# On a problem of reconstruction of a discontinuous function by its Radon transform

## Abstract

A problem of reconstruction of a discontinuous function by its Radon transform is considered. One of the approaches to the numerical solution for the problem consists in the next sequential steps: a visualization of a set of breaking points; an identification of this set; a determination of jump values; an elimination of discontinuities. We consider three of listed problems except the problem of jump values. The problems are investigated by mathematical modeling using numerical experiments. The results of simulation are satisfactory and allow to hope for the further development of the approach.

- Authors:

- Sobolev Institute of Mathematics of SB RAS, 630090, Novosibirsk (Russian Federation)
- (Russian Federation)
- H. A. Yassawe International Kazakh-Turkish University, 161200, Turkestan (Kazakhstan)

- Publication Date:

- OSTI Identifier:
- 22608258

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1759; Journal Issue: 1; Conference: ICAAM 2016: International conference on analysis and applied mathematics, Almaty (Kazakhstan), 7-10 Sep 2016; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; DATA; FUNCTIONS; MATHEMATICAL MODELS; NUMERICAL SOLUTION; SIMULATION

### Citation Formats

```
Derevtsov, Evgeny Yu., Maltseva, Svetlana V., Svetov, Ivan E., Novosibirsk State University, 630090, Novosibirsk, and Sultanov, Murat A..
```*On a problem of reconstruction of a discontinuous function by its Radon transform*. United States: N. p., 2016.
Web. doi:10.1063/1.4959633.

```
Derevtsov, Evgeny Yu., Maltseva, Svetlana V., Svetov, Ivan E., Novosibirsk State University, 630090, Novosibirsk, & Sultanov, Murat A..
```*On a problem of reconstruction of a discontinuous function by its Radon transform*. United States. doi:10.1063/1.4959633.

```
Derevtsov, Evgeny Yu., Maltseva, Svetlana V., Svetov, Ivan E., Novosibirsk State University, 630090, Novosibirsk, and Sultanov, Murat A.. Wed .
"On a problem of reconstruction of a discontinuous function by its Radon transform". United States.
doi:10.1063/1.4959633.
```

```
@article{osti_22608258,
```

title = {On a problem of reconstruction of a discontinuous function by its Radon transform},

author = {Derevtsov, Evgeny Yu. and Maltseva, Svetlana V. and Svetov, Ivan E. and Novosibirsk State University, 630090, Novosibirsk and Sultanov, Murat A.},

abstractNote = {A problem of reconstruction of a discontinuous function by its Radon transform is considered. One of the approaches to the numerical solution for the problem consists in the next sequential steps: a visualization of a set of breaking points; an identification of this set; a determination of jump values; an elimination of discontinuities. We consider three of listed problems except the problem of jump values. The problems are investigated by mathematical modeling using numerical experiments. The results of simulation are satisfactory and allow to hope for the further development of the approach.},

doi = {10.1063/1.4959633},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1759,

place = {United States},

year = {Wed Aug 10 00:00:00 EDT 2016},

month = {Wed Aug 10 00:00:00 EDT 2016}

}

DOI: 10.1063/1.4959633

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