Application of artificial neural networks and the wavelet transform for pattern recognition, noise reduction and data compression
Theory of Artificial Neural Networks (ANNs) could not provide an exact method of weights training. The training is done mostly by iterative trial and error minimisation methods which do not enable the ANNs for time incremental learning. In this thesis, it is shown that the weights successfully produced by an error minimisation method are nothing more than the scaled versions of their respective components of the sample pattern and that the training methods leaves a chance for a neuron to be deceived. An exact method of weight construction is developed in the form of a system of linear equations. A new linear classifier ANN and a number of thresholding procedures are developed. It is proved that the Hopfield network and the Boltzmann machine do not qualify as the reasonable networks. A generalised multiclass linear classifier ANN is developed which is a combination of a newly developed multiclass linear ANN and a newly developed multiclass XOR classifier ANN. A biological neuromuscular system is interpreted as a multiclass linear classifier ANN. A new technique for pattern recognition. especially for images, has been presented with a software check. The technique minimises the design topology of ANNs and enables them to classify a scaled, a mirror image, and a noisy version of the sample pattern. The Continuous Wavelet Transform (CWT), the Discrete Wavelet Transform, and the Wavelet Decomposition has been connected by developing an extend-able and intensifyable system of particular six Gaussian wavelets. A binary transform applicable for every real function is developed. The confusing automatic nature of the CWT is explained along with presenting a new style of defining wavelets. Application of the wavelet transforms for noise reduction and data compression/expansion is explained and their performance is checked through the self developed software. A modification in the CWT is made in order to make their application easier through ANNs. The ANNs are developed and their performance is checked against the self developed software. A new multiresolution zoom-out wavelet transform is developed which expands data without smoothing it. A new wavelet is deduced from the smoothing average filter. Some twodimensional wavelets for noise reduction and data compression/expansion are developed on the same style and their performance is checked through the self developed software. An ANN for CWT using a newly developed two-dimensional wavelet is developed and its activation is explained. Data compression by locating peaks and bottoms of data and setting other elements equals zero is done with the guarantee of reconstruction. The new wavelet transform is modified to reconstruct the data between peaks and bottoms. Peaks and bottoms detecting ANNs are developed and their performance is checked against the self developed software. Procedures for classification are presented with self developed software check. The theory of ANNs requires bit-wise parallel adders and multiplexors. A parallel adder circuit is developed by combining some newly developed basic units for the purpose.