643 research outputs found
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
be made for personal use only. Systematic reproduction and distribution,
duplication of any material in this paper for a fee or for commercial
purposes, or modifications of the content of this paper are prohibite
Noise Robustness of a Combined Phase Retrieval and Reconstruction Method for Phase-Contrast Tomography
Classical reconstruction methods for phase-contrast tomography consist of two
stages: phase retrieval and tomographic reconstruction. A novel algebraic
method combining the two was suggested by Kostenko et al. (Opt. Express, 21,
12185, 2013) and preliminary results demonstrating improved reconstruction
compared to a two-stage method given. Using simulated free-space propagation
experiments with a single sample-detector distance, we thoroughly compare the
novel method with the two-stage method to address limitations of the
preliminary results. We demonstrate that the novel method is substantially more
robust towards noise; our simulations point to a possible reduction in counting
times by an order of magnitude
Phase retrieval beyond the homogeneous object assumption for X-ray in-line holographic imaging
X-ray near field holography has proven to be a powerful 2D and 3D imaging
technique with applications ranging from biomedical research to material
sciences. To reconstruct meaningful and quantitative images from the
measurement intensities, however, it relies on computational phase retrieval
which in many cases assumes the phase-shift and attenuation coefficient of the
sample to be proportional. Here, we demonstrate an efficient phase retrieval
algorithm that does not rely on this homogeneous-object assumption and is a
generalization of the well-established contrast-transfer-function (CTF)
approach. We then investigate its stability and present an experimental study
comparing the proposed algorithm with established methods. The algorithm shows
superior reconstruction quality compared to the established CTF-based method at
similar computational cost. Our analysis provides a deeper fundamental
understanding of the homogeneous object assumption and the proposed algorithm
will help improve the image quality for near-field holography in biomedical
application
GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging
Tomography has made a radical impact on diverse fields ranging from the study
of 3D atomic arrangements in matter to the study of human health in medicine.
Despite its very diverse applications, the core of tomography remains the same,
that is, a mathematical method must be implemented to reconstruct the 3D
structure of an object from a number of 2D projections. In many scientific
applications, however, the number of projections that can be measured is
limited due to geometric constraints, tolerable radiation dose and/or
acquisition speed. Thus it becomes an important problem to obtain the
best-possible reconstruction from a limited number of projections. Here, we
present the mathematical implementation of a tomographic algorithm, termed
GENeralized Fourier Iterative REconstruction (GENFIRE). By iterating between
real and reciprocal space, GENFIRE searches for a global solution that is
concurrently consistent with the measured data and general physical
constraints. The algorithm requires minimal human intervention and also
incorporates angular refinement to reduce the tilt angle error. We demonstrate
that GENFIRE can produce superior results relative to several other popular
tomographic reconstruction techniques by numerical simulations, and by
experimentally by reconstructing the 3D structure of a porous material and a
frozen-hydrated marine cyanobacterium. Equipped with a graphical user
interface, GENFIRE is freely available from our website and is expected to find
broad applications across different disciplines.Comment: 18 pages, 6 figure
SIMBA: scalable inversion in optical tomography using deep denoising priors
Two features desired in a three-dimensional (3D) optical tomographic image reconstruction algorithm are the ability to reduce imaging artifacts and to do fast processing of large data volumes. Traditional iterative inversion algorithms are impractical in this context due to their heavy computational and memory requirements. We propose and experimentally validate a novel scalable iterative mini-batch algorithm (SIMBA) for fast and high-quality optical tomographic imaging. SIMBA enables highquality imaging by combining two complementary information sources: the physics of the imaging system characterized by its forward model and the imaging prior characterized by a denoising deep neural net. SIMBA easily scales to very large 3D tomographic datasets by processing only a small subset of measurements at each iteration. We establish the theoretical fixedpoint convergence of SIMBA under nonexpansive denoisers for convex data-fidelity terms. We validate SIMBA on both simulated and experimentally collected intensity diffraction tomography (IDT) datasets. Our results show that SIMBA can significantly reduce the computational burden of 3D image formation without sacrificing the imaging quality.https://arxiv.org/abs/1911.13241First author draf
TV-based conjugate gradient method and discrete L-curve for few-view CT reconstruction of X-ray in vivo data
High-resolution, three-dimensional (3D) imaging of soft tissues requires the solution of two inverse problems: phase retrieval and the reconstruction of the 3D image from a tomographic stack of two-dimensional (2D) projections. The number of projections per stack should be small to accommodate fast tomography of rapid processes and to constrain X-ray radiation dose to optimal levels to either increase the duration of in vivo time-lapse series at a given goal for spatial resolution and/or the conservation of structure under X-ray irradiation. In pursuing the 3D reconstruction problem in the sense of compressive sampling theory, we propose to reduce the number of projections by applying an advanced algebraic technique subject to the minimisation of the total variation (TV) in the reconstructed slice. This problem is formulated in a Lagrangian multiplier fashion with the parameter value determined by appealing to a discrete L-curve in conjunction with a conjugate gradient method. The usefulness of this reconstruction modality is demonstrated for simulated and in vivo data, the latter acquired in parallel-beam imaging experiments using synchrotron radiation
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