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

Three-dimensional photoacoustic imaging (3D PAI) has shown great potential in preclinical studies and clinical implementations, while it commonly has sparse sensor arrays, limiting both spatial sampling and the field of view (FOV). Freehand scanning could overcome these limitations through anatomy-adaptive scanning that extends spatial coverage and provides complementary views beyond the fixed array aperture, but its flexibility is conventionally constrained by the need for motor feedback or external pose tracking. Here we introduce PA-SfM, a tracker-free structure-from-motion (SfM) framework that recovers multiple poses directly from PA measurements with superior precision, enabling freehand 3D PAI without external pose measurements. PA-SfM integrates a differentiable acoustic radiation model with hierarchical optimization and rigid array constraints, it jointly estimates inter-view transformations and reconstructs 3D volumes. The performance of PA-SfM was demonstrated in numerical simulations, animal studies and human imaging experiments. Compared with motor encoder-based fusion of the mechanically scanned system, PA-SfM produced sharper and more continuous vascular reconstructions with an expanded FOV. In controlled quantitative validations, PA-SfM achieved high reconstruction fidelity, with PSNR values over 40 dB and SSIM values above 0.98 relative to ground truth or known pose reference reconstructions. These results demonstrate that PA-SfM enables robust freehand 3D PAI, with particular potential for clinical implementation of large-scale freehand imaging. The source code is publicly available at https://github.com/JaegerCQ/PA-SfM.