Using Biorthogonal Balanced Multiwavelets To Image Compression

Multiwavelets are a natural generalization of scalar wavelets. Multiwavelets have a lot of new features, for example, they can be simultaneously orthogonal, symmetric, short supported and of high vanishing moments while scalar wavelets cannot. So they have attracted much attention in the wavelets theory and application fields recently. When it face the application of discrete multiwavelets transposition, we must use the prefilter, but this process will destroy the important character of multiwavelets. To solve this question, we introduce the balanced multiwavelets, this multiwavelets did not need prefilter and use well.Lifting Scheme is a hot topic of wavelet theory and application, it's basic idea was based on biorthogonal wavelet and entirely reconstruction filter, it can improve the capability of wavelet by lifting and dual lifting to satisfy several application requirements. Lifting Scheme provides the frame of constructing the second generation wavelets according to specific requirement. In terms of the first generation wavelets, i.e. the existing wavelets, lifting scheme is an algorithm quicker than the commonly used Mallat algorithm. The construction of lifting scheme is simple, so the integer to integer wavelet transform is mainly based on the lifting scheme.At the third chapter, we put forward the equivalent condition between approximation and balance, and using the condition to construct the biorthogonal balanced multiwavelets by lifting schemes and use the multiwavelets to image compression. At the fourth chapter, we present a way to construct integer to integer multiwavelets and use it to lossless image compression.