Ten lectures on wavelets
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
Wavelet Image and Video Compression
Wavelet Image and Video Compression
New structures for adaptive filtering in subbands with critical sampling
IEEE Transactions on Signal Processing
Recursive biorthogonal interpolating wavelets and signal-adaptedinterpolating filter banks
IEEE Transactions on Signal Processing
The role of linear semi-infinite programming in signal-adapted QMFbank design
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Theory of optimal orthonormal subband coders
IEEE Transactions on Signal Processing
Theory and design of optimum FIR compaction filters
IEEE Transactions on Signal Processing
Theory and design of signal-adapted FIR paraunitary filter banks
IEEE Transactions on Signal Processing
Principal component filter banks for optimal multiresolutionanalysis
IEEE Transactions on Signal Processing
On the optimality of nonunitary filter banks in subband coders
IEEE Transactions on Image Processing
IEEE Transactions on Signal Processing
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In the high bit-rate data compression, the filterbanks that match the statistical properties of inputs have been widely researched. For orthonormal uniform filterbanks and biorthogonal filterbanks without order constraints, the design problems have been solved on the whole. However, for biorthogonal FIR filterbanks, an efficient method associated with an algorithm for the design still needs to be developed. In this paper, two-channel adaptive biorthogonal filterbanks via lifting scheme are investigated. Starting from an arbitrary filterbank (orthonormal or biorthogonal), two-channel biorthogonal filterbanks are designed by the adaptive lifting scheme, which is a general form of our previous work. Two adaptive lifting algorithms are developed, namely, the sequential adaptive lifting and the joint adaptive lifting. Further, it is proved that starting from a linear-phase filterbank, the optimal filterbank by the sequential adaptive lifting preserves the linear-phase property. Experimental results show that the subband coding gains can be markedly improved when an appropriate initial filterbank is chosen.