Efficient Signal Approximations

by Dr. Thierry Blu Biomedical Imaging Laboratory, Swiss Federal Institute of Technology

 :  16 Jun 2005 (Thu)
 :  11:00am - 12:00noon
Venue  :  Room 2302, 2/F (Lifts 17-18), HKUST


Approximating a signal into some adequately chosen function space is a necessary step in many Signal Processing applications. A recurrent example, especially in Medical Imaging and Remote Sensing, is that of the interpolation. Another very popular example of approximation, especially for image compression and detection, is that of the wavelet decomposition.

In this talk, I will present excerpts of my recent contributions in the field of Signal Approximation:

The first part of the presentation will be devoted to the design of optimal interpolators/approximators under various implementation constraints.

The second part will be devoted to a nonstandard approach for the efficient design of dyadic and quincunx wavelets, yielding two important classes of scaling functions, the 1D fractional splines and the (nonseparable) 2D polyharmonic splines.

The last part will deal with an application of wavelets to the spatial detection of activation in functional Magnetic Resonance Imaging (fMRI) experiments. I will in particular lay the emphasis on a new approach that couples statistical confidence level together with approximation error in order to determine the optimal, statistically meaningful joint space-wavelet thresholding scheme.

Although the results presented here are of a somewhat theoretical nature, most of them will be validated by practical experiments and complemented with a few Java demonstrations.

Th. Blu was born in Orleans, France, in 1964. He received the "Diplome d'ingenieur" from Ecole Polytechnique, France, in 1986 and from Telecom Paris (ENST), France, in 1988. In 1996, he obtained the Ph.D in electrical engineering from ENST for a study on iterated rational filterbanks, applied to wideband audio coding.

He is with the Biomedical Imaging Group at the Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, on leave from the Research and Development division of France Telecom.

He was the recipient of the 2003 best paper award (Signal Processing Theory and Methods) from the IEEE Signal Processing Society and is currently serving as an Associate Editor for the IEEE Transactions on Image Processing.


*** All are Welcome ***