631 research outputs found
Estimation of affine transformations directly from tomographic projections in two and three dimensions
This paper presents a new approach to estimate two- and three-dimensional affine transformations from tomographic projections. Instead of estimating the deformation from the reconstructed data, we introduce a method which works directly in the projection domain, using parallel and fan beam projection geometries. We show that any affine deformation can be analytically compensated, and we develop an efficient multiscale estimation framework based on the normalized cross correlation. The accuracy of the approach is verified using simulated and experimental data, and we demonstrate that the new method needs less projection angles and has a much lower computational complexity as compared to approaches based on the standard reconstruction technique
Numerical methods for coupled reconstruction and registration in digital breast tomosynthesis.
Digital Breast Tomosynthesis (DBT) provides an insight into the fine details of normal fibroglandular tissues and abnormal lesions by reconstructing a pseudo-3D image of the breast. In this respect, DBT overcomes a major limitation of conventional X-ray mam- mography by reducing the confounding effects caused by the superposition of breast tissue. In a breast cancer screening or diagnostic context, a radiologist is interested in detecting change, which might be indicative of malignant disease. To help automate this task image registration is required to establish spatial correspondence between time points. Typically, images, such as MRI or CT, are first reconstructed and then registered. This approach can be effective if reconstructing using a complete set of data. However, for ill-posed, limited-angle problems such as DBT, estimating the deformation is com- plicated by the significant artefacts associated with the reconstruction, leading to severe inaccuracies in the registration. This paper presents a mathematical framework, which couples the two tasks and jointly estimates both image intensities and the parameters of a transformation. Under this framework, we compare an iterative method and a simultaneous method, both of which tackle the problem of comparing DBT data by combining reconstruction of a pair of temporal volumes with their registration. We evaluate our methods using various computational digital phantoms, uncom- pressed breast MR images, and in-vivo DBT simulations. Firstly, we compare both iter- ative and simultaneous methods to the conventional, sequential method using an affine transformation model. We show that jointly estimating image intensities and parametric transformations gives superior results with respect to reconstruction fidelity and regis- tration accuracy. Also, we incorporate a non-rigid B-spline transformation model into our simultaneous method. The results demonstrate a visually plausible recovery of the deformation with preservation of the reconstruction fidelity
Ab initio nonrigid X-ray nanotomography
Abstract: Reaching the full potential of X-ray nanotomography, in particular for biological samples, is limited by many factors, of which one of the most serious is radiation damage. Although sample deformation caused by radiation damage can be partly mitigated by cryogenic protection, it is still present in these conditions and, as we exemplify here using a specimen extracted from scales of the Cyphochilus beetle, it will pose a limit to the achievable imaging resolution. We demonstrate a generalized tomographic model, which optimally follows the sample morphological changes and attempts to recover the original sample structure close to the ideal, damage-free reconstruction. Whereas our demonstration was performed using ptychographic X-ray tomography, the method can be adopted for any tomographic imaging modality. Our application demonstrates improved reconstruction quality of radiation-sensitive samples, which will be of increasing relevance with the higher brightness of 4th generation synchrotron sources
Metric on the space of quantum states from relative entropy. Tomographic reconstruction
In the framework of quantum information geometry, we derive, from quantum
relative Tsallis entropy, a family of quantum metrics on the space of full
rank, N level quantum states, by means of a suitably defined coordinate free
differential calculus. The cases N = 2, N = 3 are discussed in detail and
notable limits are analyzed. The radial limit procedure has been used to
recover quantum metrics for lower rank states, such as pure states. By using
the tomographic picture of quantum mechanics we have obtained the Fisher- Rao
metric for the space of quantum tomograms and derived a reconstruction formula
of the quantum metric of density states out of the tomographic one. A new
inequality obtained for probabilities of three spin-1/2 projections in three
perpendicular directions is proposed to be checked in experiments with
superconducting circuits.Comment: 31 pages. No figures. Abstract and Introduction rewritten. Minor
corrections. References adde
Reconstruction of coronary arteries from X-ray angiography: A review.
Despite continuous progress in X-ray angiography systems, X-ray coronary angiography is fundamentally limited by its 2D representation of moving coronary arterial trees, which can negatively impact assessment of coronary artery disease and guidance of percutaneous coronary intervention. To provide clinicians with 3D/3D+time information of coronary arteries, methods computing reconstructions of coronary arteries from X-ray angiography are required. Because of several aspects (e.g. cardiac and respiratory motion, type of X-ray system), reconstruction from X-ray coronary angiography has led to vast amount of research and it still remains as a challenging and dynamic research area. In this paper, we review the state-of-the-art approaches on reconstruction of high-contrast coronary arteries from X-ray angiography. We mainly focus on the theoretical features in model-based (modelling) and tomographic reconstruction of coronary arteries, and discuss the evaluation strategies. We also discuss the potential role of reconstructions in clinical decision making and interventional guidance, and highlight areas for future research
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
On Invariance and Selectivity in Representation Learning
We discuss data representation which can be learned automatically from data,
are invariant to transformations, and at the same time selective, in the sense
that two points have the same representation only if they are one the
transformation of the other. The mathematical results here sharpen some of the
key claims of i-theory -- a recent theory of feedforward processing in sensory
cortex
Generalized 3D and 4D motion compensated whole-body PET image reconstruction employing nested em deconvolution
Whole-body dynamic and parametric PET imaging has recently gained increased interest as a clinically feasible truly quantitative imaging solution for enhanced tumor detectability and treatment response monitoring in oncology. However, in comparison to static scans, dynamic PET acquisitions are longer, especially when extended to large axial field-of-view whole-body imaging, increasing the probability of voluntary (bulk) body motion. In this study we propose a generalized and novel motion-compensated PET image reconstruction (MCIR) framework to recover resolution from realistic motion-contaminated static (3D), dynamic (4D) and parametric PET images even without the need for gated acquisitions. The proposed algorithm has been designed for both single-bed and whole-body static and dynamic PET scans. It has been implemented in fully 3D space on STIR open-source platform by utilizing the concept of optimization transfer to efficiently compensate for motion at each tomographic expectation-maximization (EM) update through a nested Richardson-Lucy EM iterative deconvolution algorithm. The performance of the method, referred as nested RL-MCIR reconstruction, was evaluated on realistic 4D simulated anthropomorphic digital XCAT phantom data acquired with a clinically feasible whole-body dynamic PET protocol and contaminated with measured non-rigid motion from MRI scans of real human volunteers at multiple dynamic frames. Furthermore, in order to assess the impact of our method in whole-body PET parametric imaging, the reconstructed motion-corrected dynamic PET images were fitted with a multi-bed Patlak graphical analysis method to produce metabolic uptake rate (Ki parameter in Patlak model) images of highly quantitative value. Our quantitative Contrast-to-Noise (CNR) and noise vs. bias trade-off analysis results suggest considerable resolution enhancement in both dynamic and parametric motion-degraded whole-body PET images after applying nested RL-MCIR method, without amplification of noise
Classical and quantum aspects of tomography
We present here a set of lecture notes on tomography. The Radon transform and
some of its generalizations are considered and their inversion formulae are
proved. We will also look from a group-theoretc point of view at the more
general problem of expressing a function on a manifold in terms of its
integrals over certain submanifolds. Finally, the extension of the tomographic
maps to the quantum case is considered, as a Weyl-Wigner quantization of the
classical case.Comment: 32 pages, 9 figure
Algorithm for the reconstruction of dynamic objects in CT-scanning using optical flow
Computed Tomography is a powerful imaging technique that allows
non-destructive visualization of the interior of physical objects in different
scientific areas. In traditional reconstruction techniques the object of
interest is mostly considered to be static, which gives artefacts if the object
is moving during the data acquisition. In this paper we present a method that,
given only scan results of multiple successive scans, can estimate the motion
and correct the CT-images for this motion assuming that the motion field is
smooth over the complete domain using optical flow. The proposed method is
validated on simulated scan data. The main contribution is that we show we can
use the optical flow technique from imaging to correct CT-scan images for
motion
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