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Cone-beam CT (CBCT) is widespread in abdominal interventional imaging, but its long acquisition time makes it susceptible to patient motion. Image-based autofocus has shown success in CBCT deformable motion compensation, via deep autofocus metrics and multi-region optimization, but it is challenged by the large parameter dimensionality required to capture intricate motion trajectories. This work leverages the differentiable nature of deep autofocus metrics to build a novel optimization strategy, Multi-Stage Adaptive Spine Autofocus (MASA), for compensation of complex deformable motion in abdominal CBCT. MASA poses the autofocus problem as a multi-stage adaptive sampling strategy of the motion trajectory, sampled with Hermite spline basis with variable amplitude and knot temporal positioning. The adaptive method permits simultaneous optimization of the sampling phase, local temporal sampling density, and time-dependent amplitude of the motion trajectory. The optimization is performed in a multi-stage schedule with increasing number of knots that progressively accommodates complex trajectories in late stages, preconditioned by coarser components from early stages, and with minimal increase in dimensionality. MASA was evaluated in controlled simulation experiments with two types of motion trajectories: i) combinations of slow drifts with sudden jerk (sigmoid) motion; and ii) combinations of periodic motion sources of varying frequency into multi-frequency trajectories. Further validation was obtained in clinical data from liver CBCT featuring motion of contrast-enhanced vessels, and soft-tissue structures. The adaptive sampling strategy provided successful motion compensation in sigmoid trajectories, compared to fixed sampling strategies (mean SSIM increase of 0.026 compared to 0.011). Inspection of the estimated motion showed the capability of MASA to automatically allocate larger sampling density to parts of the scan timeline featuring sudden motion, effectively accommodating complex motion without increasing the problem dimension. Experiments on multifrequency trajectories with 3-stage MASA (5, 10, and 15 knots) yielded a twofold SSIM increase compared to single-stage autofocus with 15 knots (0.076 vs 0.040, respectively). Application of MASA to clinical datasets resulted in simultaneous improvement on the delineation of both contrast-enhanced vessels and soft-tissue structures in the liver. A new autofocus framework, MASA, was developed including a novel multi-stage technique for adaptive temporal sampling of the motion trajectory in combination with fully differentiable deep autofocus metrics. This novel adaptive sampling approach is a crucial step for application of deformable motion compensation to complex temporal motion trajectories.
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