Approximating nonlinear functions via neural networks based on discrete affine wavelet transformations

Abstract

Based on the discrete affine wavelet transforms, we develop a new "basis" for wavelet networks for better approximating non-smooth nonlinear functions. It is shown that the wavelet formalism supports a theoretical framework, and it is possible to perform both analysis and synthesis of feedforward neural networks. Using the spatio-spectral localization properties of wavelets, we can synthesize a feedforward network to reduce the training problem to one of convex optimization problem.Specifically, we have developed the algorithm for approximation of high-dimensional nonlinear functions. Finally, the inverted pendulum stabilizing problem is studied via the proposed wavelet neural networks in order to illustrate the usefulness of the developed theoretical framework. -Definition 2.1[7l : A sequence of vectors [ qJ,=., in a Hilbert space H is called a frame if there exists A>O, Beso that, for all f in H, J We call A and B the frame bounds. Definition 2.2[10] : If {(p,] is a frame in H, then the frame operator S is the linear operator from H to H defined by 0-7803-21 14-6/94/$4.00 0 1994 IEEE.

Image Denoising: An Approach Based on Wavelet Neural Network and Improved Median Filtering

“…Wavelet neural network (WNN) uses wavelet function as node functions and trains its weights, the dilation and the translation. WNN have been in wide use, such as in load forecast [11], function approximation [12][13], system identification [14][15], noise removal [18], etc.…”