Multidimensional wavelets and invariance principles for the analysis of bioimages

In this talk, we shall advocate the use of wavelets for the processing and analysis of images in biomicroscopy. We start with a short tutorial on wavelet bases, emphasizing the fact that they provide a concise multiresolution representation of signals and that they can be computed efficiently using filterbanks. We then show how they can be extended to multiple dimensions, either, by using tensor-product-basis functions, or by allowing for some level of redundancy to achieve better invariance with respect to coordinate transformations. In particular, we present a parameric family of multidimensional wavelet transforms that are translation- and rotation-invariant and perfectly reversible (tight frame property). The underlying wavelet templates are steerable—meaning that they can be spatially rotated in any direction—and tunable to some extent, which makes them ideally suited for pattern analysis and key-point detection in 2-D or 3-D. The concepts are illustrated with applications in biological imaging. These include the denoising and deconvolution of fluorescence micrographs, model-based extraction of features (detection of edges, tracing of filaments, localization of junctions), and morphological component analysis.

Michael Unser

Michael Unser is professor and director of EPFL's Biomedical Imaging Group, Lausanne, Switzerland. His primary area of investigation is biomedical image processing. He is internationally recognized for his research contributions to sampling theory, wavelets, the use of splines for image processing, and stochastic processes. He has published over 200 journal papers on those topics. From 1985 to 1997, he was with the Biomedical Engineering and Instrumentation Program, National Institutes of Health, Bethesda USA, conducting research on bioimaging. Dr. Unser has held the position of associate Editor-in-Chief (2003-2005) for the IEEE Transactions on Medical Imaging. He is currently member of the editorial boards of SIAM J. Imaging Sciences, IEEE J. Selected Topics in Signal Processing, and Foundations and Trends in Signal Processing. He is the founding chair of the technical committee on Bio Imaging and Signal Processing (BISP) of the IEEE Signal Processing Society. Prof. Unser is a fellow of the IEEE (1999), an EURASIP fellow (2009), and a member of the Swiss Academy of Engineering Sciences. He is the recipient of several international prizes including three IEEE-SPS Best Paper Awards and two Technical Achievement Awards from the IEEE (2008 SPS and EMBS 2010).Biomedical Imaging Group, EPFL