Hilbert-initialized hybrid phase retrieval for optical vortex analysis in speckle imaging

Document Type

Conference Proceeding

Publication Date

3-4-2026

Department

Department of Biomedical Engineering

Abstract

Optical vortices in speckle fields provide a compact description of phase topology and offer a promising basis for quantitative analysis in speckle imaging. Reliable vortex-based analysis, however, requires robust phase retrieval from intensity-only measurements, where iterative methods are often sensitive to initialization and convergence behavior. We present a Hilbert-initialized hybrid phase retrieval approach in which a two-dimensional (2-D) Hilbert transform provides a structured pseudo-phase estimate that is subsequently refined using phase-only gradient-descent optimization under measured amplitude constraints. Using band-limited synthetic speckle fields with ensemble averaging over multiple realizations, we quantify performance using data-fidelity cost, phase-similarity metrics including correlation and structural similarity index (SSIM), and vortex-Topology metrics based on vortex-count error, and compare against an inverse fast Fourier transform (IFFT) initialization baseline derived from the fast Fourier transform (FFT) domain. Convergence is evaluated under tolerance-and step-size (μ) sweeps using a first-hit stopping rule defined by relative vortex-count error. Relative to the IFFT-based baseline, Hilbert initialization accelerates convergence to the realization-specific (true) vortexcount target across most speckle sizes, reducing iteration counts and variability, while the IFFT baseline exhibits slower convergence. When validated against an analytic expected vortex-count baseline, agreement improves with speckle size, and both methods are near the baseline for medium-To-large speckle sizes. On a real laser speckle contrast imaging (LSCI) speckle image, results show faster cost reduction with Hilbert initialization, while IFFT initialization remains closer to its initial phase. These results demonstrate that Hilbert-initialized hybrid phase retrieval improves vortex-Topology recovery and convergence reliability, supporting vortex-based analysis in speckle imaging and downstream studies of dynamic speckle behavior.

Publication Title

Proceedings of SPIE the International Society for Optical Engineering

ISBN

9781510696136

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