Study On The Theory Of Wavelet With Dilation Factor 3/2 And The Application Of Wavelet In Edge Detection

Compared with Fourier transform and Gabor transform, wavelet transform is local space (time) and frequency transform, so it can extract information from signal effectively. Now wavelet analysis has become the hot research objective of applied mathematics, physics, computer, information, image processing and so on.Firstly, the spectrum dislocation of discrete detail in the discrete wavelet fast algorithm proposed by Mallat is analysed based on multi-rate filter banks theory.Secondly, a new discrete wavelet decomposition and reconstruction algorithm is presented based on 3/2 multiresolution analysis. The algorithm includes: the method of decimation, the structure of signal processing, the selection of scaling functions, wavelet functions and the corresponding filters. The simulation of numerical value example proves the algorithm can solve the frequency distortion in the high frequency sub-band in the process of decimation in each level. In addition, proving the math expression of rational"Littlewood-Paley"bases given in document [30] is mistake and its correct math expression is given. The given correct math expression is accepted by Professor Truchetet, one of the three authors of the document.Finally, the voriogram in geostatistics is applied to the edge detection of noisy image. Based on regionalized variable theory, a new multiscale edge detection method for noisy image is presented and two variables --ηand mean voriogram are definited. It is proved that adding r ( x , h ) in some direction and at the distance h in the image non- contaminated by Gassian White noise to the estmated variance of Gassian White noise makes the value of voriogram r ' ( x , h ) in the direction at a distance h in the image contaminated by Gassian White noise. Based on the voriogram value of the data in different regions withdifferent direction, the presented method judge whether the edge exist or not and the direction of the edge, then based on the direction of the edge in the region, the wavelet transform with different scales at horizontal and vertical direction is implemented, respectively. Furthermore, while ensuring the location accuracy of edge, false edge points produced by noise and uneven gray scale in image are wiped off as much as possible. The results of simulation indicate the proposed algorithm can weaken the effect on edge detection produced by the noise, when the image is contaminated badly by Gaussian noise. The performance of the algorithm is obviously superior to the traditional edge detection methods, thus proves the validity and feasibility of the algorithm.