Construction And Analysis Of Two Families Of Wavelets Used In Image Compression

As one of the most remarkable tools, wavelet performs better than DFT or DCT in many aspects of image processing because of its good characteristics such as compact supported, vanishing moments, regularity, MRA, time-frequency location, fast computing and so on. We focus on the construction and application of two families of wavelets used in image compression. The main results are as follows:Firstly, wavelets with fixed length and directions often lead to big coefficients around edges in the decomposition of text images and make against the coming coding. Using local information of pixels, adaptive lifting wavelets based on lifting-schemes are constructed. First, updating-operator of each pixel is selected adaptively by multi-decisions. We give a more simple proof than [16] by normalizing the weights of weighted seminorms; second, we redesign the prediction-filters by checking the pixel's local characters as whether it's in text regions and the direction of edges. As a conclusion, we point out the wavelets designed above have perfect reconstruction without side-information. Experiment shows that our wavelet has better capacity of energy focused and the decomposed image has lower entropy, this will do better to data compression, SPIHT coding validates the conlusion.Secondly, tensor-product wavelets process images in horizontal and vertical directions, ignoring information in other oritations, what's more, some high-dimension signals are unsuitable to be done in separated way. However, non-separable multiwavelets can process images isotropily and make good use of information of neighboring pixels. In order to use the advantages of non-separable multiwavelets and make sure the decomposed images have the same data structure as that of tensor-product ones' for the replanting of existed coding methods, the construction and implement of interpolatory biorthogonal non-separable multiwavelets with dilation matrix 2I₂ are mainly discussed in the paper. All these wavelets can be unified to ones with scale mask and dual scale mask symmetric about two axises after analysis. In fact, wavelets with such masks can be constructed easily under some conditions and one method of construction is supported. To have perfect reconstruction for decomposed images by non-separable multiwavelets, boundary-symmetric extension different from that of tensor-product wavelet's is presented, the PR is proved theoretically. At last, experiments of non-separable multiwavelets using in data compression are introduced as well as the analysis.