Constructing near-tight wavelet frames by neural networks

Xin Li

doi:10.1117/12.255226

23 October 1996 Constructing near-tight wavelet frames by neural networks

Xin Li

Proceedings Volume 2825, Wavelet Applications in Signal and Image Processing IV; (1996) https://doi.org/10.1117/12.255226
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

Suppose that (sigma) is a sigmoidal function which is the activation function of a neural network. Under certain assumptions on the derivatives of (sigma) , we show that a simple linear combination of dilates and translates of (sigma) generates a near tight wavelet frame for L²(R), which is then used in constructing approximation to multivariate functions by neural networks with one hidden layer.

Citation Download Citation

Xin Li "Constructing near-tight wavelet frames by neural networks", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); https://doi.org/10.1117/12.255226

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