Feldkamp algorithm

An extension of these metliods to 3D is the Feldkamp algorithm [7], a standard in 3D-tomographic reeonstruction today. In this case off-midplane voxels are taken into eonsideration through weighted filtered 3D-baekprojection. llie weighting compensates for the longer way an oblique ray has to travel. 

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. 

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. 

Using the theorem that the sufficiency condition for mathematical correctness in 3D-reconstruction is fulfilled if all planes intersecting the object have to intersect the source-trajectory at least in one point [8], it is possible to generalise Feldkamp s method. Using projection data measured after changing the sotuce-trajectory from circular to spiral focus orbit it is possible to reconstruct the sample volume in a better way with the Wang algorithm [9]. 

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

The reconstruction algorithms to be used for conventional sources are substantially different from the codes described in the previous section, due to the different acquisition geometry related to the conical shape of the beam (Burch and Lawrence, 1992 Feldkamp et al., 1984). 

Feldkamp C, Carey J. An algorithmic approach to thyroid function testing in a managed care setting ... 

Algorithms that are based upon the Feldkamp principles have found favor in practice because of their good image quality and fast computational speed. However, the circular path that the source... 

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... 

In 1984, Feldkamp et al. (1984) suggested a 3D reconstruction algorithm that has become the de-facto standard for 3D C-arm imaging. Originally designed... 

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