Learning Model in Relaxation Algorithm Influenced by Self-Organizing Maps for Image Restoration

This paper presents a learning model in relaxation algorithm influenced by self-organizing maps for reducing random-valued impulse noise. Self-organizing maps have been hitherto studied for the ordering process and the convergence phase of weight vectors. As a novel approach of self-organizing maps, a learning model in relaxation algorithm for image restoration is proposed, which creates a map containing one unit for each pixel. Utilizing pixel values as input, image inference is conducted by self-organizing maps. Then, an updating function with threshold according to the difference between input value and inferred value is introduced, so as not to respond to noisy input sensitively. Therefore the inference of an original image proceeds appropriately since any pixel is influenced by neighboring pixels corresponding to the neighboring setting. The characteristic of our approach includes the network constructing the same number of both inputs and weights for inferring the original image from a degraded image in sequential processing, unlike the distinct number in which self-organizing maps have applied to conventional techniques for the ordering and the convergence of weight vectors. In the inference process, the effect of initial threshold and initial neighborhood on accuracy is examined. Experimental results are presented in order to show that our approach is effective in quality for image restoration. Copyright © 2008 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

[1]  Richard Durbin,et al.  An analogue approach to the travelling salesman problem using an elastic net method , 1987, Nature.

[2]  H. Ritter,et al.  Convergence properties of Kohonen's topology conserving maps: fluctuations, stability, and dimension selection , 1988, Biological Cybernetics.

[3]  Erik Berglund,et al.  The parameterless self-organizing map algorithm , 2006, IEEE Transactions on Neural Networks.

[4]  Thomas Villmann,et al.  Topology preservation in self-organizing feature maps: exact definition and measurement , 1997, IEEE Trans. Neural Networks.

[5]  Dong-Chul Park,et al.  Weighted centroid neural network for edge preserving image compression , 2001, IEEE Trans. Neural Networks.

[6]  Noritaka Shigei,et al.  Adaptive Vector Quantization with Creation and Reduction Grounded in the Equinumber Principle , 2005, J. Adv. Comput. Intell. Intell. Informatics.

[7]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

[8]  Klaus Pawelzik,et al.  Quantifying the neighborhood preservation of self-organizing feature maps , 1992, IEEE Trans. Neural Networks.

[9]  S. Grossberg,et al.  Adaptive pattern classification and universal recoding: I. Parallel development and coding of neural feature detectors , 1976, Biological Cybernetics.

[10]  Thomas Martinetz,et al.  Topology representing networks , 1994, Neural Networks.

[11]  Tommy W. S. Chow,et al.  Self-Organizing and Self-Evolving Neurons: A New Neural Network for Optimization , 2007, IEEE Transactions on Neural Networks.

[12]  K. Schulten,et al.  On the stationary state of Kohonen's self-organizing sensory mapping , 2004, Biological Cybernetics.

[13]  Yu Sun,et al.  Two image restoration algorithms using variational PDE based neural network , 2007, IWCMC.

[14]  Bernard Angéniol,et al.  Self-organizing feature maps and the travelling salesman problem , 1988, Neural Networks.

[15]  Michiharu Maeda.  A Relaxation Algorithm Influenced by Self-Organizing Maps , 2003, ICANN.

[16]  Chen Hu,et al.  An iterative procedure for removing random-valued impulse noise , 2004, IEEE Signal Processing Letters.

[17]  C. Malsburg,et al.  How patterned neural connections can be set up by self-organization , 1976, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[18]  Thomas Martinetz,et al.  'Neural-gas' network for vector quantization and its application to time-series prediction , 1993, IEEE Trans. Neural Networks.

[19]  Hisashi Tamaki,et al.  Skin Image Segmentation Using a Self-Organizing Map and Genetic Algorithms , 2003 .

[20]  L. Reichl.  A modern course in statistical physics , 1980 .

[21]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.