Image analysis – Applications – Biomedical applications
Reexamination Certificate
1998-12-07
2002-08-27
Boudreau, Leo (Department: 2621)
Image analysis
Applications
Biomedical applications
C382S100000
Reexamination Certificate
active
06442288
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to a method for reconstructing a three-dimensional image of an object or a subject scanned, preferably in linear or circular fashion, in the context of a tomosyntheisis procedure of the type wherein during the scanning, several individual projection images located in a 2D projection image space are recorded in the form of digital projection image data of the object located in a 3D object space, and are back-projected into a 3D reconstruction image volume in order to produce the reconstruction image, the object being irradiated with X-rays from various projection angles &phgr; for the purpose of recording the projection images, and wherein the radiation exiting from the object is recorded using a detector that supplies digital output image signals, the output image signals representing the projection image data and being supplied to a computer for image reconstruction.
2. Description of the Prior Art
In medical imaging systems, it is known to record an object tomosynthetically and to reconstruct it three-dimensionally. Since in the tomosynthetic data recording the object to be imaged are projected onto a detector from only a few spatial directions, the object scanning is incomplete. This is expressed in a poor depth resolution of the 3D reconstruction. In a simple back-projection (identical to the summation of displaced projection images, classical slice method), without reconstructive corrections locus-frequency-dependent artefacts are contained in the tomograms. Given larger objects, these disturbances can be very extensive.
The following demands are placed on a good 3D reconstruction: best possible suppression of structures foreign to the slice, defined slice behavior or characteristic, i.e. depth resolution independent of locus frequency, purposive controlling of the characteristics of the reconstructed tomogram.
In system-theoretical terms, the tomosynthetic imaging of an object distribution f(x, y, z) to form a 3D reconstruction image g(x, y, z) can be formulated as a convolution (indicated, as is standard, by the symbol *) of the object distribution with the point image function h(x, y, z) of the imaging process:
g
(
x, y, z
)=
h
(
x, y, z
)*
f
(
x, y, z
)
The point image function h(x, y, z) describes both the “measurement process” (projection and back-projection) and also reconstructive measures, such as e.g. filterings. In the 3D Fourier space, the Fourier-transformed image G(&ohgr;
x
,&ohgr;
y
,&ohgr;
z
) is described by a multiplication of the Fourier-transformed object distribution F(&ohgr;
x
,&ohgr;
y
,&ohgr;
z
) with the 3D transmission function (or Modulation Transfer Function MTF) H(&ohgr;
x
,&ohgr;
y
,&ohgr;
z
):
G
(&ohgr;
x
,&ohgr;
y
,&ohgr;
z
)=
H
(&ohgr;
x
,&ohgr;
y
,&ohgr;
z
)·
F
(&ohgr;
x
,&ohgr;
y
,&ohgr;
z
)
with F(&ohgr;
x
,&ohgr;
y
,&ohgr;
z
) as the 3D Fourier transformation of the locus distribution f(x, y, z)
F
(&ohgr;
x
,&ohgr;
y
,&ohgr;
z
)=
F
z
F
y
F
x
f
(
x, y, z
)
and analogously for the image g(x, y, z) and the point image function h(x, y, z). By modification of the point image function h(x, y, z) or of the Modulation Transfer Function H(&ohgr;
x
,&ohgr;
y
,&ohgr;
z
) the imaging process can be purposively influenced.
The image quality of a reconstructed tomogram can be judged using the slice transmission function h(&ohgr;
x
,&ohgr;
y
|z) [D. G. Grant, TOMOSYNTHESIS: A Three-Dimensional Radiographic Imaging Technique, IEEE Trans. on Biomed. Eng. 19 (1972), 20-28].
h
(&ohgr;
x
,&ohgr;
y
|z
)=
F
z
−1
H
(&ohgr;
x
,&ohgr;
y
,&ohgr;
z
)
The slice transmission function h(&ohgr;
x
,&ohgr;
y
|z) is a hybrid of a representation in the Fourier space and in the locus space. It indicates the spectral content (frequency response) with which objects at a distance z from the reconstruction plane contribute to the reconstruction image. For z=0, it indicates the spectral content of the slice to be reconstructed, and for small z it indicates the screen characteristic of a reconstruction slice of finite thickness, and for large z, specifically in tomosynthesis, it indicates the locus-frequency-dependent feed-through of artefacts. The desired image characteristics (see above) can be formulated as follows using the slice transmission function.
A good suppression of structures foreign to the slice signifies a rapid decay of the slice transmission function h(&ohgr;
x
,&ohgr;
y
|z) into z.
Defined slice behavior, i.e. a slice profile independent of the locus frequency, is achieved by a separation of the slice transmission function h(&ohgr;
x
,&ohgr;
y
|z) into a portion H
spectrum
(&ohgr;
x
,&ohgr;
y
), which represents the spectral image content of the reconstructed tomogram, and into a portion h
profile
(z) that defines the slice profile. A complete separation is in general not possible in tomosynthesis, since as the locus frequencies decrease the scanning becomes increasingly incomplete. It is already a considerable advantage, however, if a separation is achieved for a limited locus frequency region:
h
(&ohgr;
x
,&ohgr;
y
|z
)=
H
spectrum
(&ohgr;
x
,&ohgr;
y
)·
h
profile
(
z
)
In the literature, essentially the following methods of reconstruction in tomosynthesis are found:
Simple back-projection: [D. G. Grant, TOMOSYNTHESIS: A Three-Dimensional Radiographic Imaging Technique, IEEE Trans. on Biomed. Eng. 19 (1972), 20-28]: As in the classical slice method, by simple summation of the projection images an uncorrected reconstruction image is obtained. The method is rapid, simple and robust, but yields poor image results. Simple heuristic 2D filterings of the reconstructed tomograms [R. A. J. Groenhuis, R. L. Webber and U. E. Ruttimann, Computerized Tomosynthesis of Dental Tissues, Oral Surg. 56 (1983), 206-214] improve the image impression, but do not provide image material that can be reliably interpreted, and are thus not satisfactory.
Influencing of the recording geometry: By the selection of the sampling curve, such as e.g. spirals or threefold concentric circular scanning [U. E. Ruttimann, X. Qi and R. L. Webber, An Optimal Synthetic Aperture for Circular Tomosynthesis, Med. Phys. 16 (1989), 398-405], the point image function can be manipulated. The methods require a high mechanical outlay and are inflexible, since the image corrections are already determined with the measurement data. In addition, only slight image improvements have been achieved.
Iterative methods: [U. E. Ruttimann, R. A. J. Groenhuis and R. L. Webber, Restoration of Digital Multiplane Tomosynthesis by a Constrained Iteration Method, IEEE Trans. on Medical Imaging 3 (1984), 141-148]. With the aid of an iterative reconstruction, in principle the measurement process can be flexibly modeled and corrected by approximation. The iterative method attempts to invert the point image function. Since this is not possible, due to the incomplete scanning, secondary conditions must be introduced in order to guarantee the unambiguity of the solution. The methods achieve good image quality, but are not obvious and are difficult to use. In particular, the required introduction of secondary conditions can strongly falsify the image impression in an undesired manner. In addition, there are problems with the stability of the algorithms, and the computing time is prohibitive for a routine application.
Algebraic methods: For a set of tomograms, the point image function is set up slice-by-slice, which leads to a matrix formulation of the point image function. The exact inversion of the matrix is not possible, due to the incomplete scanning in the tomosynthesis. [J. T. Dobbins, Matrix Inversion Tomosynthesis Improvements in Longitudinal X-Ray Slice Imaging, U.S. Pat. No. 4,903,204, Feb. 20, 1990] falsely claims invertibility. This method, however, uses multiple subsequent corrections of the reconstruction images, which underlines the inadequacy of his approach. No publication of the ima
Haerer Wolfgang
Lauritsch Guenter
Zellerhoff Michael
Boudreau Leo
Choobin M B
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