Lifting-based wavelet transform algorithm for lossy image/signal compression

A new wavelet transform algorithm based on a modified lifting scheme is presented. The algorithm uses the wavelet filters derived from a generalized lifting scheme at the decomposition stage. The proposed generalized framework for the lifting scheme permits to obtain easily different wavelet filter coefficients in the case of the (-N, N) lifting. The restoration stage of the lifting scheme was modified in a standard wavelet transform fashion to obtain a good rate/distortion performance because the standard lifting scheme does not perform well in the lossy data compression. The algorithm performs decomposition/restoration on the first level whereas at the next level classic wavelet filters are used. For this purpose, the restoration high-pass wavelet filter was derived from the generalized lifting scheme. The obtained restoration high-pass and low-pass wavelet filters operate as a known classic wavelet filters using data upsampling. The low-pass filter for the restoration stage uses the same coefficients of the lifting decomposition predictor. The proposed transform possesses the perfect restoration of the processed data when the quantification is not used and possesses a good energy compactation. The designed algorithm was tested on different test images and the obtained results are comparable with the JPEG2000 9/7 wavelet filtering. The proposed algorithm performs better on the images having high energy of the low-scale details.