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1

Linear over ranges iterative algorithms for image reconstruction in electrical capacitance tomography

Smolik W. T., Kryszyn J.

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2017

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T. 7, nr 1

115--120

EN

The paper concerns the non-linear algorithms for image reconstruction in electrical capacitance tomography for which Jacobi matrix computation time is very long. The paper presents the idea of an iterative linearization in nonlinear problems, which leads to a reduction in the number of steps calculating Jacobi matrix. The linear Landweber algorithm with sensitivity matrix updating and non-linear Levenberg-Marquardt algorithm with Jacobi matrix updating in selected steps only were presented.

PL

Artykuł dotyczy nieliniowych algorytmów rekonstrukcji obrazów w elektrycznej tomografii pojemnościowej, dla których czas wyznaczenia macierzy Jacobiego jest bardzo długi. W pracy przedstawiono ideę iteracyjnej linearyzacji w problemach nieliniowych, która prowadzi do zmniejszenia liczby kroków wyznaczających macierz Jacobiego. Przedstawiono liniowy algorytm Landwebera z uaktualnianiem macierzy wrażliwości oraz algorytm Levenberga-Marquardta z wyznaczaniem macierzy Jacobiego tylko w wybranych krokach.

2

An analytical iterative statistical algorithm for image reconstruction from projections

Cierniak R.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 1

7--17

EN

The main purpose of the paper is to present a statistical model-based iterative approach to the problem of image reconstruction from projections. This originally formulated reconstruction algorithm is based on a maximum likelihood method with an objective adjusted to the probability distribution of measured signals obtained from an x-ray computed tomograph with parallel beam geometry. Various forms of objectives are tested. Experimental results show that an objective that is exactly tailored statistically yields the best results, and that the proposed reconstruction algorithm reconstructs an image with better quality than a conventional algorithm with convolution and back-projection.

3

A neural network method of image reconstruction from projections using grid-"friendly" projection angles

Cierniak R.

Image Processing & Communications

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2009

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Vol. 14, no 2-3

51-58

EN

In this paper an original approach to the reconstruction problem using a recurrent neural network is presented. In our method parallel beam projections is used. To decrease the number of desired projections the grid "friendly" angles of the parallel projections are selected according to the discrete Radon transform (DRT). Performed computer simulations show that the presented neural network reconstruction algorithm outperforms the convolution/back-projection method in the reconstructed image quality.

4

A new approach to image reconstruction from projections using a recurrent neural network

Cierniak R.

International Journal of Applied Mathematics and Computer Science

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2008

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Vol. 18, no 2

147-157

EN

A new neural network approach to image reconstruction from projections considering the parallel geometry of the scanner is presented. To solve this key problem in computed tomography, a special recurrent neural network is proposed. The reconstruction process is performed during the minimization of the energy function in this network. The performed computer simulations show that the neural network reconstruction algorithm designed to work in this way outperforms conventional methods in the obtained image quality.