Evaluating Novel Matrix-Vector Multiplication Strategies in the LSTRS and TRUSTµ Methods for Large-Scale Trust-Region Subproblems and Regularization

In the regularization of ill-posed problems from image restoration, where we want to recover an image from blurred and noisy data, there are many methods that can be useful. Among those, the TRUSTmu method proposed in Rojas and Steihaug, 2002, is an efficient method for solving large-scale regularization problems with additional non-negativity constraints and is based on matrix-vector multiplication. The idea of TRUSTmu method is to solve a sequence of Trust-Region-Subproblems using the method LSTRS from Rojas, Santos and Sorensen, 2008. The goal of this project was to evaluate the performance and accuracy of LSTRS and TRUSTmu method when the following three different approaches to compute matrix-vector multiplication were used: Fast Monte Carlo Algorithms, GPU computing, and parallel computing. In order to work on the experiments, we developed a MATLAB software implemented the TRUSTmu method and used the LSTRS software from Rojas, Santos and Sorensen, 2008. The TRUSTmu software provided an interface that allows the user to pass the input matrix as an array or as a function for computing matrix-vector products, possibly with parameters. One of the application of this software was in image restoration field to recover images from blurred and noisy data.

Subject

MATLAB
regularization
large-scale
TRUSTµ
LSTRS
matrix-vector product
Fast Monte Carlo algorithm
GPU computation
parallel computing

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master thesis

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