The variable-length generalized lapped biorthogonal transform
This paper introduces a class of linear phase lapped biorthogonal transforms with basis functions of variable length (VLGLBT). The transform can be characterized by a lattice which structurally enforces both linear phase and perfect reconstruction properties as well as provides a fast and efficient transform implementation. Our main motivation of the new transform is its application in image coding. The VLGLBT has several long overlapped basis functions for representing smooth signals to avoid blocking artifacts. The rest of the bases covering high-frequency bands are constrained to be short to limit ringing artifacts. The relaxation of the orthogonal constraint allows the VLGLBT to have significantly different analysis and synthesis banks which can be tailored appropriately to obtain high-quality reconstructed images. Most importantly, the variable-length property allows us to design very fast and low-complexity transforms. Comparing to the popular DCT, a fast VLGLBT named FLT only requires 6 more multiplications and 8 more additions. Yet, image coding examples show that the FLT is far superior than the DCT and is close to the 9/7-tap biorthogonal wavelet in both objective and subjective coding performance.