Can anybody tell me the advantages of the lifting scheme and why it is better then a normal filter bank?
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$\begingroup$ Can you give more details? Which "lifting scheme" are you talking about? A link to a specific algorithm or implementation would improve the quality of your question. $\endgroup$– Peter K. ♦Commented Dec 23, 2013 at 14:06
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1$\begingroup$ Hi Peter! I am working on a jpeg2000 compressor this is a school project. Unfortunately this course is a bit messy and I want to know advantages of bi-orthogonal 9/7 lifting beyond bi-orthogonal 9/7 filer bank. Teacher said only that lifting is better. But I want to understand why. For implementation of the filter bank we used convolution and unfortunately apart from the fact that lifting is easier to implement and that the complexity is lower because there are no Fourier transform to perform, we don't know why this is better. $\endgroup$– marekszpakCommented Dec 23, 2013 at 19:35
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2$\begingroup$ You already said it all: ease of implementation, fastest for moderately short filters. The only drawback is that you have to find the factorization of the filter bank matrix first, but for the jpeg2000 wavelets, these are widely documented. -- Also, if you go to lossless transformations, the lifting scheme can be implemented in a way that rounding errors are accounted for, i.e., rounding in the trend component is compensated by a correction to the detail coefficients (losing linearity and symmetry in the lowest bits), so that reconstruction is perfect. $\endgroup$– Lutz LehmannCommented Dec 28, 2013 at 10:21
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$\begingroup$ @LutzL , I read your comment and find it very useful, I wish you posted it as an answer. $\endgroup$– MimSaadCommented Jul 17, 2017 at 18:11
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1 Answer
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Unlike the convolution, the lifting scheme can
- map integers to integers (CDF 5/3 transform in case of JPEG 2000),
- asymptotically reduces the computational complexity by a factor two,
- can be computed in-place,
- allows to simply treat signal boundaries (periodic symmetric extension in case of JPEG 2000).
