Introduction to Discrete Wavelet Transform
Tinku Acharya, Ping‐Sing Tsai · 2004
In this chapter we have discussed the theoretical foundation of the Discrete Wavelet Transform (DWT) both for convolution and lifting based approaches. We have discussed the concept of multiresolution analysis feature of the wavelet transform which makes it suitable for its application in image compression. We have discussed the pyramid algorithm for implementation of the DWT using the multiresolution approach. We have also discussed how the DWT is extended to two-dimensional signals as well. The multiresolution analysis based discrete wavelet transform is the foundation of the new JPEG2000 standard. Lifting based implementation of Discrete Wavelet Transform is new and became very popular for a number of efficient features in it. We have discussed the underlying theory behind the lifting algorithm for DWT and show how it is implemented via banded matrix multiplication. We have shown examples of the lifting factorization for the two default wavelet filter kernels (9, 7) and (5, 3) in the JPEG2000 standard. We have discussed the advantages of lifting based DWT over the traditional convolution based approach.