An Iterative Frequency-Based Approach for Gelmap Grid Deformation Correction

Expansion microscopy is becoming increasingly popular as a low-cost and accessible high-resolution imaging technique, but the quantitative estimation of uncertainty regarding specimen integrity after expansion is still of major interest. We recently published GelMap that introduces a fluorescently labeled "grid"into the expansion microscopy hydrogel, providing visual feedback about deformations and distortions. Here, we propose an iterative multi-scale algorithm capable of automatic deformation correction in post-expansion images using the Fourier-based analysis technique HARP initially developed for motion estimating in tagged MRI, in combination with spectral deconvolution using CLEAN, which effectively deals with occlusions, masking and boundary effects. We validate our approach using simulated realistic images of grids containing several types of deformations and appearance profiles as well as real data, showing that the proposed method is capable of accurate correction of deformations.