Resolution Limits in Full- and Limited-Angle Tomography

info:eu-repo/semantics/published

A regularized iterative algorithm for limited-angle inverse Radon transform

The tomography problem is investigated when the available projections are restricted to a limited angular domain. It is shown that a previous algorithm proposed for extrapolating the data to the missing cone in Fourier space is unstable in the presence of noise because of the ill-posedness of the problem. A regularized algorithm is proposed, which converges to stable solutions. The efficiency of both algorithms is tested by means of numerical simulations. © 1983 Taylor and Francis Group, LLC.

Probabilistic Evaluation of Three-Dimensional Reconstructions from X-Ray Images Spanning a Limited Angle

An important part of computed tomography is the calculation of a three-dimensional reconstruction of an object from series of X-ray images. Unfortunately, some applications do not provide sufficient X-ray images. Then, the reconstructed objects no longer truly represent the original. Inside of the volumes, the accuracy seems to vary unpredictably. In this paper, we introduce a novel method to evaluate any reconstruction, voxel by voxel. The evaluation is based on a sophisticated probabilistic handling of the measured X-rays, as well as the inclusion of a priori knowledge about the materials that the object receiving the X-ray examination consists of. For each voxel, the proposed method outputs a numerical value that represents the probability of existence of a predefined material at the position of the voxel while doing X-ray. Such a probabilistic quality measure was lacking so far. In our experiment, false reconstructed areas get detected by their low probability. In exact reconstructed areas, a high probability predominates. Receiver Operating Characteristics not only confirm the reliability of our quality measure but also demonstrate that existing methods are less suitable for evaluating a reconstruction.

Image reconstruction by an alternating minimisation

This paper focuses on the problem of incomplete data in the applications of the circular cone-beam computed tomography. This problem is frequently encountered in medical imaging sciences and some other industrial imaging systems. For example, it is crucial when the high density region of objects can only be penetrated by X-rays in a limited angular range. As the projection data are only available in an angular range, the above mentioned incomplete data problem can be attributed to the limited angle problem, which is an ill-posed inverse problem. This paper reports a modified total variation minimisation method to reduce the data insufficiency in tomographic imaging. This proposed method is robust and efficient in the task of reconstruction by showing the convergence of the alternating minimisation method. The results demonstrate that this new reconstruction method brings reasonable performance. (C) 2010 Elsevier B.V. All rights reserved.

Strategies for Inverse Profiling of Two Dimensional Dielectric Scatterers Using Electromagnetic Illumination

Electromagnetic tomography has been applied to problems in nondestructive evolution, ground-penetrating radar, synthetic aperture radar, target identification, electrical well logging, medical imaging etc. The problem of electromagnetic tomography involves the estimation of cross sectional distribution dielectric permittivity, conductivity etc based on measurement of the scattered fields. The inverse scattering problem of electromagnetic imaging is highly non linear and ill posed, and is liable to get trapped in local minima. The iterative solution techniques employed for computing the inverse scattering problem of electromagnetic imaging are highly computation intensive. Thus the solution to electromagnetic imaging problem is beset with convergence and computational issues. The attempt of this thesis is to develop methods suitable for improving the convergence and reduce the total computations for tomographic imaging of two dimensional dielectric cylinders illuminated by TM polarized waves, where the scattering problem is defmed using scalar equations. A multi resolution frequency hopping approach was proposed as opposed to the conventional frequency hopping approach employed to image large inhomogeneous scatterers. The strategy was tested on both synthetic and experimental data and gave results that were better localized and also accelerated the iterative procedure employed for the imaging. A Degree of Symmetry formulation was introduced to locate the scatterer in the investigation domain when the scatterer cross section was circular. The investigation domain could thus be reduced which reduced the degrees of freedom of the inverse scattering process. Thus the entire measured scattered data was available for the optimization of fewer numbers of pixels. This resulted in better and more robust reconstructions of the scatterer cross sectional profile. The Degree of Symmetry formulation could also be applied to the practical problem of limited angle tomography, as in the case of a buried pipeline, where the ill posedness is much larger. The formulation was also tested using experimental data generated from an experimental setup that was designed. The experimental results confirmed the practical applicability of the formulation.

Coding Strategies for X-ray Tomography

This work focuses on the construction and application of coded apertures to compressive X-ray tomography. Coded apertures can be made in a number of ways, each method having an impact on system background and signal contrast. Methods of constructing coded apertures for structuring X-ray illumination and scatter are compared and analyzed. Apertures can create structured X-ray bundles that investigate specific sets of object voxels. The tailored bundles of rays form a code (or pattern) and are later estimated through computational inversion. Structured illumination can be used to subsample object voxels and make inversion feasible for low dose computed tomography (CT) systems, or it can be used to reduce background in limited angle CT systems.

On the detection side, coded apertures modulate X-ray scatter signals to determine the position and radiance of scatter points. By forming object dependent projections in measurement space, coded apertures multiplex modulated scatter signals onto a detector. The multiplexed signals can be inverted with knowledge of the code pattern and system geometry. This work shows two systems capable of determining object position and type in a 2D plane, by illuminating objects with an X-ray `fan beam,' using coded apertures and compressive measurements. Scatter tomography can help identify materials in security and medicine that may be ambiguous with transmission tomography alone.

Beyond filtered backprojection: a reconstruction software package for ion beam microtomography data

A new version of the TomoRebuild data reduction software package is presented, for the reconstruction of scanning transmission ion microscopy tomography (STIMT) and particle induced X-ray emission tomography (PIXET) images. First, we present a state of the art of the reconstruction codes available for ion beam microtomography. The algorithm proposed here brings several advantages. It is a portable, multi-platform code, designed in C++ with well-separated classes for easier use and evolution. Data reduction is separated in different steps and the intermediate results may be checked if necessary. Although no additional graphic library or numerical tool is required to run the program as a command line, a user friendly interface was designed in Java, as an ImageJ plugin. All experimental and reconstruction parameters may be entered either through this plugin or directly in text format files. A simple standard format is proposed for the input of experimental data. Optional graphic applications using the ROOT interface may be used separately to display and fit energy spectra. Regarding the reconstruction process, the filtered backprojection (FBP) algorithm, already present in the previous version of the code, was optimized so that it is about 10 times as fast. In addition, Maximum Likelihood Expectation Maximization (MLEM) and its accelerated version Ordered Subsets Expectation Maximization (OSEM) algorithms were implemented. A detailed user guide in English is available. A reconstruction example of experimental data from a biological sample is given. It shows the capability of the code to reduce noise in the sinograms and to deal with incomplete data, which puts a new perspective on tomography using low number of projections or limited angle.

Statistical methods for polyhedral shape classification with incomplete data - application to cryo-electron tomographic images

A certain type of bacterial inclusion, known as a bacterial microcompartment, was recently identified and imaged through cryo-electron tomography. A reconstructed 3D object from single-axis limited angle tilt-series cryo-electron tomography contains missing regions and this problem is known as the missing wedge problem. Due to missing regions on the reconstructed images, analyzing their 3D structures is a challenging problem. The existing methods overcome this problem by aligning and averaging several similar shaped objects. These schemes work well if the objects are symmetric and several objects with almost similar shapes and sizes are available. Since the bacterial inclusions studied here are not symmetric, are deformed, and show a wide range of shapes and sizes, the existing approaches are not appropriate. This research develops new statistical methods for analyzing geometric properties, such as volume, symmetry, aspect ratio, polyhedral structures etc., of these bacterial inclusions in presence of missing data. These methods work with deformed and non-symmetric varied shaped objects and do not necessitate multiple objects for handling the missing wedge problem. The developed methods and contributions include: (a) an improved method for manual image segmentation, (b) a new approach to 'complete' the segmented and reconstructed incomplete 3D images, (c) a polyhedral structural distance model to predict the polyhedral shapes of these microstructures, (d) a new shape descriptor for polyhedral shapes, named as polyhedron profile statistic, and (e) the Bayes classifier, linear discriminant analysis and support vector machine based classifiers for supervised incomplete polyhedral shape classification. Finally, the predicted 3D shapes for these bacterial microstructures belong to the Johnson solids family, and these shapes along with their other geometric properties are important for better understanding of their chemical and biological characteristics.

Comparison of intraoral radiography and limited cone beam computed tomography for the assessment of root-fractured permanent teeth

AIM: To compare intraoral occlusal (OC) and periapical (PA) radiographs vs. limited cone beam computed tomography (CBCT) in diagnosing root-fractured permanent teeth. MATERIAL AND METHODS: In 38 patients (mean age 24 years, range 8-52 years) with 44 permanent teeth with horizontal root fractures, intraoral radiographs (PA and OC) and limited CBCT were used to evaluate the location (apical, middle, cervical third of the root) and angulation of the fracture line. Furthermore, the conventional radiographs and CBCT images were compared for concordance of fracture location. RESULTS: In the PA and OC radiographs, 28 fractures (63.6%) were located in the middle third of the root, 11 (25.0%) in the apical third and 5 (11.4%) in the cervical third. The PA/OC radiographs and the sagittal CBCT images (facial aspect) yielded the same level of root fracture in 70.5% of cases (31 teeth; 95% CI: 54.1-82.7%). The PA/OC radiographs and sagittal CBCT images (palatal aspect) showed the same level of root fracture in 31.8% of cases. There was a statistically significant association between the angle at which the root fracture line intersected the axis of the tooth and the level of root fracture in the facial aspect of the sagittal CBCT images. CONCLUSIONS: The diagnosis of the location and angulation of root fractures based on limited CBCT imaging differs significantly from diagnostic procedures based on intraoral radiographs (PA/OC) alone. The clinical significance for treatment strategies and for the prognosis of root-fractured teeth has to be addressed in future studies.

QTL for root angle and number in a population developed from bread wheats (Triticum aestivum) with contrasting adaptation to water-limited environments

Root architecture traits in wheat are important in deep soil moisture acquisition and may be used to improve adaptation to water-limited environments. The genetic architecture of two root traits, seminal root angle and seminal root number, were investigated using a doubled haploid population derived from SeriM82 and Hartog. Multiple novel quantitative trait loci (QTL) were identified, each one having a modest effect. For seminal root angle, four QTL (-log10(P) >3) were identified on 2A, 3D, 6A and 6B, and two suggestive QTL (-log10(P) >2) on 5D and 6B. For root number, two QTL were identified on 4A and 6A with four suggestive QTL on 1B, 3A, 3B and 4A. QTL for root angle and root number did not co-locate. Transgressive segregation was found for both traits. Known major height and phenology loci appear to have little effect on root angle and number. Presence or absence of the T1BL.1RS translocation did not significantly influence root angle. Broad sense heritability (h 2) was estimated as 50 % for root angle and 31 % for root number. Root angle QTL were found to be segregating between wheat cultivars adapted to the target production region indicating potential to select for root angle in breeding programs. © 2013 Springer-Verlag Berlin Heidelberg.

Hamiltonian Tomography in an Access-Limited Setting without State Initialization

We propose a scheme for the determination of the coupling parameters in a chain of interacting spins. This requires only time-resolved measurements over a single particle, simple data postprocessing and no state initialization or prior knowledge of the state of the chain. The protocol fits well into the context of quantum-dynamics characterization and is efficient even when the spin chain is affected by general dissipative and dephasing channels. We illustrate the performance of the scheme by analyzing explicit examples and discuss possible extensions.

Assessment of CT numbers in limited and medium field-of-view scans taken using Accuitomo 170 and Veraviewepocs 3De cone-beam computed tomography scanners

To assess the influence of anatomic location on the relationship between computed tomography (CT) number and X-ray attenuation in limited and medium field-of-view (FOV) scans. Materials and Methods Tubes containing solutions with different concentrations of K2HPO4 were placed in the tooth sockets of a human head phantom. Cone-beam computed tomography (CBCT) scans were acquired, and CT numbers of the K2HPO4 solutions were measured. The relationship between CT number and K2HPO4 concentration was examined by linear regression analyses. Then, the variation in CT number according to anatomic location was examined. Results The relationship between K2HPO4 concentration and CT number was strongly linear. The slopes of the linear regressions for the limited FOVs were almost 2-fold lower than those for the medium FOVs. The absolute CT number differed between imaging protocols and anatomic locations. Conclusion There is a strong linear relationship between X-ray attenuation and CT number. The specific imaging protocol and anatomic location of the object strongly influence this relationship.

Morphology of the nasopalatine canal and dental implant surgery: a radiographic analysis of 100 consecutive patients using limited cone-beam computed tomography

To analyze the dimensions and anatomic characteristics of the nasopalatine canal and the corresponding buccal bone plate of the alveolar process, using limited cone-beam computed tomography (CBCT) imaging.

Evaluation of location and dimensions of lingual foramina using limited cone-beam computed tomography

To assess retrospectively the frequency and location of mandibular lingual foramina and their bony canals with limited cone-beam computed tomography.

Comparison of periapical radiography and limited cone-beam computed tomography in mandibular molars for analysis of anatomical landmarks before apical surgery

The purpose of the present study was to evaluate the detectability and dimensions of periapical lesions, the relationship of the mandibular canal to the roots of the respective teeth, and the dimension of the buccal bone by using limited cone-beam computed tomography (CBCT) in comparison to conventional periapical (PA) radiographs for evaluation of mandibular molars before apical surgery.