16 research outputs found
Automatic alignment for three-dimensional tomographic reconstruction
In tomographic reconstruction, the goal is to reconstruct an unknown object
from a collection of line integrals. Given a complete sampling of such line
integrals for various angles and directions, explicit inverse formulas exist to
reconstruct the object. Given noisy and incomplete measurements, the inverse
problem is typically solved through a regularized least-squares approach. A
challenge for both approaches is that in practice the exact directions and
offsets of the x-rays are only known approximately due to, e.g. calibration
errors. Such errors lead to artifacts in the reconstructed image. In the case
of sufficient sampling and geometrically simple misalignment, the measurements
can be corrected by exploiting so-called consistency conditions. In other
cases, such conditions may not apply and we have to solve an additional inverse
problem to retrieve the angles and shifts. In this paper we propose a general
algorithmic framework for retrieving these parameters in conjunction with an
algebraic reconstruction technique. The proposed approach is illustrated by
numerical examples for both simulated data and an electron tomography dataset
Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems
Like many other advanced imaging methods, x-ray phase contrast imaging and
tomography require mathematical inversion of the observed data to obtain
real-space information. While an accurate forward model describing the
generally nonlinear image formation from a given object to the observations is
often available, explicit inversion formulas are typically not known. Moreover,
the measured data might be insufficient for stable image reconstruction, in
which case it has to be complemented by suitable a priori information. In this
work, regularized Newton methods are presented as a general framework for the
solution of such ill-posed nonlinear imaging problems. For a proof of
principle, the approach is applied to x-ray phase contrast imaging in the
near-field propagation regime. Simultaneous recovery of the phase- and
amplitude from a single near-field diffraction pattern without homogeneity
constraints is demonstrated for the first time. The presented methods further
permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval
and tomographic inversion. We demonstrate the potential of this approach by
three-dimensional imaging of a colloidal crystal at 95 nm isotropic resolution.Comment: (C)2016 Optical Society of America. One print or electronic copy may
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Transient growth in linearly stable Taylor-Couette flows
Non-normal transient growth of disturbances is considered as an essential
prerequisite for subcritical transition in shear flows, i.e. transition to
turbulence despite linear stability of the laminar flow. In this work we
present numerical and analytical computations of linear transient growth
covering all linearly stable regimes of Taylor--Couette flow. Our numerical
experiments reveal comparable energy amplifications in the different regimes.
For high shear Reynolds numbers Re the optimal transient energy growth always
follows a 2/3-scaling with Re, which allows for large amplifications even in
regimes where the presence of turbulence remains debated. In co-rotating
Rayleigh-stable flows the optimal perturbations become increasingly columnar in
their structure, as the optimal axial wavenumber goes to zero. In this limit of
axially invariant perturbations we show that linear stability and transient
growth are independent of the cylinders' rotation-ratio and we derive a
universal 2/3-scaling of optimal energy growth with Re using WKB-theory. Based
on this, a semi-empirical formula for the estimation of linear transient growth
valid in all regimes is obtained.Comment: Published version: Revised according to JFM referee comments,
incorporating various small corrections and clarifications compared to
previous submission