Combining $2D$ synchrosqueezed wave packet transform with optimization for crystal image analysis

TL;DR

This paper introduces a variational optimization approach that enhances crystal defect and deformation analysis in atomic resolution images by combining 2D synchrosqueezed transform data with a nonlinear conjugate gradient method.

Contribution

It presents a novel method integrating SST with variational optimization to improve accuracy in crystal image analysis, especially for deformation gradients and defect detection.

Findings

Effective in identifying crystal defects and rotations

Improves deformation gradient estimates outside defect regions

Validated on simulated and experimental images

Abstract

We develop a variational optimization method for crystal analysis in atomic resolution images, which uses information from a 2D synchrosqueezed transform (SST) as input. The synchrosqueezed transform is applied to extract initial information from atomic crystal images: crystal defects, rotations and the gradient of elastic deformation. The deformation gradient estimate is then improved outside the identified defect region via a variational approach, to obtain more robust results agreeing better with the physical constraints. The variational model is optimized by a nonlinear projected conjugate gradient method. Both examples of images from computer simulations and imaging experiments are analyzed, with results demonstrating the effectiveness of the proposed method.