PA-SfM: Tracker-free differentiable acoustic radiation for freehand 3D photoacoustic imaging

Three-dimensional photoacoustic imaging (3D PAI) commonly relies on sparse sensor arrays, which restrict angular sampling, detection aperture, and instantaneous field-of-view (FOV). Moving the sensor array relative to the target provides an effective route to multi-view imaging and large volume photoacoustic mapping, but accurate fusion of multiple poses conventionally depends on motor feedback or external tracking hardware. Such tracking increases system complexity and can suffer from calibration errors, backlash, and motion instability. Here we introduce PA-SfM, a tracker-free differentiable acoustic structure-from-motion (SfM) framework that recovers sensor array poses directly from photoacoustic measurements. By integrating a differentiable acoustic radiation model with hierarchical optimization and rigid-array constraints, PA-SfM jointly estimates inter-view transformations and reconstructs 3D photoacoustic volumes without external pose measurements. We validated PA-SfM using numerical simulations, in vivo rat kidney and liver imaging with known relative geometry, and a mechanically scanned 3D PAI system. In mechanically rotated mouse liver imaging, PA-SfM produced sharper and more continuous vascular reconstructions than encoder-based fusion. In translational multi-pose imaging, PA-SfM supported expanded FOV vascular mapping without translation-stage pose input. In controlled quantitative validations, PA-SfM achieved high reconstruction fidelity, with PSNRs of 38.90–41.42 dB and SSIMs of 0.9637–0.9864 relative to groundtruth or known-pose reference reconstructions. These results establish PA-SfM as a robust computational framework for tracker-free multi-view and expanded FOV 3D PAI, providing a complete algorithmic foundation for freehand 3D PAI. The source code is publicly available at https://github.com/JaegerCQ/PA-SfM .