Author: Chan, Sing-ping Edwin Title: Wavelet transformation in image processing Degree: M.Sc. Year: 1997 Subject: Image compression -- Data processingVideo compressionCoding theoryWavelets (Mathematics)Hong Kong Polytechnic University -- Dissertations Department: Multi-disciplinary Studies Pages: vii, 126 leaves : ill. ; 30 cm Language: English Abstract: This thesis discusses one of the relatively recently developed image transformation techniques and its application to digital image and video compression. This transformation technique uses multiple resolutions of the signal and is based on the wavelet theory. In this thesis, we are trying to use the simplest wavelet two-bands filter bank coding scheme to implement the image decomposition and reconstruction. All the images used are 8-bit gray level 256x256 size standard images. They can be disintegrated down to six levels subband images which sizes are 128x128, 64x64, 32x32, 16x16, 8x8 and the last level is 4x4. As wavelet decomposition is multiresolution in nature, so the upper level details subbands including the finial approximation subband are coming from the previous approximation subband. A Lenna image decomposed at one, three as well as six levels can demonstrate this multiresolution theory. Both of our wavelet high-pass and low-pass filters in wavelet transform are originated from the filter coefficients which are determined by the inputted alpha and beta values. By applying difference alpha and beta values, we can get a series of wavelet filters. The Lenna image is decomposed and reconstructed by this set of filters and their Root Mean Square Error (RMSE) is computed to determine the filters performance. Some of filters show perfect reconstruction which means the RMSE is zero, whereas some of the extremely worst filters can generate the RMSE greater than 23. Since the error will be accumulated during transformation, so the higher the wavelet level, the greater the RMSE will get. In order for image compression, some of the unimportant information can be removed. Thus we also cut-off some details information or the approximation information at difference level to understand their error change. Besides the Lenna image, the baboon and pepper images are also tested. Their RMSE and rebuild images are printed for comparison. If more information is cut, the higher the RMSE will be gotten. Also the approximation information contain the major data for reconstruction, so it should not be reduced. Only the details information, especially for the higher wavelet level, could be sacrificed. Rights: All rights reserved Access: restricted access

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