A single layer linear feedforward neural network for signal estimation in the wavelet domain

A model of adaptive signal estimation in the presence of noise is proposed using the wavelet transform and single layer linear feedforward neural networks. The networks successively estimate the residual of the approximations (details) of the input at different scales from coarse scales (low frequencies) to fine scales by minimizing the error of each channel of the wavelet transform separately. Since learning takes place in subspaces of the signal space one needs to train the networks with fewer weights. The rate of convergence of the learning algorithm in several transform channels is investigated. It is shown that learning in the input space may diverge, whereas convergence is achieved in wavelet spaces. Experimental results are presented which compare the proposed approximation method with adaptive approximation using sigmodal functions and exponentially decaying kernels.