# Lars Lidvall: Image Deblurring with Regularized Least Squares and Beyond

## Bachelor thesis presentation

**Time: **
Wed 2022-06-08 09.00 - 10.00

**Location: **
Kräftriket, house 6, room 306

**Respondent: **
Lars Lidvall

**Abstract:**

In this report we study the optimization problem least squares minx ∥b − Ax∥ 2 2 with applications to image deblurring. Least squares can be solved directly in four ways: by the normal equation, the pseudoinverse, QR-decomposition and regularization. The theory for these methods are covered in detail. Least squares can be solved iteratively using a gradient descent method. Specifically gradient descent and Polyak heavy ball are covered, with focus on the theory of convergence for these methods. Finally, a direct and an iterative method are compared on a specific example of deblurring, where other ways to deblur are also discussed.