We propose efficient algorithms based on a band-limited version of 2D
synchrosqueezed transforms to extract mesoscopic and microscopic information
from atomic crystal images. The methods analyze atomic crystal images as an
assemblage of non-overlapping segments of 2D general intrinsic mode type
functions, which are superpositions of non-linear wave-like components. In
particular, crystal defects are interpreted as the irregularity of local
energy; crystal rotations are described as the angle deviation of local wave
vectors from their references; the gradient of a crystal elastic deformation
can be obtained by a linear system generated by local wave vectors. Several
numerical examples of synthetic and real crystal images are provided to
illustrate the efficiency, robustness, and reliability of our methods.Comment: 27 pages, 17 figure
