THE REES DISTINGUISHED LECTURER SERIES
Professor Fadil Santosa
Director, Institute for Mathematics and its Applications
School of Mathematics
University of Minnesota
Compressed sensing -- Seeing with less
(Undergraduate Talk)
Thursday, November 6, 2008
116 Gore Hall
3:30 - 4:30
Compressed sensing is a technique for recovering a signal or image from a limited set of sensor data. The method basically allows one to solve a set of linear equations where there are more unknowns than equations. In order to do so, additional information about the unknown is assumed. The presentation discusses some important applications of this technique, an explanation of how it works, and its limitations. Trends in this "hot" area of research will be indicated.
Friday, November 7, 2008
116 Gore Hall
3:30
- 4:30
Progressive addition lenses are prescribed to patients who need correction for both far and near visions. A progressive lens needs to have power that gradually changes from the far vision zone, used for example in driving, and the near vision zone, used for example in reading a map. The basics of optics and lens design will be described. In particular, it will be shown that the problem can be reduced to one of surface design. The surface design problem itself is solved by a variational approach, which can be further simplified by linearization, leading to a fourth order elliptic PDE. Analysis of the resulting equations and development of a computational method are described. Numerical results are presented to illustrate the process of lens design.