A Fast Lapped Transform for Image Coding

This paper introduces a class of linear phase lapped biorthogonal transforms with basis functions of variable length. A lattice is used to enforce both linear phase and perfect reconstruction properties as well as to provide a fast and efficient transform implementation for image coding applications. In the proposed formulation which we call fast lapped transform (FLT), the higher frequency filters (basis functions) are those of the DCT, which are compact to limit ringing. The lower frequency filters (basis functions) are overlapped for representing smooth signals while avoiding blocking artifacts. A great part of the FLT computation is spent at the DCT stage, which can be implemented through fast algorithms, while just a few more operations are needed to implement the extra stages. For example, compared to the DCT, an FLT with good performance can be implemented with only 8 extra additions and 6 extra multiplications for an 8-sample block. Yet, image coding examples show that the FLT is far superior to the DCT and is close to the 9/7-tap biorthogonal wavelet in subjective coding performance.