Wavelet and Data Compression

Description

Wavelets are functions, usually defined on the reals, whose graphs resemble highly localized, little waves. They are used to approximate other functions, or data in much the same way as polynomials are used to approximate a function on some interval, or trigonometric polynomials to approximate a periodic function.

In this course we will develop the basic ideas and concentrate on applications to signal processing. This is a large, important  area in engineering and science with numerous applications. Here are a few examples. There are many others.
• Image compression - e.g. films have to be compressed to fit on DVDs (and uncompressed to watch them). This must be done quickly. The storage and transmission of images might also require compression for practical reasons.
• Denoising signals - getting rubbish (back-ground noise, ...) out of  a signal. Important in medical imaging, seismology, cleaning old audio recording,
• Analysing financial data - The data sets, such as share price indices, typically involve both pseudo--random and intermittent deterministic processes. There is often a large financial incentive to solve prediction problems. (The application of wavelets to this area in still in its infancy when compared with other applications.)