Wavelet Theory And Its Application In Image Compression And Digital Watermarking

Wavelet theories and their application is an important subject. This thesis focuses on the construction of biorthonormal multiresolution analyses (MRAs) with finite length filters, image compression and image watermarking based on wavelet transform. The main contributions are as follows:1. The construction of biorthonormal MRAs with filter length 4 and 5 is studied respectively. The region of the filter coefficients which can generate biorthonormal MRAs is searched. The regularity of the scale functions in the region is analyzed. In case of filter length 5, both the existence of unique symmetric biorthonormal MRA and the inexistence of antisymmetric ones are proved. Some examples of wavelet are given, and their validity applied to image compression is analyzed .2. A coding scheme is proposed to eliminate the redundancy of output vectors in pyramidal lattice vector quantization (PLVQ). A fast algorithm of labeling lattice points and a fast algorithm of finding lattice points are presented. And the transmission priority in case of Asynchronous Transfer Mode is suggested.3. By use of D4 lattice, PLVQ and zerotree coding (ZR) are conjoined. Zero lattice vectors are disposed by adopting improved zerotree coding. The significant map is scanned twice from down to up and from up to down respectively in order to reduce the computation complexity of zerotree coding. Experimental results demonstrate that the proposed algorithm performs better than traditional entropy coding based on run length.4. A CBR (constant bit rate) coding algorithm based on traits of human visual system (HVS) is proposed. Different bit rates are allocated to wavelet blocks according to energy the wavelet blocks include. Bit rates in wavelet blocks are adaptively adjusted in coding process. By use of bipartition, the entropy of each wavelet block approximates to the target bit rate of one.5. An efficient algorithm is presented for constructing quantization tables of wavelet blocks with optimal bit allocations for a given image. The algorithm uses wavelet coefficient distribution statistics in a novel way, and pays attention to the traits of HVS. A dynamic programming strategy to produce optimal quantization tables over a wide range of bit rates is also adopted.6. Based on wavelet coefficient distribution and a quantitative analysis on the magnitudes of wavelet coefficients, a new embedding strategy for watermarking is proposed based on dyadic discrete wavelet transform (DDWT) domain and multi_band DWT domain (MDWT) respectively. It is claimed that different embedding formulae should be applied on the low frequency subband and high frequency subbands respectively.7. By applying above embedding strategy, an adaptive algorithm incorporating the feature of visual masking of HVS into watermarking is proposed. The algorithm applies a novelmethod to classify these wavelet blocks. Based on the result of classification, watermark components with different strength are inserted into different wavelet coefficients. The experimental results show that the watermarks generated with the proposed algorithm are invisible and robust against noise and commonly used image processing techniques.8. An invisible image watermarking algorithm for embedding meaningful watermarks is proposed. The features of the proposed algorithm include that: (l)The algorithm reduces error probabilities of detection by use of BCH code. (2) The algorithm detects the embedded watermark without using original image. (3)The embedded watermark can be extracted only by using a secret key. Additionally, the proposed algorithm also can embed a meaningful logo. The experimental results show that the watermarks generated with the proposed algorithm is robust.9. Applying above embedding strategy, an adaptive watermarking algorithm is presented based on MDWT. The robustness of watermarking based on DDWT and MDWT is compared.