2,611 research outputs found
Distributed optimization for nonrigid nano-tomography
Resolution level and reconstruction quality in nano-computed tomography
(nano-CT) are in part limited by the stability of microscopes, because the
magnitude of mechanical vibrations during scanning becomes comparable to the
imaging resolution, and the ability of the samples to resist beam damage during
data acquisition. In such cases, there is no incentive in recovering the sample
state at different time steps like in time-resolved reconstruction methods, but
instead the goal is to retrieve a single reconstruction at the highest possible
spatial resolution and without any imaging artifacts. Here we propose a joint
solver for imaging samples at the nanoscale with projection alignment,
unwarping and regularization. Projection data consistency is regulated by dense
optical flow estimated by Farneback's algorithm, leading to sharp sample
reconstructions with less artifacts. Synthetic data tests show robustness of
the method to Poisson and low-frequency background noise. Applicability of the
method is demonstrated on two large-scale nano-imaging experimental data sets.Comment: Manuscript and supplementary materia
Polychromatic X-ray CT Image Reconstruction and Mass-Attenuation Spectrum Estimation
We develop a method for sparse image reconstruction from polychromatic
computed tomography (CT) measurements under the blind scenario where the
material of the inspected object and the incident-energy spectrum are unknown.
We obtain a parsimonious measurement-model parameterization by changing the
integral variable from photon energy to mass attenuation, which allows us to
combine the variations brought by the unknown incident spectrum and mass
attenuation into a single unknown mass-attenuation spectrum function; the
resulting measurement equation has the Laplace integral form. The
mass-attenuation spectrum is then expanded into first order B-spline basis
functions. We derive a block coordinate-descent algorithm for constrained
minimization of a penalized negative log-likelihood (NLL) cost function, where
penalty terms ensure nonnegativity of the spline coefficients and nonnegativity
and sparsity of the density map. The image sparsity is imposed using
total-variation (TV) and norms, applied to the density-map image and
its discrete wavelet transform (DWT) coefficients, respectively. This algorithm
alternates between Nesterov's proximal-gradient (NPG) and limited-memory
Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGS-B) steps for
updating the image and mass-attenuation spectrum parameters. To accelerate
convergence of the density-map NPG step, we apply a step-size selection scheme
that accounts for varying local Lipschitz constant of the NLL. We consider
lognormal and Poisson noise models and establish conditions for biconvexity of
the corresponding NLLs. We also prove the Kurdyka-{\L}ojasiewicz property of
the objective function, which is important for establishing local convergence
of the algorithm. Numerical experiments with simulated and real X-ray CT data
demonstrate the performance of the proposed scheme
Recommended from our members
Tomographic Inverse Problems: Theory and Applications
This was the tenth Oberwolfach conference on the
mathematics of tomography. The field rests on the interplay between
the theoretical and applied; practical questions lead to new
mathematics and pure mathematics motivates new algorithms. This
workshop encompassed classical areas such as X-ray computed tomography
(CT) as well as new modalities and applications such as dynamic
imaging, Compton scattering tomography, hybrid imaging, optical
tomography or multi-energy CT and addressed inter alia the use of
methods from machine learning
Registration of phase contrast images in propagation-based X-ray phase tomography
International audienceX-ray phase tomography aims at reconstructing the 3D electron density distribution of an object. It offers enhanced sensitivity compared to attenuation-based X-ray absorption tomography. In propagation-based methods, phase contrast is achieved by letting the beam propagate after interaction with the object. The phase shift is then retrieved at each projection angle, and subsequently used in tomographic reconstruction to obtain the refractive index decrement distribution, which is proportional to the electron density. Accurate phase retrieval is achieved by combining images at different propagation distances. For reconstructions of good quality, the phase-contrast images recorded at different distances need to be accurately aligned. In this work, we characterise the artefacts related to misalignment of the phase-contrast images, and investigate the use of different registration algorithms for aligning in-line phase-contrast images. The characterisation of artefacts is done by a simulation study and comparison with experimental data. Loss in resolution due to vibrations is found to be comparable to attenuation-based computed tomography. Further, it is shown that registration of phase-contrast images is nontrivial due to the difference in contrast between the different images, and the often periodical artefacts present in the phase-contrast images if multilayer X-ray optics are used. To address this, we compared two registration algorithms for aligning phase-contrast images acquired by magnified X-ray nanotomography: one based on cross-correlation and one based on mutual information. We found that the mutual information-based registration algorithm was more robust than a correlation-based method
- …