27 research outputs found
Crystal image analysis using synchrosqueezed transforms
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
Combining synchrosqueezed wave packet transform with optimization for crystal image analysis
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
Non-Oscillatory Pattern Learning for Non-Stationary Signals
This paper proposes a novel non-oscillatory pattern (NOP) learning scheme for
several oscillatory data analysis problems including signal decomposition,
super-resolution, and signal sub-sampling. To the best of our knowledge, the
proposed NOP is the first algorithm for these problems with fully
non-stationary oscillatory data with close and crossover frequencies, and
general oscillatory patterns. NOP is capable of handling complicated situations
while existing algorithms fail; even in simple cases, e.g., stationary cases
with trigonometric patterns, numerical examples show that NOP admits
competitive or better performance in terms of accuracy and robustness than
several state-of-the-art algorithms