Purpose: To facilitate fast and accurate iterative volumetric image reconstruction from limited-angle on-board projections. Methods: Intrafraction motion hinders the clinical applicability of modern radiotherapy techniques, such as lung stereotactic body radiation therapy (SBRT). The LIVE system may impact clinical practice by recovering volumetric information via Digital Tomosynthesis (DTS), thus entailing low time and radiation dose for image acquisition during treatment. The DTS is estimated as a deformation of prior CT via iterative registration with on-board images; this shifts the challenge to the computational domain, owing largely to repeated projection computations across iterations. We address this issue by composing efficient digital projection operators from their constituent parts. This allows us to separate the static (projection geometry) and dynamic (volume/image data) parts of projection operations by means of pre-computations, enabling fast on-board processing, while also relaxing constraints on underlying numerical models (e.g. regridding interpolation kernels). Further decoupling the projectors into simpler ones ensures the incurred memory overhead remains low, within the capacity of a single GPU. These operators depend only on the treatment plan and may be reused across iterations and patients. The dynamic processing load is kept to a minimum and maps well to the GPU computational model. Results: We have integrated efficient, pre-computable modules for volumetric ray-casting and FDK-based back-projection with the LIVE processing pipeline. Our results show a 60x acceleration of the DTS computations, compared to the previous version, using a single GPU; presently, reconstruction is attained within a couple of minutes. The present implementation allows for significant flexibility in terms of the numerical and operational projection model; we are investigating the benefit of further optimizations and accurate digital projection sub-kernels. Conclusion: Composable projection operators constitute a versatile research tool which can greatly accelerate iterative registration algorithms and may be conducive to the clinical applicability of LIVE. National Institutes of Health Grant No. R01-CA184173; GPU donation by NVIDIA Corporation