Only a Few Angles Tomography in Science and Technology

Back Ill-Posed Problems in a physical experiment

Presented design professor, Ph.D., Phylonin O.V. in the field of tomography for scientific applications

It describes the software packages for problems a few tomography diagnosis, including the processes of the full simulation of the process.

Only a few projections tomography diagnostics of plasma, plasma flows, streams of high gas

Application of methods and algorithms tomography to study the internal structure of objects (defectoscopy, introscopy)

Applications few-projection methods and algorithms for biomedical diagnostics

Algorithms and software packages developed in the laboratory of CT, focused on a plane geometry of the collection of baseline data, or a fan. Their schemes are presented in Figures.

Note that the study of plasma objects, we often have to deal with a fairly smooth, flowing plasma formations, they can model, relying on a priori information, for example, see the model package/

When tomographic diagnosis of plasma objects is very limited number of projections, from 2 to 6, rarely realize getting 12, 24 projections, but we note that the resulting projections are usually two-dimensional, in any case it is not hard to do, if not, for example, restrictions on performance when you have to apply the linear CCD structure, with special systems survey. The chart below shows the standard procedure for reconstruction of the parameters of physical objects used in the developed packages.

In contrast to the reconstruction of plasma objects, where the reconstructed functions are sufficiently; smooth and in some approximation can be approximated by continuous functions, and tomography diagnosis of solids we are dealing with a rather pronounced local inclusions - defects, mortgages, reinforcements, etc.

Therefore, in terms of tomography, it is necessary to use other methods of interpolation in the sense of calculating the intermediate times in the projections, and the calculation of the intermediate projections of themselves, and in some cases, required an unconventional way of getting the original projections, for example, multimalorakursny way to register.

In some cases it is appropriate to move in - Fourier space, interpolation procedures are simpler, such as the use of Chebyshev polynomials on circular harmonics, the selection of additional filters and stuff.

When reconstruction of few large role played by optimization algorithms used to go to the Fourier transform of the polar region in a Cartesian coordinate system corresponding to the illustration shown below:

Example of two-dimensional Fourier spectrum in polar coordinates.

Example of two-dimensional Fourier spectrum in Cartesian coordinates.

Conversion error in passing the CPM in the DSC.

 Tomography applications in medical diagnostics are some promising trends, combining traditional methods of obtaining background information, such as radiology, radiography, etc., with methods and algorithms for tomography reconstruction, including three-dimensional. Such an approach at low cost to get information much more high-end, compared with existing ones. Note that the classical tomography diagnosis, even where it is available may not always be offered for a particular patient, for there are a sufficient number of contraindications.

Only a few projections diagnosis, is essentially a hardware and software in addition to standard diagnostic systems and has a minuscule cost compared to classical imaging, usually, in practice for the implementation of few diagnosis requires a standard computer interface card, the system will collect baseline data is either the electromechanical scanner for X-rays or CCD - detector, see other pages on your site.

Software packages designed for the reconstruction of biomedical objects are more narrowly focused in terms of selection of reconstruction algorithms, such as for the detection and localization of tumors was quite effective RFP \u0026quot;Tomography\u0026quot;. Here the reconstruction is \u0026quot;direct\u0026quot; convolution, the calculation of intermediate times are projected to calculation of additional projections in the space of signals, as input, standard X-ray images obtained in the approximation of plane parallel geometry.

Another equally important factor in our view is the use of cluster methods of information processing in networks, so developing a package written in C + + based on the use of the operating system UNIX.

Effective is the use of tomography in dentistry, not only for determining the shape of channels in treatment, fillings, etc., but to determine the shape of the periosteum for the precise manufacture of implants. Note that in some cases, if possible should be used longitudinal tomograms obtained for example by NMR tomography, with which constructed three-dimensional image jaw, which greatly simplifies the manufacture of overhead of the implant, the patient in this case is only one operation. This package is currently under development and debugging.

Example of calculating the intermediate times at various ways of interpolation can be seen here, used cubic splines, calculated as the mean and variance. Example of reconstruction of impurity transport in tokamak plasma produced by TOMOS RFP is shown below.

The following figure shows the radial distribution of impurity

Below provides 2D tomogram flow at the nozzle exit high gas turbojet engine rebuilt with the help of the RFP FIERS;

 To pre-simulation and analysis of reconstruction algorithms for fault detection and imaging problems may be appropriate to use the package programs CT

Examples of reconstruction of the structure of composite materials are shown in the figures below, we used convolution algorithms with additional filtering and calculating projections – IFR STUCT;

Examples of reconstruction of the structure of composite materials are shown in the figures below, we used convolution algorithms with additional filtering and calculating projections - IFR STUCT;

Another section of the same sample

 Also developed tomography techniques that allow for 3 X-rays to reconstruct the configuration of the spine - which is very relevant today. Obtained some positive results suggest that that this technique would be workable. In the figure below shows the experimental stereo for the study of scoliosis.

The software package implements a given task TOMOSCAN; allows you to submit the investigated area of the object in a 3D model that is different from that shown in the figure and synthesized in the form of; axonometric; set of vertebrae strung; on-line calculated arcuate determining the ultimate degree of scoliosis, in the form of anaglyph stereo pair, ie as images of red and blue colors.