A Coherent Methodology and Software Toolkit for Wavelet De-Noising

The wavelet transform has generated excitement among researchers from a wide range of disciplines. Wavelets have an extremely rich mathematical foundation and have been proven valuable for a variety of applications. New ideas are being pursued at a breathtaking pace leading to innovative algorithms. The challenge before us now is to identify and harness these ideas and develop a coherent set of tools which can be applied to practical problems in signal and image processing. The central focus of this proposal is to develop a complete and mature methodology for signal recovery and de-noising based on wavelets. We use the term wavelets in a broad sense to include the many wavelet-like transforms such as wavelet packets and local cosine bases. We will improve and extend existing procedures to correct for artifacts and handle more general problems. Based on our research, we will build an object-oriented software toolkit using the S-Plus language. The toolkit will provide a rich foundation of tools for wavelet de-noising. We will evaluate the procedures using real and simulated data drawn from a variety of applications, including signal recovery, signal detection and classification, inverse problems (parameter estimation), density estimation, and image and image array reconstruction and enhancement.