3.7 Wavelet and Subband Coding

Subband coding and wavelet coding are closely related and operate by decomposing an image into frequency components [10 15]. This decomposition is performed by iterative low- and high-pass filtering. The result of the high-pass filter is retained. The result of the low-pass filter is decimated and again low- and high-pass filtered. This is continued for the number of levels desired (typically 3 or 4). See Figure 3.16.

This filtering is performed on the entire image, not on small blocks like the DCT. This eliminates the blocking artifact normally associated with DCTalgorithms. At each frequency band, there is a filtered version of the image whose spatial resolution is proportional to the frequency. For example, low-frequency bands have low spatial resolution that represent larger areas of the image. High-frequency bands have high spatial resolution that represent local edge and texture detail. While the DCT coefficients represent a decomposition based on frequency-related cosines, the wavelet transform. is a decomposition based on frequency-related complex waveforms or wavelets. The result of the wavelet transform is a hierarchical representation of the image where each level in the hierarchy is a map of the image information contained within a specific frequency band. This hierarchy is represented by a tree structure of filtered pixels, with the lowest frequency pixels at the root. Each pixel at one level is linked to multiple pixels at the next level. The lowest frequency level is the called the reference signal. The other levels are the detail signals.

There...