Data Compression and Harmonic Analysis

In this article we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon’s R(D) theory in the case of Gaussian stationary processes, which says that transforming into a Fourier basis followed by block coding gives an optimal lossy compression technique; practical developments like transformbased image compression (JPEG) have been inspired by this result. In this article we also discuss connections perhaps less familiar to the Information Theory community, growing out of the field of harmonic analysis. Recent harmonic analysis constructions, such as wavelet transforms and Gabor transforms, are essentially optimal transforms for transform coding in certain settings. Some of these transforms are under consideration for future compression standards, like JPEG-2000. We discuss some of the lessons of harmonic analysis in this century. Typically, the problems and achievements of this field have involved goals that were no...

• Type: Journal
• Year: 1998
• Where: TIT
• Authors: David L. Donoho, Martin Vetterli, Ronald A. DeVore, Ingrid Daubechies
• Keywords: Data Compression, Harmonic Analysis, TIT 1998, Transform Coding