Neural networks for linear inverse problems with incomplete data especially in applications to signal and image reconstruction

Cichocki, Andrzej; Unbehauen, R.; Lendl, Markus; Weinzierl, К.

doi:10.1016/0925-2312(94)e0063-w

Cited by 19 publications

(5 citation statements)

References 21 publications

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“…(ANN) based methods [186], principle component analysis [187] or its derivative independent component analysis [188], multivariate state estimation technique [189], and support vector machines [190].…”

Section: Validation Issuesmentioning

confidence: 99%

Designing a reliable leak bio-detection system for natural gas pipelines

Batzias

Siontorou

Spanidis³

2011

Journal of Hazardous Materials

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Section: Validation Issuesmentioning

confidence: 99%

Designing a reliable leak bio-detection system for natural gas pipelines

Batzias

Siontorou

Spanidis³

2011

Journal of Hazardous Materials

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“…The recursive neural network structure for 1D signal reconstruction was proposed for the first time in [ 23 ] and later in [ 15 , 24 ]. The network realizes the image reconstruction from projections by the deconvolution of relationship ( 22 ).…”

Section: Neural Network Reconstruction Algorithmmentioning

confidence: 99%

“…Reconstruction algorithms based on supervised neural networks have been presented in various papers, for example [ 11 – 14 ]. Other structures representing the so-called algebraic approach to image reconstruction from projections and based on recurrent neural networks have been studied by several authors [ 15 – 17 ]. Their approach can be characterized as a unidimensional signal reconstruction problem.…”

Section: Introductionmentioning

confidence: 99%

Neural network algorithm for image reconstruction using the “grid-friendly” projections

Cierniak

2011

Australas Phys Eng Sci Med

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The presented paper describes a development of original approach to the reconstruction problem using a recurrent neural network. Particularly, the “grid-friendly” angles of performed projections are selected according to the discrete Radon transform (DRT) concept to decrease the number of projections required. The methodology of our approach is consistent with analytical reconstruction algorithms. Reconstruction problem is reformulated in our approach to optimization problem. This problem is solved in present concept using method based on the maximum likelihood methodology. The reconstruction algorithm proposed in this work is consequently adapted for more practical discrete fan beam projections. Computer simulation results show that the neural network reconstruction algorithm designed to work in this way improves obtained results and outperforms conventional methods in reconstructed image quality.

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“…The network studied in the paper resembles a Hopfield structure. Similar structures were proposed in (Cichocki et al, 1995;Ingman and Merlis, 1992;Luo and Unbehauen, 1998) to solve the 1D signal reconstruction problem. That idea will be adopted to the algorithm of image reconstruction from projections in 2D.…”

Section: Introductionmentioning

confidence: 97%

“…The recurrent neural network structure presented in Fig. 5 was proposed for the first time in (Cichocki et al, 1995;Ingman and Merlis, 1992;Luo and Unbehauen, 1998). The network performs image reconstruction from projection by the deconvolution of the relation (17).…”

Section: 32mentioning

confidence: 99%

A New Approach to Image Reconstruction from Projections Using a Recurrent Neural Network

Cierniak¹

2008

International Journal of Applied Mathematics and Computer Science

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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.

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Neural networks for linear inverse problems with incomplete data especially in applications to signal and image reconstruction

Cited by 19 publications

References 21 publications

Designing a reliable leak bio-detection system for natural gas pipelines

Designing a reliable leak bio-detection system for natural gas pipelines

Neural network algorithm for image reconstruction using the “grid-friendly” projections

A New Approach to Image Reconstruction from Projections Using a Recurrent Neural Network

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