X-ray or gamma ray systems or devices – Specific application – Computerized tomography
Reexamination Certificate
2001-02-15
2003-01-14
Bruce, David V. (Department: 2882)
X-ray or gamma ray systems or devices
Specific application
Computerized tomography
C378S004000, C378S005000, C378S094000
Reexamination Certificate
active
06507633
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to statistical methods for reconstructing a polyenergetic X-ray computed tomography image and image reconstructor apparatus and, in particular, to methods and reconstructor apparatus which reconstruct such images from a single X-ray CT scan having a polyenergetic source spectrum.
2. Background Art
X-ray computed or computerized tomography (i.e. CT) provides structural information about tissue anatomy. Its strength lies in the fact that it can provide “slice” images, taken through a three-dimensional volume with enhanced contrast and reduced structure noise relative to projection radiography.
FIG. 1
illustrates a simple CT system. An X-ray source is collimated and its rays are scanned through the plane of interest. The intensity of the X-ray photons is diminished by tissue attenuation. A detector measures the photon flux that emerges from the object. This procedure is repeated at sufficiently close angular samples over 180° or 360°. The data from different projections are organized with the projection angles on one axis and the projection bins (radial distance) on the other. This array is referred to as the sinogram, because the sinogram of a single point traces a sinusoidal wave. Reconstruction techniques have the goal of estimating the attenuation map of the object that gave rise to the measured sinogram.
FIGS. 2
a
-
2
c
illustrate the evolution of CT geometries.
FIG. 2
a
is a parallel-beam (single ray) arrangement, much like what was found in a first-generation CT scanner. The major drawback of this arrangement is long scan time, since the source detector arrangement has to be translated and rotated.
The fan-beam geometry of
FIG. 2
b
reduces the scan time to a fraction of a second by eliminating the need for translation. By translating the patient table as the source detector arrangement rotates, one gets an effective helical path around the object leading to increased exposure volume and three-dimensional imaging.
The latest CT geometry is the cone-beam arrangement, shown in
FIG. 2
c
. It further reduces scan time by providing three-dimensional information in one rotation. It is most efficient in its usage of the X-ray tube, but it suffers from high scatter (≧40%). It is also the most challenging in terms of reconstruction algorithm implementation.
Two dominant effects, both a function of the X-ray source spectrum, govern tissue attenuation. At the lower energies of interest in the diagnostic region, the photoelectric effect dominates. At higher energies, Compton scattering is the most significant source of tissue attenuation.
The linear attenuation coefficient &mgr;(x,y,z,E) characterizes the overall attenuation property of tissue. It depends on the spatial coordinates and the beam energy, and has units of inverse distance. For a ray of infinitesimal width, the mean photon flux detected along a particular projection line L
i
is given by:
E[Y
i
]=∫I
i
(
E
)
e
−∫L
i
&mgr;(x,y,z,E)dl
dE
(1)
where the integral in the exponent is taken over the line L
i
and I
i
(E) incorporates the energy dependence of the incident ray and detector sensitivity. The goal of any CT algorithm is to reconstruct the attenuation map &mgr; from the measured data [Y
1
, . . . , Y
N
] where N is the number of rays measured.
Filtered Back Projection
Filtered back projection (FBP) is the standard reconstruction technique for X-ray CT. It is an analytic technique based on the Fourier slice theorem.
Use of the FFT in the filtering step of FBP renders the algorithm quite fast. Moreover, its properties are well understood. However, because it ignores the noise statistics of the data, it results in biased estimators. It also suffers from streak artifacts when imaging objects with metallic implants or other high-density structures.
Polyenergetic X-ray CT
In reality, the attenuation coefficient &mgr; is energy dependent and the X-ray beam is polyenergetic. Lower energy X-rays are preferentially attenuated.
FIG. 7
shows the energy dependence of the attenuation coefficients of water (density 1.0 gm/cm
3
) and bone (at density 1.92 gm/cm
3
). A hard X-ray beam is one with higher average energy. Beam hardening is a process whereby the average energy of the X-ray beam increases as the beam propagates through a material. This increase in average energy is a direct consequence of the energy dependence of the attenuation coefficient.
With a polyenergetic source, the expected detected photon flux along path L
i
is given by (1). If one were to ignore the energy dependence of the measurements and simply apply FBP to the log processed data, some attenuation map {circumflex over (&mgr;)} would be reconstructed that is indirectly related to the source spectrum and object attenuation properties.
Beam hardening leads to several disturbing artifacts in image reconstruction.
FIGS. 8 and 9
show the effect of beam hardening on the line integral in bone and water. In the monoenergetic case, the line integral increases linearly with thickness. With a polyenergetic beam, the soft tissue line integral departs slightly from the linear behavior. The effect is more pronounced for high Z (atomic number) tissue such as bone.
This non-linear behavior generally leads to a reduction in the attenuation coefficient. In bone, beam hardening can cause reductions of up to 10%. Thick bones also generate dark streaks. In soft tissue, the values are depressed in a non-uniform manner, leading to what has been termed the “cupping” effect. In addition, bone areas can “spill over” into soft tissue, leading to a perceived increase in the attenuation coefficient.
Beam Hardening Correction Methods
Because of SNR considerations, monoenergetic X-ray scanning is not practical. Beam hardening correction methods are therefore necessary for reconstructing artifact-free attenuation coefficient images. An ideal reconstruction method would be quantitatively accurate and portable to different scanning geometries. It would somehow reconstruct &mgr;(x,y,E), retaining the energy dependence of the attenuation process. This is difficult, if not impossible, to achieve with a single source spectrum. A more realistic goal is to remove or reduce the beam hardening artifacts by compensating for the energy dependence in the data.
There are a wide variety of schemes for beam hardening artifact reduction. Existing methods fall into three categories: dual-energy imaging, preprocessing of projection data and post-processing of the reconstructed image.
Dual-energy imaging has been described as the most theoretically elegant approach to eliminate beam hardening artifacts. The approach is based on expressing the spectral dependence of the attenuation coefficient as a linear combination of two basis function, scaled by constants independent of energy. The two basis functions are intended to model the photo-electric effect and Compton scattering. This technique provides complete energy dependence information for CT imaging. An attenuation coefficient image can, in principle, be presented at any energy, free from beam hardening artifacts. The method's major drawback is the requirement for two independent energy measurements. This has inhibited its use in clinical applications, despite the potential diagnostic benefit of energy information. Recently, some work has been presented on the use of multi-energy X-ray CT for imaging small animals. For that particular application, the CT scanner was custom built with an energy-selective detector arrangement.
Commercial beam hardening correction methods usually involve both pre-processing and post-processing, and are often implemented with a parallel or fan-beam geometry in mind. They also make the assumption that the object consists of soft tissue (water-like) and bone (high Z). Recently, these methods were generalized to three base materials and cone-beam geometry.
Pre-processing works well when the object consists of homogeneous soft tissue. Artifacts caused by high Z materials such as bo
Elbakri Idris A.
Fessler Jeffrey A.
Brooks & Kushman P.C.
Bruce David V.
The Regents of the University of Michigan
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