Statistical outlier detection for polarity-invariant accelerated autofocusing in lensless in-line digital holography

Automatic focusing in lensless in-line digital holography typically reconstructs candidate axial planes, evaluates a scalar focus metric, and searches for its extremum. This approach faces two limitations: focal response polarity depends on the object type and underlying focus operator, whereas exhaustive fine-grid scanning requires numerous propagations over wide axial ranges. To address these limitations, we propose a polarity-invariant accelerated autofocus framework based on statistical outlier detection of axial metric sequences generated by existing focus operators. The axial metric sequence is modeled as a dominant defocus background with sparse focal deviations, and a two-tailed standardized deviation converts deviations of either polarity into a unified maximization problem, eliminating the need for object-type priors or manual polarity selection. A focal–nonfocal separation condition characterizes when the focal response remains dominant. For single-plane autofocus, an online background estimator is combined with a coarse-to-fine search in which a significant local anomaly triggers early stopping and local refinement. Simulations and real-hologram experiments with multiple underlying focus operators show that the proposed framework resolves polarity inconsistency for amplitude, phase, and mixed amplitude–phase scenes. In the single-plane setting, the accelerated search produces focal estimates consistent with exhaustive fine scanning, with propagation-evaluation speedup factors of 4.9 to 6.4 in the representative simulations and 3.5 to 3.8 on real holograms; the corresponding runtime speedup factors on real holograms are 3.7 to 4.3.