Source-linked AI summary
PAGS: Autofocusing Photoacoustic Tomography via Speed-of-Sound-Adaptive Gaussian Splatting
Jiarui Ge, Jintao Ma, Bangxu Fan, Jinyan Zhang, Xiaokang Yang, Shuai Na, Xiaoyun Yuan
TL;DR
Unknown speed-of-sound heterogeneity can defocus PACT reconstructions, while existing adaptive approaches are costly or difficult to scale in 3D. PAGS jointly optimizes sparse Gaussian sources and a latent anisotropic path-averaged SoS field, improving focusing under heterogeneous media while reducing analytic-projection runtime from 6.7 s to 2.3 s.
Problem
Unknown, path-dependent speed-of-sound variations cause arrival-time errors and defocusing, making aberration correction a central challenge for high-resolution PACT.
Method
PAGS jointly optimizes sparse Gaussian PA sources and a latent anisotropic path-averaged SoS field with an analytic Gaussian acoustic projection from measured signals.
Results
PAGS shows improved focusing under heterogeneous acoustic media and sparse-view settings, while analytic projection reduces runtime from 6.7 s to 2.3 s.
Takeaways & Limitations
PAGS offers a signal-domain autofocusing approach for PACT that avoids calibrated SoS priors and explicit dense acoustic-medium recovery.
Takeaways & Limitations
Dense-grid and implicit-function acoustic-field representations remain computationally demanding, limiting scalability and memory efficiency in complex 3D environments.
Abstract
from arXiv · showhide
Photoacoustic computed tomography (PACT) combines optical absorption contrast with acoustic detection for high-resolution deep-tissue imaging. A persistent challenge is that unknown speed-of-sound (SoS) heterogeneity changes acoustic time-of-flight, causing defocusing artifacts when reconstruction assumes a uniform SoS. Existing SoS-adaptive methods either rely on calibrated acoustic priors or optimize dense physical medium models, which becomes expensive and difficult to scale in 3D. We propose PAGS, a differentiable framework for blind autofocusing PACT via speed-of-sound-adaptive Gaussian splatting. PAGS represents the initial pressure field with sparse Gaussian photoacoustic (PA) sources and replaces explicit medium recovery with a compact anisotropic path-averaged SoS (ASoS) field parameterized by spherical harmonic probes. This latent propagation field directly controls source-to-transducer arrival-time alignment, while an analytic Gaussian acoustic projection maps the source representation to transducer signals efficiently. The resulting closed-loop signal-domain optimization jointly updates the Gaussian PA source parameters and the ASoS field from measured data, without calibrated SoS priors. Experiments on simulated and physical phantom data demonstrate improved reconstruction sharpness under heterogeneous acoustic media, robustness to sparse-view sampling, and computational benefits from the analytic Gaussian projection.
1 Introduction
PAGS addresses speed-of-sound-induced defocusing in PACT by jointly learning sparse Gaussian photoacoustic sources and a compact anisotropic path-averaged SoS field directly from measured signals. Its analytic Gaussian projection enables differentiable blind autofocusing without calibrated SoS priors or explicit dense medium recovery.
- Background: PACT reconstructs high-resolution initial pressure from broadband ultrasound generated by laser-induced thermoelastic expansion and recorded by surrounding transducers.It combines optical absorption contrast with acoustic detection.
- Problem: Uniform-SoS reconstruction produces path-dependent arrival-time errors in heterogeneous tissue, causing defocusing, geometric distortion, and loss of fine vascular detail.The same source can exhibit different path-averaged SoS values toward different transducers.
- Related work: Existing SoS-adaptive methods trade calibrated acoustic priors for dense physical-medium or scalar-SoS optimization, limiting generality and scalability.Calibrated approaches may require segmentation or auxiliary measurements.
- Method: PAGS replaces explicit medium recovery with a latent anisotropic path-averaged SoS field that directly controls source-to-transducer arrival-time alignment.The field is parameterized by compact spherical harmonic probes anchored on a spatial grid.
- Contributions: Sparse Gaussian PA sources, spherical harmonic probes, and analytic Gaussian acoustic projection are jointly optimized in a single signal-domain loop from measured transducer signals.The framework is validated on simulated and physical phantom data, including sparse-view settings and component ablations, with improved focusing and favorable efficiency.
2 Related Work
Prior PACT reconstruction methods trade computational efficiency, robustness, and physical modeling fidelity, but commonly depend on homogeneous or predefined SoS assumptions. Gaussian splatting offers efficient tomographic representations, while PAGS addresses prior Gaussian PACT limitations with analytic projection and learnable path-level SoS correction.
- Conventional reconstruction: Analytical PACT methods such as UBP and DAS are computationally efficient but assume straight-ray propagation in a homogeneous medium.Acoustic heterogeneity causes refraction and time-of-flight mismatches that global SoS tuning cannot compensate for.
- Iterative reconstruction: Model-based iterative methods improve resilience to sparse sampling and noise, but repeated forward and adjoint evaluations are computationally and memory intensive.They typically also require a predefined SoS map for accurate forward modeling, which is difficult to acquire in realistic tissues.
- Learning-based reconstruction: Deep learning and physics-aware methods reduce artifacts and can recover SoS fields jointly with absorption, combining learned priors with acoustic physical models.These approaches target sparse-view, limited-aperture, and wavefront-aberration settings.
- Gaussian representations: Gaussian splatting uses learnable anisotropic 3D primitives and efficient differentiable rasterization, motivating adaptations to CT and ultrasound tomography.The representation provides structural flexibility and computational efficiency for spatial modeling.
- Gaussian PACT reconstruction: SlingBAG represents initial pressure with Gaussian PA sources but uses concentric spherical-shell approximations and assumes globally homogeneous SoS.PAGS retains the sparse Gaussian sources, replaces that approximation with analytic Gaussian acoustic projection, and learns an anisotropic path-averaged SoS field using compact spherical harmonic probes.
3 Method
PAGS performs blind PACT autofocusing by jointly optimizing a compact Gaussian PA source representation and a latent anisotropic path-averaged SoS field through differentiable signal matching. Its spatially anchored SH-probe field and analytic Gaussian projection correct arrival-time alignment without explicitly recovering the physical acoustic medium.
- Gaussian PA sources: PAGS represents the initial pressure field with sparse Gaussian PA sources whose centers, amplitudes, and spatial scales form a compact, continuous, differentiable representation.The representation is suited to localized PA structures such as vessels.
- Joint optimization: PAGS jointly updates Gaussian source parameters and propagation parameters by matching synthesized detector signals to measurements in a closed-loop differentiable objective.Source updates refine the initial pressure field, while propagation updates correct the arrival-time alignment controlling focus.
- ASoS propagation field: The latent ASoS field replaces explicit medium recovery by providing direction-dependent path-averaged SoS values for source-to-transducer delay estimation.It compensates for propagation-induced arrival-time errors rather than recovering the local physical SoS distribution.
- ASoS parameterization: PAGS stores second-order spherical-harmonic SoS probes on a regular 3D grid, decoupling propagation parameters from Gaussian sources that may move, split, or be pruned.Each probe contains nine SH weights, with trilinear interpolation producing local weights before directional evaluation.
- Efficiency: 12.5K× reduction: in a representative setting, PAGS uses 36.9K probe-grid weights instead of 460M direct source-to-transducer ASoS scalars.The setting contains 100K active Gaussian PA sources and 4.6K transducers.
- Analytic acoustic projection: The far-field analytic projection retains the outgoing Gaussian acoustic term and remains differentiable with respect to source and ASoS parameters through R and vavg.It uses a single exponential evaluation per source, transducer, and time sample, while parameterization controls field complexity without an explicit geometry-specific regularizer.
4 Experiments · 4.1 Experimental Setup
The experiments evaluate PAGS on complementary simulated and physical phantom datasets, using controlled heterogeneous-SoS simulation and real acquisition conditions. The setup compares PAGS with SoS- and representation-based baselines, applies reference-based quantitative evaluation for simulations, and specifies GPU-based implementation settings.
- 4.1.1 Datasets: PAGS is evaluated on simulated and physical phantom datasets to test controlled reconstruction quality and robustness to real acquisition imperfections.The simulated dataset uses a digital vascular phantom and a realistic reference reconstruction, while the physical dataset captures real acquisition conditions.
- 4.1.1 Datasets: The simulated dataset uses k-Wave to generate acoustic measurements from a 3D vascular phantom with heterogeneous speed of sound.The SoS map contains a 1450 m/s background and a 1550 m/s ellipsoidal inclusion.
- 4.1.1 Datasets: The simulated detector geometry contains 4600 point transducers on a spherical cap, with 1024 samples per detector at 50 MHz.The ground-truth initial pressure volume uses a 0.1 mm voxel size and is the simulation source rather than the quantitative evaluation target.
- 4.1.1 Datasets: The physical phantom contains absorptive structures, approximately 5%–8% acoustic contrast to water, and 575 transducer elements sampled over eight rotational views.The acquisition yields 4600 effective transducer positions, with 4096 samples per channel at 20 MHz.
- 4.1.2 Baselines: PAGS is compared with Vanilla UBP, Dual-SoS UBP, and Vanilla SlingBAG, with all methods sharing identical preprocessing.Vanilla UBP assumes a globally uniform SoS of 1450 m/s, whereas Dual-SoS UBP uses a known tissue–water boundary and path-averaged SoS without refraction modeling.
- 4.1.3 Evaluation: Simulated reconstructions are evaluated using PSNR, RMSE, and SSIM against a reference volume incorporating realistic opto-acoustic and transducer responses.Reconstructions are peak-normalized and rigidly registered before metric computation over a central region of interest with 0.1 mm isotropic voxels.
- 4.1.4 Implementation: PAGS experiments run in PyTorch on a single NVIDIA A100 GPU, using SH degree D = 2 with 9 SH coefficients.The SH probe grid resolution ranges from 83 to 163, and Gaussian PA sources are initialized with approximately 105–106 primitives.
4.2 In Silico Evaluation
In silico evaluation shows that PAGS corrects heterogeneous-medium reconstruction artifacts without calibrated SoS priors. Joint optimization of Gaussian PA sources and the ASoS field produces sharper, more continuous vessels and the best quantitative scores among compared methods.
- Evaluation setup: The controlled in silico test evaluates correction of heterogeneous-medium artifacts without using the tissue–water boundary as a calibrated SoS prior.The comparison uses reconstructed vascular structures in a heterogeneous acoustic medium.
- Baseline behavior: Vanilla UBP shows geometric shift and defocus because a single uniform SoS cannot align arrival times across propagation paths.Vanilla SlingBAG produces a cleaner background through sparse Gaussian PA source representation, but its fixed back-projection cannot adapt to residual signal mismatch.
- PAGS reconstruction: PAGS reconstructs sharper, more continuous vessel branches while maintaining a clean background by jointly optimizing Gaussian PA sources and the ASoS field.Signal residuals update both Gaussian PA source parameters and path-level propagation correction.
- Quantitative results: 1.3 dB PSNR improvement, RMSE reduction from 0.0354 to 0.0305, and SSIM increase by 0.206 over vanilla SlingBAG make PAGS the best-scoring method.Metrics are reported against the uniform-SoS UBP reference after rigid registration and peak-intensity normalization.
4.3 Experimental Validation on a Physical Phantom
Physical-phantom measurements show that PAGS improves image sharpness, local contrast, and separation of neighboring structures under blind SoS adaptation. The evaluation relies on visual structure and local profile sharpness because voxel-level ground truth is unavailable.
- Experimental setting: Physical phantom signals include finite transducer bandwidth, electronic noise, acoustic attenuation, and element-dependent sensitivity, making the evaluation reflect real system effects.Because voxel-level ground truth is unavailable, Fig. 4 evaluates visual structure and local profile sharpness.
- Global reconstruction comparison: Vanilla UBP shows broad structural blur and reduced contrast, while Dual-SoS UBP leaves residual defocus despite using a prescribed tissue–water boundary.The reported residual defocus is attributed to Dual-SoS UBP’s simple boundary model and open-loop back-projection.
- Local sharpness and contrast: Joint source and ASoS optimization produces higher-contrast absorber responses and makes neighboring structures more separable than in uniform-SoS baselines.The zoomed regions and line profiles indicate improved focusing rather than only a change in global intensity scaling.
- Overall finding: Compared with uniform-SoS UBP, prior-informed Dual-SoS UBP, and vanilla SlingBAG, PAGS produces sharper absorber boundaries, improved local contrast, and clearer neighboring-structure separation.Together, image-domain sharpening and improved local contrast suggest compensation for dominant arrival-time errors while retaining a blind reconstruction method.
4.4 Robustness under Sparse Sampling
PAGS remains robust as detector sampling becomes increasingly sparse: major vascular structure and branch connectivity persist at 12.5% sampling, with degradation primarily affecting fine-detail contrast. Its sparse Gaussian source representation and smooth low-order SH propagation model support stable reconstruction under limited measurements.
- Sparse-view performance: PAGS degrades gracefully as detector sampling decreases from 50% to 12.5%, preserving major vascular trunks and branch connectivity at the lowest sampling ratio.The main degradation is reduced fine-detail contrast rather than severe streak artifacts.
- Sparse-view performance: The Gaussian PA source representation provides a sparse structural constraint that supports robustness when the inverse problem becomes increasingly underdetermined.The experiment uniformly retained 50%, 25%, and 12.5% of detector channels from physical phantom measurements.
- Propagation-model robustness: Low-order SH parameterization biases the ASoS field toward smooth path-level variations, reducing nonphysical high-frequency SoS fitting of sparse-view artifacts.This preserves a compact source distribution and stable propagation correction with fewer detector channels.
4.5 Ablation Study and Efficiency Analysis
The ablation study separates PAGS’s analytic Gaussian projection and SH-parameterized ASoS field, showing that their combination achieves the lowest signal residual while retaining most computational savings. The analytic model provides the main speedup, whereas ASoS adds only minor runtime overhead.
- Ablation design: PAGS ablates the 10-sphere versus analytic Gaussian forward model and uniform SoS versus the SH-parameterized ASoS field in a 2 × 2 design.The four configurations are vanilla SlingBAG, + ASoS field, + Analytic, and Full PAGS.
- Optimization behavior: The ASoS field substantially lowers the final signal-domain residual, while Full PAGS reaches the lowest final signal residual.The ASoS field provides latent propagation correction for measurements acquired through heterogeneous acoustic media.
- Efficiency analysis: The analytic Gaussian forward model reduces per-iteration runtime from 6.7 s to 2.3 s by replacing repeated error-function evaluations with a single closed-form Gaussian response.It preserves a similar convergence trend to the 10-sphere approximation.
- Efficiency analysis: Adding the ASoS field increases runtime from 2.3 s to 2.4 s in the analytic setting, indicating only minor overhead.All runtime comparisons use identical hardware and problem scale.
5 Conclusion
PAGS is a differentiable autofocusing framework for PACT that learns a path-averaged SoS field to align acoustic arrivals without recovering a dense acoustic medium. Simulated and physical phantom experiments show sharper reconstructions under heterogeneous media and robustness to sparse-view sampling, while validation remains limited to these settings.
- 5 Conclusion: PAGS learns an anisotropic path-averaged SoS field whose values directly determine source-to-transducer arrival-time alignment, avoiding dense acoustic-medium recovery.The propagation field is coupled with sparse Gaussian PA sources and an analytic projection.
- 5 Conclusion: PAGS produces sharper reconstructions under heterogeneous acoustic media and remains robust to sparse-view sampling in simulated and physical phantom experiments.The ASoS field and analytic projection provide complementary benefits.
- 5 Conclusion: PAGS estimates an effective path-level propagation field rather than a physical SoS map, and current validation is limited to simulated and phantom data.Future work will address more complex acoustic settings and broader biological validation.
Abbreviations
This section defines the abbreviations used throughout the paper, covering imaging methods, reconstruction techniques, acoustic concepts, optimization terms, and evaluation metrics.
- PACT denotes photoacoustic computed tomography, while PA denotes photoacoustic and PAGS denotes speed-of-sound-adaptive Gaussian splatting.
- ASoS denotes anisotropic path-averaged speed of sound, SoS denotes speed of sound, and ToF denotes time of flight.
- The listed reconstruction and imaging abbreviations include 3DGS, CT, DAS, UBP, GPU, SH, and TV, alongside MSE, PSNR, RMSE, and SSIM metrics.