Coding of still images under MPEG-4 [1] and the recent decision by the JPEG committee to recommend a new standard under JPEG2000 [2] has brought up a new image compression technique. The committee has decided to recommend a new way of coding still images based on the wavelet transform, in sharp contrast to the discrete cosine transform (DCT) used in the other standard codecs, as well as the original JPEG. In this Chapter we introduce this wavelet transform and show how it can be used for image compression.

4.1 Why wavelet transform?

Before describing the wavelet transform and its usage in image compression it is essential to answer two fundamental questions:

1. What is wrong with the DCT and why should we use wavelet?

2. If wavelet is superior to DCT, why did the original JPEG not use it?

The answer to the first part is as follows. The DCT and the other block-based transforms partition an image into nonoverlapping blocks and process each block separately. At very low bit rates, the transform coefficients need to be coarsely quantised and so there will be a significant reconstruction error after the decoding. This error is more visible at the block boundaries, by causing a discontinuity in the image, and is best known as the blocking artefact. One way of reducing this artefact is to allow the basis functions to decay towards zero at these points, or to overlap over the adjacent blocks. The latter technique is called the lapped orthogonal transform [3]. The...