[Colloquium] Gene Golub talk - Thurs. Oct 30th at TTI

[Meridel Trimble]

*TOYOTA TECHNOLOGICAL INSTITUTE TALK*

Speaker: Gene Golub
Stanford University
Speaker’s homepage: http://sccm.stanford.edu/faculty/nf-golub.html

Date: Thursday, October 30th, 2003
Time: 12:15pm
Place: Toyota Technological Institute (Press Building – 1427 E. 60th St., 2nd 
Floor)
*LUNCH PROVIDED*

Title: Computing the Shape from Moments

Abstract: We discuss the problem of recovering a planar polygon from its 
measured complex moments. These moments correspond to an indicator function 
defined over the polygon's support. Previous work on this problem gave 
necessary and sufficient conditions for such successful recovery process and 
focused mainly on the case of exact measurements being given. We extend these 
results and treat the same problem in the case where a longer than necessary 
series of noise corrupted moments is given. Similar to methods found in array 
processing, system identification, and signal processing, we discuss a set of 
possible estimation procedures which are based on the Prony and the Pencil 
methods, relate them one to the other, and compare them through simulations. We 
then present an improvement over these methods based on the direct use of the 
Maximum-Likelihood estimator, exploiting the above methods as initialization. 
We show that VarPro algorithm can be used for boost accuracy of the estimated 
vertices. Finally, we show how regularization, and thus Maximum A-posteriori 
Probability estimator could be applied to reflect prior knowledge about the 
recovered polygon. Numerical examples that illustrate the proposed algorithms 
and their performance are shown. 

* Joint work with Peyman Milanfar and Michael Elad

For further information, please contact Meridel Trimble (4-9873/mtrimble at tti-
c.org)

For information on future speakers and events, please consult the TTI Events 
homepage: http://www.tti-c.org/events.shtml