Filtered back-projection algorithm

The images are shown in Fig. 6 al to a3. The device weighs 110 g and hence is portable. The images obtained are reconstructed by filtered back projection algorithm. The device is such that it can be connected to a computer in which the image processing can be performed. This can also thus be extremely crucial in telemedicine [3]. 

While the Fourier slice theorem implies that given a sufficient number of projections, an estimate of the two-dimensional transform of the object could be assembled and by inversion an estimate of the object obtained, this simple conceptual model of tomography is not implemented in practice. The approach that is usually adopted for straight ray tomography is that known as the filtered back-projection algorithm. This method has the advantage that the reconstruction can be started as soon as the first projection has been taken. Also, if numerical interpolation is necessary to compute the contribution of each projection to an image point, it is usually more accinate to conduct this in physical space rather than in frequency space. 

One can then use the classical algorithm of tomographic reconstruction by summation of filtered back-projections ... 

A. Katsevich, Exact Filtered Back Projection (FPB) Algorithm for Spiral Computer Tomography, US Patent 6,574,277 (2003). 

U van Stevendaal, J-P Schlomka, A Harding and M Grass (2003) A reconstruction algorithm for coherent scatter CT based on filtered back-projection. Med. Phys. 30, 2465-2474. 

One-dimensional images of toluic acid were obtained with a stationary sample. For two-dimensional images, the 4-bromobenzoic acid crystal was rotated about an axis orthogonal to the gradient direction in constant increments of either 3° or 6° over a range of 180° to collect sets of 60 or 30 one-dimensional projections, respectively. The two-dimensional images were calculated with the filtered back-projection reconstruction algorithm (36). 

The signals for the detected photons are reconstructed into an image using algorithms originally based on those used for X-ray tomography but which allowed for photon attenuation and Compton scattering. A typical method would be the filtered back-projection approach. 

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],... 

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. 

---