Reconstruction methods

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. 

It seems to be expidiently to develop new scanning geometries, which combining with exact reconstruction methods provide high quality of 3D tomographic images. 

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. 

Figure Bl.17.10. Principles of 3D reconstruction methods, (a) Principle of single axis tomography a particle is projected from different angles to record correspondmg images (left panel) this is most easily realized in the case of a helical complex (right panel), (b) Principle of data processing and data merging to obtain a complete 3D structure from a set of projections.

Introduction of heme residues and different artificial receptors in protein molecules in chemical modification of structures and functions of proteins by the cofactor reconstruction method 99Ef0539. 

Figure 1 shows the simulation of a galaxy observed with a PSF which is typical of an adaptive optics system. The noisy blurred image in Fig. 1 will be used to compare various image reconstruction methods described in this course. 

Vosegaard and Massiot [144] showed that it is possible to create a high-resolution 2D spectrum correlating the chemical shifts with the second-order quadrupolar lineshapes from several spectra recorded at different magnetic field strengths using a projection-reconstruction method called chemical shift-quadrupolar projection-reconstruction of one-dimensional spectra (CQ-PRODI). 

Hein, J. (1989). A tree reconstruction method that simultaneously aligns and reconstructs ancestral sequences for any number of homologous sequences, when the phylogeny is given. Mol. Biol. Evol. 6, 649-668. 

An inert nitrogen atmosphere is required during the reconstruction process when a non-carbonate anion is incorporated by rehydration because the carbonate LDH generally forms preferentially in the presence of atmospheric CO2. The reconstruction method fails to give LDH materials if an anion such as tartrate, which has a strong tendency to complex metal cations, is used [142]. 

The 3D reconstruction method was also applied to solve the 3D structures of a series mesoporous materials (Kenedaeta/. 2002). 

The projected potential can be reconstructed. This reconstruction method is demonstrated in Fig. 10 on HREM images of K20-7Nb205. This method is especially powerful for crystals with high symmetries. 

Here the principles of constructing a 3D structure model from several HREM images of projections of inorganic crystals will be presented. Some of the principles may also be applied to non-periodic objects. A complex quasicrystal approximant v-AlCrFe is used as an example (Zou et al., 2003). Procedures for ab initio structure determination by 3D reconstruction are described in detail. The software CRISP, ELD. Triple and 3D-Map are used for 3D reconstruction. The 3D reconstruction method was demonstrated on the silicate mineral (Wenk et al. 1992). It was also applied to solve the 3D structures of a series mesoporous materials (Keneda etal. 2002). 

Thus Fourier transformation of J q) along a single direction yields B(r) along a single direction. This recognition is the basis of the Fourier reconstruction method [145,146] for II( p). 

Application of these reconstruction methods can be described as the interpolation of object composition between sample points by means of an exponential function, characterised by the correlation constant. 

Using advances in computer reconstruction methods (see e.g. Kikkinides and Burganos, 2000 Torquato, 2001) and past experience with discrete particle deposit simulations (Konstandopoulos, 2000), we have developed algorithmic as well as process-based reconstruction techniques to generate three-dimensional (3D) digital materials that are faithful representations of DPF microstructures. We refer to this approach as DPF microflow simulation (MicroFlowS). MicroFlowS is thus a short name for a computational approach, which combines... 

The mesoscopic modeling approach consists of a stochastic reconstruction method for the generation of the CL and GDL microstructures, and a two-phase lattice Boltzmann method for studying liquid water transport and flooding phenomena in the reconstructed microstructures. 

The stochastic reconstruction method is based on the idea that an arbitrarily complex porous structure can be described by a binary phase function which assumes a value 0 in the pore space and 1 in the solid matrix29 The intrinsic randomness of the phase function can be adequately qualified by the low order statistical moments, namely porosity and two-point autocorrelation function.29 The porosity is the probability that a voxel is in the pore space. The two-point autocorrelation function is the probability that two... 

When we speak of mathematical models for biology, we usually refer to formulae (such as the Hardy-Weinberg theorem, or the Lotka-Volterra equations) that effectively describe some features of living systems. In our case, embryonic development is not described by integrals and deconvolutions, and the formulae of the reconstruction algorithms cannot be a direct description of what happens in embryos. There is however another type of mathematical model. The formulae of energy, entropy and information, for example, apply to all natural processes, irrespective of their mechanisms, and at this more general level there could indeed be a link between reconstruction methods and embryonic development. For our purposes, in fact, what really matters are not the formulae per se, but... 

The Memory Reconstruction Method, in conclusion, gives us two general principles that must be valid for all systems which increase their own complexity, and embryos are such systems. The MRM model predicts therefore the existence of biological structures which are equivalent to reconstruction codes and to memory matrices. More precisely, the model leads to the conclusion that in embryos there must be codes and memories which are made of organic molecules, i.e. organic codes and organic memories. At this point, therefore, we can go back to biology and look for the existence of such structures in real life. 

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