Abstract

The application of wavelet and ridgelet transforms in pattern recognition is still in its infancy; while their use in denoising has been a very hot topic in recent years. The aim of this thesis is to study these two important problems. In the area of pattern recognition, we develop a handwritten numeral recognition descriptor using multi-wavelets and neural networks. We perform multiwavelet orthonormal shell expansion on the contour to get several resolution levels and the average. Then we use the shell coefficients as features to input into a feed-forward neural network to recognize the handwritten numerals. We also present two novel descriptors for feature extraction by using ridgelets. Fourier spectrum and wavelet cycle-spinning are used to achieve rotational invariance. The descriptors are very robust to noise even when the noise level is high. Experimental results show that the new descriptors are excellent choices for pattern recognition. In the area of denoising, we first study multiwavelet thresholding by incorporating neighbouring coefficients. Experimental results show that this approach outperforms neighbour single wavelet denoising for some standard test signals and real life images. Then, we propose a wavelet image thresholding scheme by incorporating neighbouring coefficients. Experimental results show that translation invariant (TI) denoising with neighbour dependency is better than VisuShrink and the TI denoising method developed by Yu et al. Finally, we propose to use Simulated Annealing to find both the customized wavelet filters and the customized threshold for the given noisy image at the same time. The results we obtained are promising compared to other results published in the literature.