Regularized Finite-Element Global Reconstruction for High-Fidelity OCT Vibrometry

Optical Coherence Tomography (OCT) vibrometry provides sub-nanometer displacement sensitivity and has become a key technique for mapping complex vibration patterns, particularly in hearing research where frequency-dependent motion of middle-ear structures is central to diagnosing pathology. However, at high frequencies, OCT measurements often approach the noise floor, degrading the accuracy and interpretability of reconstructed displacement fields, which is especially critical for fast and reliable assessment. We introduce a robust, regularized finite-element (FE) global reconstruction framework that utilizes higher-order shape functions and L-curve optimization to recover continuous, high-fidelity displacement fields. Through comprehensive simulation and experimental validation, we demonstrate that this method significantly outperforms traditional unregularized filters. Statistical validation via two-sample t-tests indicates that the regularized approach achieves significantly lower mean reconstruction errors compared to lower-order methods (p < 0.01). Most importantly, variance testing proves that regularized filtering always improves the variance (p < 0.01), consistently reducing noise-propagation while preserving the underlying accuracy of the reconstructed field. This workflow provides an objective, reproducible method for quantitative vibration analysis, bridging the gap between raw OCT data and high-fidelity mechanical modeling.