Wavelet based denoising integrated into multilayered perceptron

A denoising unit based on wavelet multiresolution analysis is added ahead of the multilayered perceptron. The cost function used in neural network learning is also applied as the denoising criterion and hence denoising itself is treated as a part of the integrated model. By introducing continuously derivable generalized soft thresholding function and infinite thresholds, a gradient based learning algorithm for simultaneous setting of all free parameters of the model is derived. The proposed model outmatches the classical multilayered perceptron and the multilayered perceptron with statistical denoising in noisy time series prediction problems.