4,657 research outputs found
Efficient binary tomographic reconstruction
Tomographic reconstruction of a binary image from few projections is
considered. A novel {\em heuristic} algorithm is proposed, the central element
of which is a nonlinear transformation of the
probability that a pixel of the sought image be 1-valued. It consists of
backprojections based on and iterative corrections. Application of
this algorithm to a series of artificial test cases leads to exact binary
reconstructions, (i.e recovery of the binary image for each single pixel) from
the knowledge of projection data over a few directions. Images up to
pixels are reconstructed in a few seconds. A series of test cases is performed
for comparison with previous methods, showing a better efficiency and reduced
computation times
The Discrete radon transform: A more efficient approach to image reconstruction
The Radon transform and its inversion are the mathematical keys that enable tomography. Radon transforms are defined for continuous objects with continuous projections at all angles in [0,π). In practice, however, we pre-filter discrete projections take
Capturing Nucleation at 4D Atomic Resolution
Nucleation plays a critical role in many physical and biological phenomena
ranging from crystallization, melting and evaporation to the formation of
clouds and the initiation of neurodegenerative diseases. However, nucleation is
a challenging process to study in experiments especially in the early stage
when several atoms/molecules start to form a new phase from its parent phase.
Here, we advance atomic electron tomography to study early stage nucleation at
4D atomic resolution. Using FePt nanoparticles as a model system, we reveal
that early stage nuclei are irregularly shaped, each has a core of one to few
atoms with the maximum order parameter, and the order parameter gradient points
from the core to the boundary of the nucleus. We capture the structure and
dynamics of the same nuclei undergoing growth, fluctuation, dissolution,
merging and/or division, which are regulated by the order parameter
distribution and its gradient. These experimental observations differ from
classical nucleation theory (CNT) and to explain them we propose the order
parameter gradient (OPG) model. We show the OPG model generalizes CNT and
energetically favours diffuse interfaces for small nuclei and sharp interfaces
for large nuclei. We further corroborate this model using molecular dynamics
simulations of heterogeneous and homogeneous nucleation in liquid-solid phase
transitions of Pt. We anticipate that the OPG model is applicable to different
nucleation processes and our experimental method opens the door to study the
structure and dynamics of materials with 4D atomic resolution.Comment: 42 pages, 5 figures, 12 supplementary figures and one supplementary
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