| In this thesis, we study the application of wavelet transforms in two important areas: pattern recognition and de-noising. In the area of pattern recognition, we propose and implement two invariant descriptors for the recognition of 2-D patterns. The first invariant descriptor is concerned with patterns which can be represented by periodic 1-D signals. The method first performs orthonormal shell decomposition on the periodic 1-D signals, then applies Fourier transform on each scale of the shell coefficients. The essential advantage of the descriptor is that a multi-resolution querying strategy can be employed in the recognition process and that it is invariant to rotation of the original 2-D pattern. The second invariant descriptor can be used for any pattern. We first transform the pattern to polar coordinate (r, 0) using the centre of mass of the pattern as origin, then apply the Fourier transform along the axis of polar angle 0 and the wavelet transform along the axis of radius r. The features thus obtained are invariant to translation and rotation. Experimental results show that the two invariant descriptors are efficient representation which can provide for reliable recognition.; In de-noising, we develop a new translation-invariant(TI) multiwavelet de-noising algorithm. Instead of using univariate thresholding developed by Donoho, we adopt bivariate thresholding as pioneered by Downie and Silverman. Numerical simulation shows that TI multiwavelet de-noising is better than TI single wavelet de-noising when soft thresholding is used. |
