Cone-beam algorithm

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

The system is ideal for examining the rearrangement of microstractural composition of soft-solid materials with variation in temperature. An example of a material that is practically impossible to image in the natural state by conventional optical microscopy is shown in (Fig. 26.58a). The volumes depicted are child volumes, containing a region of interest (ROl), extracted fipom the reconstruction of a frozen four-phase soft-solid structure. The reconstructed volume is derived from 720 filtered and back-project frames using the Feldkamp cone-beam algorithm, with a resolution of 512 X 512 pixels per frame. 

Feldkamp LA, Davis LC, Kress JW (1984) Practical cone-beam algorithm. J Opt Soc Am A 612-619... 

Micro-CT imaging not only allows study of lung anatomy down to the alveolar level, but also it provides a testing ground for improved cone-beam algorithms which can then be translated up to future clinical scanners. Micro-CT imaging has seen a rapid transition from one-of-a-kind laboratory instruments to commercially developed systems which have moved from use in the study of high contrast static structures (such as postmortem specimens of bone) towards... 

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. ... 

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. 

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. 

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],... 

To apply these relations in practice the cone beam reconstruction algorithm would involve the following arithmetic operations. 

The scanning schemes that have been adapted to the above principle may involve the spiral/ helical motion that requires lateral displacement with rotation. Extensions of the Feldkamp algorithm, for quite general three-dimensional scaiming loci, have been developed by Wang et al. For further discussions on the approximate and accurate cone-beam reconstruction the reader is referred to Ref. 17. 

Ning R, Tang X, Conover DL (2002) X-ray scatter suppression algorithm for cone-beam volume CT. In Medical Imaging 2002 Physics of Medical Imaging. San Diego, CA, pp 774-781... 

From a mathematical point of view, 1 and 2 enforce approximate reconstruction techniques. The standard approach for this type of cone-beam tomography is the so-called Feldkamp algorithm. 

Tang X, Ning R, Yu R, Conover D. Cone beam volume CT image artifacts caused by defective cells in X-ray flat panel imagers and the artifact removal using a wavelet-analysis-based algorithm. Med Phys 2001 28(5) 812-825. 

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