This chapter provides the simple high-level insights, based on the intuitive concept of time frequency representations, into why wavelets are good for image coding. As a way of highlighting the benefits of having a sparse representation, such as that provided by the wavelet decomposition, consider the lowest frequency band in the top level of the three-level wavelet hierarchy. This band is just a down sampled and smoothed version of the original image. A very simple way of achieving compression is to simply retain this lowpass version and throw away the rest of the wavelet data, instantly achieving a compression ratio of 64:1. Another attractive aspect of the coarse-to-fine nature of the wavelet representation naturally facilitates a transmission scheme that progressively refines the received image quality. That is, it would be highly beneficial to have an encoded bitstream that can be chopped offat any desired point to provide a commensurate reconstruction image quality. This is known as a progressive transmission feature or as an embedded bitstream. This is ideally suited, for example, to Internet image applications. These are some of the high-level reasons why wavelets represent a superior alternative to traditional Fourier-based methods for compressing natural images: that is why the Joint Photographic Experts Group 2000 standard uses wavelets instead of the Fourier-based discrete cosine transform. 2009 Elsevier Inc. All rights reserved.
