Chapter 4: Subband and Wavelet

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 wavelet transform is a special type of such transform and hence it is expected to eliminate blocking artefacts.

The answer to the second part relates to the state of the art in image coding in the mid 1980s, the time when the original JPEG was under development. At that time although the wavelet transform and its predecessor, subband coding, were known, there was no efficient method of coding the wavelet transform coefficients, to be comparable with the DCT. In fact the proposals submitted to the JPEG committee were all DCT-based codecs, none on the wavelet. Also almost at the same time, out of the 15 proposals to the H.261 committee, there were 14 DCT-based codecs and one vector quartisation method and none on the wavelet transform. Thus in the mid 1980s, the compression performance, coupled with the considerable momentum already behind the DCT, led the JPEG committee to adopt DCT-based coding as the foundation of JPEG.

However, the state of the wavelet-transform-based image compression techniques have significantly improved since the introduction of the original JPEG. Much of the credit should go to Jussef Shapiro, who by the introduction of the embedded zero tree wavelet (EZW) made a significant breakthrough in coding of the wavelet coefficients [4]. At the end of this Chapter this method, and the other similar methods that exploit the multiresolution properties of the wavelet transform to give a computationally simple but efficient compression algorithm, will be introduced.



Standard Codecs(c) Image Compression to Advanced Video Coding
Standard Codecs: Image Compression to Advanced Video Coding (IET Telecommunications Series)
ISBN: 0852967101
EAN: 2147483647
Year: 2005
Pages: 148
Authors: M. Ghanbari

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