Wavelet Filter Design based on the Lifting Scheme and its Application in Lossless Image Compression

The description of filter banks using lifting structures does not only benefit low-complexity implementation in software or hardware, but is also advantageous for the design of filter banks because of the guaranteed perfect reconstruction property. This paper proposes a new design method for wavelet filter banks, which is explained based on a single lifting structure suitable for 9/7 filter pairs. The filters are derived directly, the factorisation of known filters is not necessary. In addition, it is shown that the signal boundaries can be treated with little computational efforts. The modification of the standard design constraints leads to families of related filter pairs with varying characteristics. It includes a filter bank that can be implemented in integer arithmetic without divisions, shows better performance than the standard 9/7 filter bank for lossless image compression and competitive performance when applied in lossy compression. Key–Words: Lifting scheme, Filter design, Wavelet transform, Image coding