointness checks, achieving six-digit validation accuracy (Mitsuhashi et al., 2017). Experimental reconstructions, particularly those modeling inelastic skull propagation, yield artifact-suppressed and anatomically accurate images unattainable via fluid-only or back-projection methods.

While Pano’s current implementation assumes homogeneous sound speed, future directions include extending the model to heterogeneous media (for transcranial or abdominal imaging), exploring implicit neural fields for volumetric compression, and conducting in-vivo human studies with sparse ground-truth availability. Enhancements in physics-based regularization, operator loss design, and scalable network architectures are active areas for improving real-time performance and robustness to acoustic parameter uncertainty.

7. Practical and Clinical Implications

The ability of Pano to deliver artifact-minimized, high-fidelity 3D PACT reconstructions from minimal data acquisition opens new opportunities for functional brain imaging, breast cancer detection, whole-body small animal studies, and other domains demanding real-time, cost-effective volumetric imaging. By integrating physically consistent operator theory, spherical geometry preservation, and deep neural learning, Pano constitutes a comprehensive solution for next-generation photoacoustic tomography, facilitating improved diagnostic outcomes and practical system implementation in both laboratory and clinical environments.

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In summary, Pano exemplifies the synthesis of physical modeling and neural operator theory in biomedical imaging. Its technical and architectural innovations provide both theoretical rigor and practicality, directly addressing persistent limitations in traditional PACT reconstruction and opening pathways to rapid, robust volumetric imaging under reduced hardware constraints (Wang et al., 11 Sep 2025, Yao et al., 4 Sep 2024, Mitsuhashi et al., 2017, Wang et al., 5 Nov 2024, Poudel et al., 2019).