Speaker:  Misha E. Kilmer

Affiliation:  Tufts University, Dept. of Mathematics

Title:  Krylov Subspace Recycling in Diffuse Optical Tomography


Abstract:

The need to solve a sequence of large-scale linear systems involving matrices 
whose characteristics vary slowly from one subsequent system to the next 
arises frequently in image reconstruction problems.  In tomography applications
(electrical impedance or diffuse optical tomography), for example, one often 
needs a nonlinear forward model in the form of a discretized partial 
differential equation (PDE) to describe the relationship between the desired 
quantity (e.g. a 3D image of the diffusion of light in tissue) and the measured
 data.   To find the desired image requires the solution of a nonlinear 
optimization problem for the unknown voxel values in the image, which in 
turn requires the solution of multiple linear systems (the discretized PDEs) 
-- one or more such systems in each iteration of the optimization algorithm.   

In this talk, we analyze matrix characteristics and techniques for 
reducing the computational complexity of the sequence of systems 
arising in tomography applications.  In particular, we derive strategies 
for recycling Krylov subspace information that exploit properties of the 
application and the nonlinear optimization algorithm to significantly 
reduce the total number of iterations over all linear systems.  Although 
we focus on a particular application, our approach is applicable generally to 
problems where sequences of linear systems must be solved.  Examples illustrate
 the promise of our approach in reducing the overall computational 
complexity of nonlinear image reconstruction problems.