M.Sc Student | Spivakovsky Alexander |
---|---|

Subject | Algorithms for Solving Large-Scale Regularized Structured Total Least Squares Problems |

Department | Department of Industrial Engineering and Management |

Supervisor | Professor Amir Beck |

Full Thesis text |

In this work, we seek an estimate to the solution of the linear system **A**b ?*
***b**, where **b** is submitted to noise, and A is submitted to structured
noise. To stabilize the solution, we add a convex regularization function *R*(**x**).
The arising problem is the so-called regularized structured total least squares
(RSTLS) problem.

We develop several algorithms for a smooth and quadratic regularization

*R*(**x**) = *||***Gx***||*^{2}. In
particular, we propose a block-coordinate descent method, and an accelerated
gradient algorithm. The methods have been specially adapted to deal with image
deblurring problems, exploiting fast Fourier/cosine transforms. We also propose
gradient-based methods for the RSTLS problem with nonsmooth regularizer such as
total variation and the l_{1}
norm of a wavelet transform. Several numerical experiments demonstrate the effectiveness
of the suggested algorithms.