Separable Fourier-Domain Analysis of the Mean Shift Operator for Efficient Super-Resolution Microscopy
Esley Torres
Abstract
High-resolution imaging is essential for uncovering dynamic biological processes, yet many super-resolution microscopy methods
face fundamental trade-offs between acquisition speed, phototoxicity, and computational complexity. Mean Shift Super Resolution
(MSSR) has recently emerged as a parameter-light approach capable of enhancing resolution from single or a few frames, making
it attractive for live-cell imaging. However, the original spatial-domain implementation of MSSR imposes prohibitive computational
costs for large images or volumetric datasets, limiting its adoption in high-throughput or real-time applications. Here, we reformulate
MSSR in the Fourier domain, allowing for efficient computation in Fourier space. This approach reduces algorithmic complexity
from quadratic to quasi-linear scaling, while preserving the resolution gains and noise-robustness of the spatial implementation. We
demonstrate that Fourier-MSSR accelerates processing by more than an order of magnitude, enabling the real-time reconstruction
of live-cell dynamics with a minimal phototoxic load. Beyond microscopy, the method is broadly applicable to any field where
resolution and computational efficiency are critical, including remote sensing, materials science, and astronomy. By bridging a
biologically relevant imaging algorithm with efficient spectral computation, Fourier-MSSR makes super-resolution accessible for
large-scale and live-cell applications, expanding the practical reach of resolution enhancement methods across disciplines.