SlingBAG: Sliding ball adaptive growth algorithm with differentiable radiation enables super-efficient iterative 3D photoacoustic image reconstruction

High-quality 3D photoacoustic imaging (PAI) reconstruction under sparse view or limited view has long been challenging. Traditional 3D iterative-based reconstruction methods suffer from both slow speed and high memory consumption. Recently, in computer graphics, the differentiable rendering has made significant progress, particularly with the rise of 3D Gaussian Splatting. Inspired by these, we introduce differentiable radiation into PAI, developing a novel reconstruction algorithm: the Sliding Ball Adaptive Growth algorithm (SlingBAG) for 3D PAI, which shows ability in high-quality 3D PAI reconstruction both under extremely sparse view and limited view. We established the point cloud dataset in PAI, and used unique differentiable rapid radiator based on the spherical decomposition strategy and the randomly initialized point cloud adaptively optimized according to sparse sensor data. Each point undergoes updates in 3D coordinates, initial pressure, and resolution (denoted by the radius of ball). Points undergo adaptive growth during iterative process, including point destroying, splitting and duplicating along the gradient of their positions, manifesting the sliding ball effect. Finally, our point cloud to voxel grid shader renders the final reconstruction results. Simulation and in vivo experiments demonstrate that our SlingBAG reconstruction result's SNR can be more than 40 dB under extremely sparse view, while the SNR of traditional back-projection algorithm's result is less than 20 dB. Moreover, the result of SlingBAG's structural similarity to the ground truth is significantly higher, with an SSIM value of 95.6%. Notably, our differentiable rapid radiator can conduct forward PA simulation in homogeneous, non-viscous media substantially faster than current methods that numerically simulate the wave propagation, such as k-Wave. The dataset and all code will be open source.