An Approach to Fast Integer Reversible Wavelet Transforms for Image Compression

In this paper, we propose a general method for creating integer wavelet transforms which can be used in both lossless (reversible) and lossy compression of signals and images with arbitrary size. This method allows us to get a series of transformations which are very close to the corresponding biorthogonal wavelet transforms or some non-orthogonal wavelet transforms, but can be calculated with only integer addition and bit-shift operations. In addition, the integer wavelet transforms created in this paper possess a property of precision preservation (PPP). This property is very useful for conserving memory in both compression and decompression, and speed up the whole procedure in some applications. The motivation of this paper comes from the lifting scheme [1] and S+P transform [3]. * This work has been partially supported by the US Navy under SBIR Contract N0003994-C-0013. ** The author is partially supported by the National Science Foundation of P. R. China and the Science Foundation of Zhongshan University.