We investigate a nonlinear technique for restoration of images distorted in color and space, using a class of extended radial basis function networks called the Gaussian mixture basis function networks (GMBFN). We report computer simulation results that indicate usefulness of this new approach.

We investigate a technique for image restoration using nonlinear networks based on radial basis functions. The technique is also based on the concept of training or learning by examples. When trained properly, these networks are used as spatially invariant feedforward nonlinear filters that can perform restoration of images degraded by nonlinear degradation mechanisms. We examine a number of network structures including the Gaussian radial basis function network (RBFN) and some extensions of it, as well as a number of training algorithms including the stochastic gradient (SG) algorithm that we have proposed earlier. We also propose a modified structure based on the Gaussian-mixture model and a learning algorithm for the modified network. Experimental results indicate that the radial basis function network and its extensions can be very useful in restoring images degraded by nonlinear distortion and noise.

It is generally recognized that digital channel equalization can be interpreted as a problem of nonlinear classification. Networks capable of approximating nonlinear mappings can be quite useful in such applications. The radial basis function network (RBFN) is one such network. We consider an extension of the RBFN for complex-valued signals (the complex RBFN or CRBFN). We also propose a stochastic-gradient (SG) training algorithm that adapts all free parameters of the network. We then consider the problem of equalization of complex nonlinear channels using the CRBFN as part of an equalizer. Results of simulations we have carried out show that the CRBFN with the SG algorithm can be quite effective in channel equalization.>

In this paper we investigate radial basis function networks (RBFNs) for application in adaptive interference cancellation. We study the problem from the perspective of optimal signal estimation. Optimum interference cancellation usually requires nonlinear processing of signals. RBFNs, owing to their nonlinear function approximation capability, can be expected to be able to implement or approximate the operation of optimum interference cancellation with appropriate network configuration and training. We examine a number of different RBFN structures as well as training algorithms. In particular, we show that in some special cases the optimum interference canceler can be exactly implemented by a class of normalized RBFNs that we have recently proposed. Through a number of simulation examples, we demonstrate that the various neural networks based on radial basis functions can be very useful for interference cancellation problems in which traditional linear cancelers may fail badly. We also discuss issues related to network performance and learning algorithms, and some practical considerations. Wir untersuchen Netzwerke mit radialen Basisfunktionen (RBFNs) in ihrer Anwendung zur adaptiven Störkompensation. Wir gehen an das Problem vom Blickwinkel optimaler Signalschätzung aus heran. Optimale Interferenzlöschung erfordert normalerweise eine nichtlineare Signalverarbeitung. Von RBFNs kann man erwarten, daβ sie aufgrund ihrer Fähigkeit zur Nachbildung nichtlinearer Funktionen in der Lage sind, die Operation optimaler Störbeseitigung mit einer passenden Netzwerkkonfiguration und geeignetem Training zumindest näherungsweise zu realisieren. Wir prüfen eine Reihe verschiedener RBFN-Strukturen sowie Trainingsalgorithmen. Insbesondere zeigen wir, daβ der optimale Inter-ferenzkompensator in einigen Sonderfällen durch eine Klasse normalisierter RBFNs exakt realisiert werden kann, die wir kürzlich vorgeschlagen haben. Anhand einer Reihe von Simulationsbeispielen demonstrieren wir, daβ die verschiedenen Netzwerke auf der Grundlage radialer Basisfunktionen sehr nützlich für Störlöschungsprobleme sein können, in denen herkömmliche lineare Entstörer manchmal völlig versagen. Wir sprechen auch Fragen von Netzwerkleistungsfähigkeit und Lernverfahren an sowie einige praktische Überlegungen. Nous étudions dans cet article les réseaux de fonctions radiales (RBFN) dans le cadre d'application à l'annulation adaptative d'interférences. Nous envisageons ce problème dans la perspective de l'estimation optimale des signaux. L'annulation d'interférence optimale requiert habituellement un traitement non linéaire des signaux. Les RBFN, du fait de leur capacité d'approximation de fonction non linéaires, devraient permettre d'implanter ou d'approximer l'opération de suppression d'interférence optimale à l'aide d'une configuration appropriée du réseau et d'un apprentissage. Nous examinons un certain nombre de structures de RBFN différentes ainsi que des algorithmes d'apprentissage. En particulier, nous montrons que dans certains cas spéciaux Pannulateur d'interférence optimal peut être exactement implanté par une classe de RBFN normalisés que nous avons récemment introduite. A l'aide d'un certain nombre d'exemples de simulation, nous montrons que les différents réseaux neuronaux basés sur les fonctions radiales peuvent être très utiles pour les problèmes d'annulation d'interférences dans lesquels les annulateurs linéaires traditionnels peuvent échouer. Nous discutons également les questions touchant aux performances des réseaux et des algorithmes d'apprentissage, et certaines considérations pratiques.

We investigate a nonlinear technique for image restoration using radial basis function networks. Computer simulation results indicate this new technique can be very useful.>