Cone-beam

In Dynamic Spatial Reconstructor at the expense of use 2D matrix of detectors there was the opportunity to use a divergent cone beam of source emission. This system had a number of lacks. In particular the number of projections is rigidly limited by the number of x-ray sources. The dispersion of source emission results in errors of data collected.. However the system confirmed basic advantages of application of conic beams and 2D matrices of detectors for collecting information about 3D object. 

The systems of such type have been developed of all last 10 years. We shall bring some characteristics of one of the last development within the framework of European BRITE project, carried out in LETT This 3D cone-beam tomograph is referred to as EVA Bench or Equipment for Voludensimetry Analysis. It is oriented on NDT of industrial products from ceramics and other composites. One of the main task of this tomograph is achievement of high resolution at study of whole internal volume of researched object. For test sample of the size 10mm spatial resolution in 50mm was obtained [14]. 

Thus, the systems with cone beam and 2D detector have number of the important advantages ... 

For the maximum use of advantages of a cone beam at collecting of data, it is necessary to study and develop effective algorithms of reconstmction for cone-beam projection data. The theory of reconstruction in cone beams is referred to as cone-beam tomography. It had developments in papers of many researchers. ... 

The analysis of a plenty of references shows applicability for creating tomographs of a method of slice by slice scatming and method of the simultaneous collecting of data by cone beam. The second method has many advantages. 

The practical implementation of cone-beam systems requires a choice of scanning geometry and of a reconstruction method. The good answers to both these questions simultaneously can hardly be obtained. 

Finch D. Cone-beam reconstruction with sources on a curve., SIAM J. Appl. Math., V. 45(4), 1985,p.665-673. 

Grangeat P. Mathematical framework of cone beam three-dimensional reconstruction via the first derivative of the Radon transform.. Math. Methods in Tomography, V.1947 of Springer Lecturre Notes in Math-cs, Springer-Verlag, Berlin, 1991, p.66-97. 

LETI. 3D cone-beam X-ray Tomograph EVA ( Equipment for Volumedensitometry Analysis) Bench, 1996. 

Peyrin F. The generalized backprojection theorem for cone-beam reconstruction., IEEE Trans. Nucl. Sci., V. NS-32, 1985, p.1512-1519. 

Smith B.D. Image reconstruction from cone-beam projections necessary and sufficient conditions and reconstruction methods., IEEE Trans. Med. Imaging, V. 4, 1985, p. 14-28. 

In traditional Fan-Beam CT the radiation emitted from the X-ray tube is collimated to a planar fan, and so most of the intensity is wasted in the collimator blades (Fig. 2a). Cone-Beam CT, where the X-rays not only diverge in the horizontal, but also in the vertical direction, allows to use nearly the whole emitted beam-profile and so makes best use of the available LINAC photon flux (Fig. 2b). So fast scanning of the samples three-dimensional structure is possible. For Cone-Beam 3D-reconstruction special algorithms, taking in consideration the vertical beam divergence of the rays, were developed. 

The main disadvantage of Feldkamp s approaeh is the fact, that it is mathematically correct only in tire midplane of the beam. With larger Cone-Beam angles the error grows and over 30 degrees severe artefacts can be observed In the reconstruction. 

Another efficient and practical method for exact 3D-reconstruction is the Grangeat algorithm [11]. First the derivative of the three-dimensional Radon transfomi is computed from the Cone-Beam projections. Afterwards the 3D-Object is reconstructed from the derivative of the Radon transform. At present time this method is not available for spiral orbits, instead two perpendicular circular trajectories are suitable to meet the above sufficiency condition. 

L.A. Feldkamp, L.C. Davis, J.W. Kress Practical Cone-Beam Algorithm... 

Fourier Methods in 3D-Reconstruction from Cone-Beam Data... 

Reconstruction in Spiral Cone-Beam CT at small Cone-Angles... 

The GAMMASCAN 1500 HR is a combined system for two-dimensional (2D-CT) and three-dimensional (3D-CT) computed tomography, as well as digital radiography (DR). The system is equipped with two separate detector systems for the fan-beam and cone-beam CT. The sire of the objects is limited to a height of four meters, maximum diameters of 1.5 meters and a weight of up to 15 tons. The turntable which carries the test samples can be moved along and across the beam direction ( X- and Y- direction). The radiation source and the detector systems can be moved in Z- direction, both, simultaneously and independently. 

Therefore it is reasonable to prepare already the data acquisition for a three dimensional evaluation in cone-beam-technique by means of two-dimensional detectors. The system is already prepared to integrate a second detector- system for this purpose. An array of up to four flat panel detectors is foreseen. The detector- elements are based on amorphous silicon. Because of the high photon energy and the high dose rates special attention was necessary to protect the read-out electronics. Details of the detector arrangement and the software for reconstruction, visualisation and comparison between the CT results and CAD data are part of a separate paper during this conference [2]. 

Multi-row detector systems are referred to as cone-beam systems. With a moving conveyor they become helical cone-beam systems. The cone-beam designation is in contrast to the fan-beam geometry used in Figures 3 and 4, where the source and detectors are aU in a single plane. 

Figure 6 A multi-row detector array is used in a cone-beam system. In this case, the detector rows fall along circular arcs centered on the X-ray source s x, y coordinate values. Detectors of equal size therefore subtend equal angles with respect to the source. This characteristic and other system and data-analysis considerations often make curved detector rows more attractive than straight ones like those of Figures 3 and 4.

The last twenty years have seen the introduction of novel XDI geometries based on pencil beams [4], cone beams [5], fan beams [6], parallel sheet beams [7] and inverse fan beams [6], These are all, indeed, special cases of a general 3-D arrangement synthesized from a generic 2-D section [6],... 

Fig. 4. Direct tomographic, energy-dispersive X-ray diffraction imaging system. Suitcase enters device at left of Figure where spatial landmarks for registration purposes are measured by pre-scanner. In main housing centre-right of Figure, a primary cone-beam executes a meander scan, either of a region-of-interest or suitcase in its entirety. Illustration courtesy of GE Security, Germany.

It is beyond the scope of this chapter to discuss filtered back-projection (FBP) reconstruction procedures or their 3-D extensions to cone-beam CT for which reference should be made to other works [39],... 

Here A is the average wavelength of the used radiation. The reconstruction algorithm is based on FBP. Filtering is carried out in the same manner as in 3-D (cone-beam) transmission CT, and back-projection is performed along curved trajectories. Details of the FBP algorithm can be found elsewhere [40],... 

Fig. 13.1. Forty-five-year-old female presents for evaluation of left lump. Precontrast (left) and postcontrast (right) sagittal cone beam CT (Koning Corporation,...

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