Image compression have long been found very crucial role in the multimedia information technique. Currently,transforming coding is one of the most used approach for image coding,where the discrete cosine transform(DCT),the discrete wavelet transform(DWT),and the lapped biorthogonal transform(LBT) are widely utilized. How to reduce the complexity of these discrete transforms,is the key technique to image compression.In this thesis,a type of lapped biorthogonal transform which can map integers to integers is considered. Based on the computational structure of the proposed lapped transform,an efficient multiplierless algorithm for the lapped biorthogonal transform (LBT),called integer lapped biorthogonal transform (IntLBT),is proposed. The proposed IntLBT is implemented by a series of dyadic lifting steps,and provides fast,efficient computation of the transform coefficients as well as the ability to map integers to integers. Application of the novel IntLBT in lossy image coding gains very competitive results comparing to the performance of the much more complex CohenDaubechiesFeauveau (CDF) 9 7tap biorthogonal wavelet with irrational coefficients.Lifting scheme can be used to calculate Discrete Wavelet Transform (DWT) efficiently,it is composed of a number of lifting steps and the scaling transform. When it is used to calculate multilevel DWT and multidimensional DWT,there exist many redundant multiplications. Here we propose,a new technique,called PostScaling Lifting Algorithm (PSLift),which needs fewer multiplications. PSLift first calculate all lifting steps of each level and each dimensional DWT,and then calculate the scaling transform. For example,when five level decompositions is implemented for CDF 9 7 wavelet,compared to the known methods,the number of multiplication needed is reduced by 20% and 28% corresponds to one dimensional DWT and two dimensional DWT,respectively.Based on lifting scheme and Cohen  Daubechies  Feauveau theorem constructing biorthogonal wavelets ,we construct a new symmetric biorthogonal 9 7 tap wavelet (LS97). The compression performance of the LS97 wavelet is almost the same as that of CDF 9 7 wavelet,which is adopted by JPEG2000. Furthermore,the inverse of LS97 wavelet can be replaced by CDF 9 7 wavelet in image compression,and vice versa. Only one coefficient is irrational number in LS97 wavelet,the others are simple rational number,while all coefficients are irrational number in CDF 9 7 wavelet. Therefore,The LS97 wavelet can reduce computational complexity of image compression and video compression remarkably.
