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

A. Cichocki, R. Unbehauen, M. Lendl, K. Weinzierl

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

In this paper a generalized minimum norm principle and/or a maximum entropy principle are used as general criteria, e.g. for reconstructing images or signals from noisy and incomplete projection data. The linear inverse problem is reformulated as an optimization problem and solved by a unified analog neural network. Moreover, in order to reduce the network complexity a new approach is proposed which makes it possible to construct simply and effectively a neural network containing only one single artificial neuron with an on chip adaptive learning algorithm. The correctness and performance of the proposed neural network architectures are illustrated by extensive computer simulation experiments.

Original languageEnglish
Pages (from-to)7-41
Number of pages35
JournalNeurocomputing
Volume8
Issue number1
DOIs
Publication statusPublished - May 1995
Externally publishedYes

Keywords

  • Hopfield recurrent neural networks
  • Inverse problems
  • Maximum entropy
  • Minimum L-norm criteria
  • Optimization
  • Real-time neurocomputing

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