Signal and Image Processing Seminar

During the last decade, the explosively developing wavelet theory has proven to be a powerful mathematical tool for signal analysis and synthesis and has found a wide range of successful applications in the area of digital signal processing (DSP). Compared to their counterparts in the Fourier realm, wavelet techniques permit significantly more flexibility in system design for many applications such as multirate filtering, sampling and interpolation, signal modeling and approximation, noise reduction, signal enhancement, feature extraction, and image data compression. Most classical wavelet systems have been constructed from a primarily mathematical point of view, and they are fundamentally suitable for representing continuous-domain functions rather than discrete-domain data. From a discrete-time or DSP perspective, we develop new wavelet systems.

This talk focuses on the theory, design, and applications of several novel classes of one-dimensional and multi-dimensional Coiflet-type wavelet systems. In particular, we propose a novel generalized Coifman criterion for designing high-performance wavelet systems, which emphasizes the vanishing moments of both wavelets and scaling functions. The resulting new wavelet systems are appropriate for representing discrete-domain data and enjoy a number of interesting and useful properties such as

• sparse representations for smooth signals,
• interpolating scaling functions,
• linear phase filterbanks, and
• dyadic frational filter coefficients,