A cone beam circular half-scan scheme is becoming an attractive
imaging method in cone beam CT since it improves the temporal
resolution. Traditionally, the redundant data in the circular
half-scan range is weighted by a central scanning plane-dependent
weighting function; FDK algorithm is then applied on the weighted
projection data for reconstruction. However, this scheme still
suffers the attenuation coefficient drop inherited with FDK when
the cone angle becomes large. A new heuristic cone beam
geometry-dependent weighting scheme is proposed based on the idea
that there exists less redundancy for the projection data away
from the central scanning plane. The performance of FDKHSCW scheme
is evaluated by comparing it to the FDK full-scan (FDKFS) scheme
and the traditional FDK half-scan scheme with Parker's fan beam
weighting function (FDKHSFW). Computer simulation is employed and
conducted on a 3D Shepp-Logan phantom. The result illustrates a
correction of FDKHSCW to the attenuation coefficient drop in the
off-scanning plane associated with FDKFS and FDKHSFW while
maintaining the same spatial resolution.

Dong Yang

Ruola Ning

FDK Half-Scan with a Heuristic Weighting Scheme on a Flat Panel Detector-Based Cone Beam CT (FDKHSCW)

A three-dimensional (3D) weighted helical cone beam filtered
backprojection (CB-FBP) algorithm (namely, original 3D weighted
helical CB-FBP algorithm) has already been proposed to reconstruct
images from the projection data acquired along a helical
trajectory in angular ranges up to <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mi>π</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>. However, an
overscan is usually employed in the clinic to reconstruct
tomographic images with superior noise characteristics at the most
challenging anatomic structures, such as head and spine,
extremity imaging, and CT angiography as well. To obtain the most
achievable noise characteristics or dose efficiency in a helical
overscan, we extended the 3D weighted helical CB-FBP algorithm to
handle helical pitches that are smaller than <mml:math id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mn>1</mml:mn></mml:math> (namely
extended 3D weighted helical CB-FBP algorithm). By decomposing a
helical over scan with an angular range of <mml:math id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mi>π</mml:mi><mml:mo>+</mml:mo><mml:mi>Δ</mml:mi><mml:mi>β</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math> into a union of full scans corresponding to an angular
range of <mml:math id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mi>π</mml:mi></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>, the extended 3D weighted function is a
summation of all 3D weighting functions corresponding to each full
scan. An experimental evaluation shows that the extended 3D
weighted helical CB-FBP algorithm can improve noise
characteristics or dose efficiency of the 3D weighted helical
CB-FBP algorithm at a helical pitch smaller than <mml:math id="E5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>1</mml:mn><mml:mo>:</mml:mo><mml:mn>1</mml:mn></mml:math>, while its
reconstruction accuracy and computational efficiency are
maintained. It is believed that, such an efficient CB
reconstruction algorithm that can provide superior noise
characteristics or dose efficiency at low helical pitches may find
its extensive applications in CT medical imaging.

Xiangyang Tang

Jiang Hsieh

Roy A. Nilsen

Scott M. McOlash

Extending Three-Dimensional Weighted Cone Beam Filtered Backprojection (CB-FBP) Algorithm for Image Reconstruction in Volumetric CT at Low Helical Pitches

Cone-beam (CB) acquisition is increasingly used for trulythree-dimensional X-ray computerized tomography (CT). However,tomographic reconstruction from data collected along a circulartrajectory with the popular Feldkamp algorithm is known to produce theso-called CB artifacts. These artifacts result from theincompleteness of the source trajectory and the resulting missingdata in the Radon space increasing with the distance to the planecontaining the source orbit. In the context of the development ofintegrated PET/CT microscanners, we introduced a noveloff-centered circular CT cone-beam geometry. We proposed ageneralized Feldkamp formula (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03B1;</mml:mi></mml:math>-FDK) adapted to thisgeometry, but reconstructions suffer from increased CB artifacts.In this paper, we evaluate and compare four differentreconstruction methods for correcting CB artifacts in off-centeredgeometry. We consider the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03B1;</mml:mi></mml:math>-FDK algorithm, theshift-variant FBP method derived from the T-FDK, an FBP methodbased on the Grangeat formula, and an iterative algebraic method(SART). The results show that the low contrast artifacts can beefficiently corrected by the shift-variant method and the SARTmethod to achieve good quality images at the expense of increasedcomputation time, but the geometrical deformations are still notcompensated for by these techniques.

S.  Valton

F.  Peyrin

D.  Sappey-Marinier

Analysis of Cone-Beam Artifacts in off-Centered Circular CT for Four Reconstruction Methods

Hengyong Yu

Patrick J. La Rivière

Development of Computed Tomography Algorithms

Statistical image reconstruction methods based on
maximum a posteriori (MAP) principle have been developed for
emission tomography. The prior distribution of the unknown image
plays an important role in MAP reconstruction. The most commonly
used prior are Gaussian priors, whose logarithm has a quadratic
form. Gaussian priors are relatively easy to analyze. It has been
shown that the effect of a Gaussian prior can be approximated by
linear filtering a maximum likelihood (ML) reconstruction. As a
result, sharp edges in reconstructed images are not preserved. To
preserve sharp transitions,  non-Gaussian priors have been
proposed. However, their effect on clinical tasks is less obvious.
In this paper, we compare MAP reconstruction with Gaussian and
non-Gaussian priors for lesion detection and region of interest
quantification using computer simulation. We evaluate three
representative priors: Gaussian prior, Huber prior, and
Geman-McClure prior. We simulate imaging a prostate tumor using
positron emission tomography (PET). The detectability of a known
tumor in either a fixed background or a random background is
measured using a channelized Hotelling observer. The bias-variance
tradeoff curves are calculated for quantification of the total
tumor activity. The results show that for the detection and
quantification tasks, the Gaussian prior is as effective as
non-Gaussian priors.

Jinyi Qi

Comparison of Lesion Detection and Quantification in MAP Reconstruction with Gaussian and Non-Gaussian Priors

Multislice computed tomography (MSCT) scanners offer new
perspectives for cardiac kinetics evaluation with 4D dynamic
sequences of high contrast and spatiotemporal resolutions. A new
method is proposed for cardiac motion extraction in multislice CT.
Based on a 4D hierarchical surface-volume matching process, it
provides the detection of the heart left cavities along the
acquired sequence and the estimation of their 3D surface velocity
fields. A Markov random field model is defined to find, according
to topological descriptors, the best correspondences between a 3D
mesh describing the left endocardium at one time and the 3D
acquired volume at the following time. The global optimization of
the correspondences is realized with a multiresolution process.
Results obtained on simulated and real data show the capabilities
to extract clinically relevant global and local motion parameters
and highlight new perspectives in cardiac computed tomography
imaging.

Mireille Garreau

Antoine Simon

Dominique Boulmier

Jean-Louis Coatrieux

Hervé Le Breton

Assessment of Left Ventricular Function in Cardiac MSCT Imaging by a 4D Hierarchical Surface-Volume Matching Process

The use of iterative algorithms in tomographic reconstruction always leads to a frequency adapted rate of convergence in that low frequencies are accurately reconstructed after a few iterations, while high frequencies sometimes require many more computations. In this paper, we propose to build frequency adapted (FA) algorithms based on a condition of incomplete backprojection and propose an FA simultaneous algebraic reconstruction technique (FA-SART) algorithm as an example. The results obtained with the FA-SART algorithm demonstrate a very fast convergence on a highly detailed phantom when compared to the original SART algorithm. Though the use of such an FA algorithm may seem difficult, we specify in which case it is relevant and propose several ways to improve the reconstruction process with FA algorithms.

Vincent Israel-Jost

Philippe Choquet

Andr&#xe9; Constantinesco

A Prospective Study on Algorithms Adapted to the Spatial Frequency in Tomography

FDK algorithm is a well-known 3D (three-dimensional) approximate algorithm for CT (computed tomography) image reconstruction and is also known to suffer from considerable artifacts when the scanning cone angle is large. Recently, it has been improved by performing the ramp filtering along the tangential direction of the X-ray source helix for dealing with the large cone angle problem. In this paper, we present an FDK-type approximate reconstruction algorithm for gantry-tilted CT imaging. The proposed method improves the image reconstruction by filtering the projection data along a proper direction which is determined by CT parameters and gantry-tilted angle. As a result, the proposed algorithm for gantry-tilted CT reconstruction can provide more scanning flexibilities in clinical CT scanning and is efficient in computation. The performance of the proposed algorithm is evaluated with turbell clock phantom and thorax phantom and compared with FDK algorithm and a popular 2D (two-dimensional) approximate algorithm. The results show that the proposed algorithm can achieve better image quality for gantry-tilted CT image reconstruction.

Ming  Yan

Cishen  Zhang

Hongzhu  Liang

An Approximate Cone Beam Reconstruction Algorithm for Gantry-Tilted CT Using Tangential Filtering

For spiral cone-beam CT, parallel computing is an effective
approach to resolving the problem of heavy computation burden. It
is well known that the major computation time is spent in the
backprojection step for either filtered-backprojection (FBP) or
backprojected-filtration (BPF) algorithms. By the cone-beam cover
method [1], the backprojection procedure is driven by cone-beam
projections, and every cone-beam projection can be backprojected
independently. Basing on this fact, we develop a parallel
implementation of Katsevich's FBP algorithm. We do all the
numerical experiments on a Linux cluster. In one typical
experiment, the sequential reconstruction time is 781.3 seconds,
while the parallel reconstruction time is 25.7 seconds with 32
processors.

Jiansheng Yang

Xiaohu Guo

Qiang Kong

Tie Zhou

Ming Jiang

Parallel Implementation of Katsevich's FBP Algorithm

We have compared the performance of two different penalty choices
for a penalized-likelihood sinogram-restoration strategy we have
been developing. One is a quadratic penalty we have employed
previously and the other is a new median-based penalty. We
compared the approaches to a noniterative adaptive filter that
loosely but not explicitly models data statistics. We found that
the two approaches produced similar resolution-variance tradeoffs
to each other and that they outperformed the adaptive filter in
the low-dose regime, which suggests that the particular choice of
penalty in our approach may be less important than the fact that
we are explicitly modeling data statistics at all. Since the
quadratic penalty allows for derivation of an algorithm that is
guaranteed to monotonically increase the penalized-likelihood
objective function, we find it to be preferable to the median-based penalty.

Junguo Bian

Phillip A. Vargas

Comparison of Quadratic- and Median-Based Roughness Penalties for Penalized-Likelihood Sinogram Restoration in Computed Tomography

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International Journal of Biomedical Imaging aims to promote research and development of biomedical imaging by publishing high-quality research articles and reviews in this rapidly growing interdisciplinary field.

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International Journal of Biomedical Imaging

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Papers are published upon acceptance, regardless of the Special Issue publication date.

International Journal of Biomedical Imaging

Development of Computed Tomography Algorithms

Development of Computed Tomography Algorithms

Articles

FDK Half-Scan with a Heuristic Weighting Scheme on a Flat Panel Detector-Based Cone Beam CT (FDKHSCW)

Extending Three-Dimensional Weighted Cone Beam Filtered Backprojection (CB-FBP) Algorithm for Image Reconstruction in Volumetric CT at Low Helical Pitches

Analysis of Cone-Beam Artifacts in off-Centered Circular CT for Four Reconstruction Methods

Development of Computed Tomography Algorithms

Comparison of Lesion Detection and Quantification in MAP Reconstruction with Gaussian and Non-Gaussian Priors

Assessment of Left Ventricular Function in Cardiac MSCT Imaging by a 4D Hierarchical Surface-Volume Matching Process

A Prospective Study on Algorithms Adapted to the Spatial Frequency in Tomography

An Approximate Cone Beam Reconstruction Algorithm for Gantry-Tilted CT Using Tangential Filtering

Parallel Implementation of Katsevich's FBP Algorithm

Comparison of Quadratic- and Median-Based Roughness Penalties for Penalized-Likelihood Sinogram Restoration in Computed Tomography