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 applications, but sparse sensor arrays commonly limit 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, enabling freehand 3D PAI without external pose measurements. PA-SfM integrates a differentiable acoustic radiation model with hierarchical optimization and rigid array constraints to jointly estimate transformations between views and reconstruct 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 reduced vessel misalignment in expanded FOV reconstructions. Controlled quantitative validations yielded peak signal-to-noise ratio (PSNR) values over 40 dB and structural similarity index (SSIM) values about 0.98 relative to ground truth or known pose reference reconstructions. Freehand experiments further demonstrated robust pose recovery at high scan speeds, with inter-frame displacements of 9 mm at intervals of 0.1 s. These results support PA-SfM as a tracker-free approach to large-scale freehand 3D PAI and provide a basis for further evaluation in clinical settings.