Solution of ill-posed inverse problems pertaining to signal restoration

Solution of ill-posed inverse problems pertaining to signal restoration

Thu, 08/03/2012
14:00 		Professor Rosie Renaut (Arizona State University) Computational Mathematics and Applications Add to calendar Gibson Grd floor SR
Solution of ill-posed inverse problems pertaining to signal restoration
In this talk I review the use of the spectral decomposition for understanding the solution of ill-posed inverse problems. It is immediate to see that regularization is needed in order to find stable solutions. These solutions, however, do not typically allow reconstruction of signal features such as edges. Generalized regularization assists but is still insufficient and methods of total variation are commonly suggested as an alternative. In the talk I consider application of standard approaches from Tikhonov regularization for finding appropriate regularization parameters in the total variation augmented Lagrangian implementations. Areas for future research will be considered.