Scatter is an important problem in computed tomography especially with the increase of X-ray illumination coverage in one single view. Poor scatter correction results in CT HU number inaccuracy, degrades low contrast detectability, and introduces artifacts. Hardware method can be used to handle scatter problem. However, hardware design optimization and scatter correction improvement require an efficient scatter simulation tool. Although Monte Carlo (MC) method can perform precise scatter simulation, simulated noise due to its statistical nature affects the simulation results. In this paper, a deterministic scatter simulation method with radiative transfer equation (RTE) is proposed. Compared to MC method, the deterministic RTE method is free from statistical noise. In order to solve the RTE, a novel iterative spherical harmonics integral formula is developed. Compared to MC method, the results show the accuracy of the proposed method.
Dual-energy computed tomography (DECT) is a recent advancement in CT technology, which can potentially reduce artifacts and provide accurate quantitative information for diagnosis. Recently, statistical iterative reconstruction (SIR) methods were introduced to DECT for radiation dose reduction. The statistical noise modeling of measurement data plays an important role in SIR and impacts on the image quality. Contrary to the conventional CT projection data, of which noise is independent from ray to ray, in spectral CT the basis material sinogram data has strong correlations. In order to analyze the image quality improvement by applying correlated noise model, we compare the effects of two different noise models (i.e., correlated noise model and independent model by ignoring correlations) by analyzing the bias and variance trade-off. The results indicate that in the same bias level, the correlated noise modeling results in up to 20.02% noise reduction compared to the independent noise model. In addition, their impacts to different numerical are also evaluated. The results show that using the non-diagonal covariance matrix in SIR is challenging, where some numerical algorithms such as a direct application of separable paraboloidal surrogates (SPS) cannot converge to the correct results.
Spectral CT requires two or more independent measurements for each ray path in order to extract complete energydependent
information of the object attenuation. The number of required measurements is equivalent to the number of
independent basis functions needed to describe the attenuation of the imaged objects. For example, two independent
measurements are sufficient if only photoelectric absorption and Compton scattering are dominating. If additional Kedge(
s) is present in the energy range of interest, more than two measurements are necessary.
In this study, we present a pre-reconstruction decomposition method that utilizes spectral data redundancy to improve
image quality. We assume projection data are acquired with an M-energy-bin photon counting detector that generates M
independent measurements, and the attenuation of the objects can be described with N (M < M) basis functions. The
method addresses un-balanced noise level of data from different energy bins of the photon counting detector. During a
CT scan, with the non-uniform attenuation of a typical patient, spectral shape and beam intensity can change drastically
from detector to detector, from view to view. As a consequence, a detector unit is subject to significantly varying
incident x-ray spectra. Hardware adjustment approaches are limited by current detector and mechanical technology, and
almost not possible in a typical clinical CT scan with e.g., 1800 views / 0.5 s.
Our method applies adaptive noise balance weighting to data acquired from different energy bins, post data acquisition
and prior data decomposition. The results show substantially improved quality in spectral images reconstructed from
photon counting detector data.
The linearity between CT numbers and iodine concentrations is proved analytically provided the correlations between
the atoms are negligible. This relationship is applied to correct the CT numbers in the ICA regions in monochromatic
images of dual energy CT with the slow kV-switching technique where one scan with a low/high tube voltage follows by
another scan with a high/low voltage. The iodine concentration may change significantly during the kV-switching. The
resultant CT numbers in ICA regions may not be meaningful in the monochromatic images from pre-reconstruction
decompositions because the data with the low/high voltages are not consistent. Using the linearity between CT numbers
and iodine concentrations, the CT numbers in ICA regions can be corrected by referring to the CT numbers in the
polychromatic images with the low/high voltages. A numerical simulation and a phantom study are performed to
examine the linearity between CT numbers and iodine concentrations. The CT number correction by use of the linearity
is tested in the numerical simulation study in slow kV-switching dual energy CT. The results show that the corrected CT
numbers by use of the linearity are accurate.
We propose a method for material separation using dual energy data. Our method is suitable to separation of three or
more materials. In this work we describe our method and show results of numerical simulation and with real dual-energy
data of a head phantom. The proposed method of constructing the material separation map consists of the following
steps: Data-domain dual energy decomposition - Vector plot - Density plot - Clustering - Color assignment. Density
plots are introduced to allow automatic cluster separation. We use special image processing methods, including Gaussian
decomposition, to improve the accuracy of material separation. We also propose using the HSL color model for better
visualization and to bring a new dimension in material separation display. We study applications of bone removal and
virtual contrast removal. Evaluation shows improved accuracy compared to standard methods.
A method to remove stents and consequently to eliminate the blooming artifacts off the stents is proposed in dual energy
CT. The method could also reduce the blooming artifacts off calcified plaques. A phantom study is performed to test the
method. The phantom consists of a stainless steel stent and a dumbbell shaped plastic (Delrin) cylinders. With the dual
energy technique and the knowledge of the stent material, we separate the stent from the Delrin at each image voxels
accurately. The large and small diameters of the Delrin are measured from the images by the full width at half maximum
as 2.8 mm and 1.4 mm, respectively. They are very close to the true values of 2.4 mm and 1.2 mm. By respectively
discarding even and odd view data for the low and high voltages, we simulate the fast kV-switching acquisitions where
one view mis-registration exists between the low/high voltage scans. Comparing with the original images by the slow
kV-switching where a perfect registration is realized between the low/high voltage scans, the images from the fast kVswitching
show no significant differences except for the noise pattern.
Fast kV-switching is a dual energy acquisition technique in CT in which alternating views correspond to the low and
high tube voltages. Its high temporal resolution and its suitability to a variety of source trajectories make it an
attractive option for dual energy data acquisition. Its disadvantages include a one view mis-registration between the
data for high and low voltages, the potential for poor spectrum separation because the fast kV-switching waveform
may be more like a sine wave than the desired square wave, and the higher noise in the low voltage data because of the
technical difficulty of swinging the tube current to counter the loss of x-ray production efficiency and loss of
penetration at lower tube voltages. These issues are investigated with a recently developed pre-reconstruction
decomposition method by the authors. Results include that symmetric view matching eliminates streaks from the view
mis-registration, a sinusoidal waveform swinging between 80 and 135 kV gives sufficient spectrum separation, and
that contrast-to-noise for the simulated imaging task maximizes at monochromatic energy of 75 keV.
Both flat-panel detectors and cylindrical detectors have been used in CT systems for data acquisition. The cylindrical detector generally offers a sampling of a transverse image plane more uniformly than does a flat-panel detector. However, in the longitudinal dimension, the cylindrical and flat-panel detectors offer similar sampling of the image space. In this work, we investigate a detector of spherical shape, which can yield uniform sampling of the 3D image space because the solid angle subtended by each individual detector bin remains unchanged. We have extended the backprojection-filtration (BPF) algorithm, which we have developed previously for cone-beam CT, to reconstruct images in cone-beam CT with a spherical detector. We also conduct computer-simulation studies to validate the extended BPF algorithm. Quantitative results in these numerical studies indicate that accurate images can be obtained from data acquired with a spherical detector by use of our extended BPF cone-beam algorithms.
A formula was recently described by Clackdoyle et. al. for image reconstruction within a region of interest (ROI) from knowledge of its truncated 2D Radon transform. In this work, we present an alternative, simple derivation of the formula by using the well-known relationship between the parallel-beam and fan-beam geometries. Based upon our derivation, the role of parameter t in the formula in ROI-image reconstruction can be clearly identified. We show that the parameter t determines the size of a reconstructible ROI from parallel-beam data containing truncations. Numerical studies were performed to by use of the formula with different t. We show that the formula yields ROI images with smaller sizes and lower quality than does our backprojection filtration algorithm.
In this work, we investigate exact image reconstruction
within a 3D region of interest from data acquired with
a circle-arc trajectory. In particular, the data
may contain both longitudinal and transverse truncations.
This work may find applications
in lung or heart imaging using a C-arm scanner.
When the arc portion of the trajectory is posterior
or anterior to the patient, exact images within the
lung or heart region can be reconstructed from truncated
data.
We develop a reconstruction algorithm for local cone-beam X-ray tomography for use with generalized scanning
trajectories. The algorithm is based upon an extension of a recently-developed chord-based theory for exact conebeam
image reconstruction. Being chord-based, it is distinct mathematically and conceptually from conventional
local tomography reconstruction algorithms. A computer-simulation study is conducted to demonstrate the
algorithm, and compare its performance to an existing algorithm.
In helical cone-beam computerized tomography, the data within the Tam-Danielsson window is sufficient for exact reconstruction of the images. In some practical situation, the projections outside the Tam-Danielsson window are available that indicate the data redundancy.
In this work, we investigate image reconstruction on n-PI lines from data within n-PI window. We performed a preliminary numerical study, and the results in these studies shown that our algorithm can exactly reconstruct images from n-PI data.
Recently, a 3D filtered-backprojection (FBP)-based algorithm for image reconstruction on PI-line segments in a helical cone-beam CT scan has been developed (Zou and Pan, 2004). In the present work, we derive new reconstruction algorithms for circular cone-beam scans based upon this algorithm and a concept of virtual PI-line. We prove that, in the case of conventional full- and short-scan, the newly derived algorithms are mathematically identical to existing algorithms. More importantly, in the case of reduced-scans in which the scanning angle range is less than that in a short-scan, the new algorithms can yield exact region of interest (ROI) reconstruction in mid-plane and approximate ROI reconstruction in off-mid-planes. We have performed a preliminary numerical study that verifies our theoretical assertions.
Recent algorithm development for image reconstruction for cone-beam CT has tackled exact image reconstruction for very general scanning configurations. The heart of the new algorithms is the concept of reconstruction on the chordn of a general source trajectory. Volume ROI reconstruction becomes possible by concatenating the chords on which the image has been obtained. For some scanning trajectories there maybe points in the image space where the image can theoretically be obtained exactly, yet no chord intersects these points. This article provides a consistency condition, based on the ideas of John's equation, that may be used to rebin cone-beam data so that all points satisfying Tuy's condition are reconstructible
by a chord algorithm.
In fan-beam computed tomography (CT), one may be interested in image reconstruction in a region of interest (ROI) from truncated data acquired over an angular range less than half-scan data. We developed recently a backprojection filtration (BPF) algorithm to reconstruct an ROI image from reduced scan data containing data truncations. In a reduced scan, the truncated data may still contain redundancy. In this work, we describe a new algorithm that can exploit data redundancy in truncated data for potentially suppressing the aliasing and noise artifacts in reconstructed images.
We have performed numerical studies to demonstrate the BPF algorithm.
In many applications of circular cone-beam CT, it is not uncommon that the size of the field of view (FOV) is smaller than that of the imaging object, thus leading to transverse truncation in projection data. Exact reconstruction in any region is not possible from such truncated data using conventional algorithms. Recently, an exact algorithm for image reconstruction on PI-line segments in helical cone-beam CT has been proposed. This algorithm, which we refer to as the backprojection-filtration (BPF) algorithm, can naturally address the problem of exact region of interest (ROI) reconstruction from such truncated data. In this work, we modified this algorithm to reconstructing images in circular cone-beam scan. The unique property of this modified algorithm is that it can reconstruct exact ROIs in midplane and approximate ROIs in other planes from transversely truncated data. We have performed computer-simulation studies to validate the theoretical assertions. Preliminary results demonstrate that the proposed algorithm provides a solution to the truncation problems caused by limited FOV size.
An important breakthrough in helical cone-beam reconstruction is the development of Katsevich's algorithms,
which appear to have numerous advantages over the algorithms developed previously. The original algorithm
proposed by Katsevich has a simple form and requires only once the computation of the data filtering. It, however,
invokes a derivative of the data function with respect to the rotation angle along the helical trajectory and thus
makes the algorithm numerically susceptible to the sample aliasing along the helical trajectory. A modified
version of the algorithm later developed by Katsevich that avoids the explicit computation of the derivative
of the data function along the helical trajectory. However, this modified algorithm contains more terms than
does the original algorithm and involves two different filtering of the data function. Therefore, this modified
algorithm is computationally more complex and demanding than does the original Katsevich's algorithm. In this
work, based upon the original Katsevich's algorithm, we present a new algorithm that not only avoids explicit
computation of the derivative of the data function along the helical trajectory but also requires only one filtering
of the data function. Therefore, in general, our algorithm is quantitatively more accurate than the original
Katsevich's algorithm and is computationally more efficient than the modified Katsevich's algorithm.
We proposed a new reconstruction algorithm for image reconstruction from helical cone-beam data only within the
Tam-Danielsson window, thus allowing the potential reduction of radiation dose to patients. The new algorithm
can be expressed as two terms. The first term dominates the contribution to the reconstructed image, and the
second term provides only a small correction. In fact, such a correction is generally negligible as compared to that
from the first term and introduces a detectable DC-type shift to the reconstructed images only in the situations
where the ratio between the size of field of view and the helical radius approaches to 0.625, which is the limit to
the validity of the first term. Based on the Grangeat formula, we have developed an algorithm to calculate the
correction (i.e., the second) term from the data within the window.
The effect of polychromatic x-rays on image reconstruction in helical cone-beam computed tomography is investigated.
A pre-reconstruction dual-energy technique is developed to reduce beam-hardening artifacts and enhance contrast in soft tissue. The effect of realistic signal noise on the dual-energy method
is studied.
Thermoacoustic tomography (TAT) is an emerging imaging technique with great potential for a wide range of biomedical imaging applications. In this work, we propose and investigate reconstruction approaches for TAT that are based on the half-time reflectivity tomography paradigm. We demonstrate that half-time reconstruction approaches can produce images in TAT that possess better statistical properties than images produced by use of conventional reconstruction approaches.
Reflectivity tomography is an imaging technique that seeks to reconstruct the reflectivity distribution that characterizes a weakly reflecting object. As in other tomographic imaging modalities, in certain applications of reflectivity tomography it may be necessary to reconstruct an accurate image from measurement data that are incomplete, e.g., reduced-scan measurement data. Recently, we have developed a so-called 'potato peeler' perspective for heuristically demonstrating the possibility of reconstructing accurate images from reduced-scan measurement data. In this work we describe a mathematical formulation of the potato peeler perspective, which provides a theoretical justification for the
development and application of reduced-scan reconstruction algorithms in reflectivity tomography. Simulation results are presented to corroborate our theoretical assertions.
The quasi-exact algorithms developed by Kudo et al. can reconstruct accurate images from data acquired in helical cone-beam configuration. The current formulation of such algorithms, however, prevents their direct application to data acquired in a practical configuration that may be used in helical cone-beam computed tomography (CT) in which the longitudinal axis of the area detector always remains parallel to the longitudinal axis of helical CT system.
Interpolation can be used to convert data acquired with the practical
helical cone-beam configuration into the form required by the current quasi-exact algorithms. Such an interpolation can reduce spatial resolution in reconstructed images. In this work, we derive a new filtering function that can be used in the quasi-exact algorithms so that they can be used to reconstruct images directly from data acquired with a practical scanning configuration thereby avoiding interpolation. We also performed computer simulation studies, and numerical results from these studies confirm that accurate images can be reconstructed by use of these generalized quasi-exact algorithms. The practical implication of the generalized quasi-exact algorithms is that they can yield images with potentially enhanced spatial resolution by avoiding data interpolation.
In parallel beam computed tomography, the measured projections at conjugate views are mathematically identical, and, consequently, this symmetry can be exploited for reducing either the scanning angle or the size of the detector arrays. However, in single-photon emission computed tomography (SPECT), because the gamma-rays in the conjugate views suffer different photon attenuation, the measured projections at conjugate views are generally different. Therefore, it had been widely considered that projections measured data over a full angular range of 360 degrees and over the whole detector face are generally required for exactly reconstructing the distributions of gamma-ray emitters. Recently, it has been revealed that exact image can be reconstructed from projections acquired with a full detector over disjoint angular intervals whose summation is 180 degree when the attenuation medium is uniform. In this work, we show that exact SPECT images can also be reconstructed from projections over 360 degrees, but acquired with a half detector viewing half of the image space. We present an heuristic perspective that supports this claim for SPECT with both uniform and non-uniform attenuation.
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