APPLIED MATH SEMINAR

Speaker: Gitta Kutyniok, Institute for Mathematics, University of Osnabrueck

Title:  "Data Separation via Sparse Approximation in Neurobiological Imaging"

When/where: Tuesday, March 15th, 4:15 pm, AKW 200

Abstract:

Along with the deluge of data we face today, it is not surprising that the complexity of such
data is also increasing. One instance of this phenomenon is the occurrence of multiple
components, and hence, analyzing such data typically involves a separation step. One most
intriguing example comes from neurobiological imaging, where images of neurons from
Alzheimer infected brains are studied with the hope to detect specific artifacts of this
disease. The prominent parts of images of neurons are spines (pointlike structures)
and dendrites (curvelike structures), which require separate analyzes, for instance,
counting the number of spines of a particular shape, and determining the thickness of
dendrites.

In this talk, we will first introduce a general methodology for separating morphologically
distinct components using ideas from sparse approximation. More precisely, this methodology
utilizes two representation systems each providing sparse approximations of one of the
components; the separation is then performed by thresholding. After introducing this method,
we provide an estimate for its accuracy. We then study this separation approach using a
pair of wavelets (adapted to pointlike structures) and shearlets (adapted to curvelike
structures) for separating spines and dendrites. Finally, we discuss details of the implementation
and present numerical examples to illustrate the performance of our methodology.

This is joint work with David Donoho (Stanford University) and Wang-Q Lim (University of Osnabrueck).