Ibrahim Yavuz

A Method for Reducing the Complexity of Inverse Problems

Friday, December 10, 1999
11:00 AM
410 Dana

Abstract

The regularized least squares methods for the solution of ill-posed inverse prob- lems are summarized, and appropriate references are stated. Additionally, an adap- tive multi-scale algorithm is proposed to solve highly ill-posed inverse problems with fewer degrees of freedom and comparable performance. The algorithm controls the level of detail in the reconstruction by distributing the �ne scale information to the appropriate intervals in the overall estimation interval. The method is applied to a linear inverse problem, namely the reconstruction of a signal from its blurred and noisy version. The results are stated, compared with the regular �ne scale approach and the relevant properties are explained. This treatment is seen as a step for the application of the algorithm to the nonlinear inverse problems where it is forseen to provide a decrease in the complexity of the inversion as well as better convergence in the solution space than the regular approach.

Advisor: Prof. Eric L. Miller