Time and Location: February 4, 2004, 2-3:00pm, Room 1314.
Title: Recovering sparse expansions after noisy
Speaker: Ingrid Daubechies, Princeton University
and Courant Institute
An image that is blurred (by e.g. convolution with a gaussian kernel)
cannot be recovered perfectly in a numerically stable way. To get
around this, many regularization methods have been proposed. Typically
they exploit known general properties of the class of images under
study to restore some measure of stability to the problem; they also
give estimates on how much resolution one can hope to gain.
In this talk we show how to use the prior knowledge that the image
has a sparse expansion in a wavelet basis. (This talk picks up
essentially where the speaker left off in her Applied Math talk in
December, but it is not necessary to have heard that talk.) In
particular, we discuss the algorithm and proofs in some detail, as well
as some generalizations of the approach.