Nonconvex optimization for image reconstruction

When
Start: 10/06/2010 - 4:15pm
End  : 10/06/2010 - 5:15pm

Category
Colloquium

Speaker
Rick Chartrand Los Alamos National Laboratory

Abstract

In this talk we'll look at two areas where image reconstruction capabilities are dramatically improved by using nonconvex optimization.
The fi rst topic is a fairly new area of applied mathematics, one that includes many exciting results showing that most images and other signals can be reconstructed from many fewer data than previously thought possible, using simple, efficient algorithms. This new and popular fi eld is known as compressive sensing, because the results show that it is possible to directly measure a compressed version of a signal, without knowledge of the signal itself. The many potential applications include reducing exposure time in medical imaging, reducing the data storage/transmission/processing burden on deployed sensor systems, and national security applications.
We'll see how substituting a nonconvex objective function into the convex optimization problem typically used in this fi eld has the eff ect of reducing still further the number of measurements needed to reconstruct a signal. A very surprising result is that simple algorithms, designed only for finding one of the many local minima of the optimization problem, typically find the global minimum.
We'll also look at the topic of image denoising, as an example of a wider class of inverse problems where regularization is used to suppress noise. Using nonconvex regularization functionals lead to better preservation of shapes within images than typical image restoration algorithms.

Where
Millikan 134, Pomona College

Misc. Information

Refreshments served at 3:45 p.m.
Harry Mullikin Room, Millikan 209
The dinner will be hosted by Prof. Stephan Garcia.
If interested in attending, email stephan.garcia@pomona.edu