Least Squares Algorithms for Box-Constrained Image Deblurring

Abstract

Image deblurring problems are often solved by finding minimizer of a suitable objective function. However, in practice, there are constraints in the minimization process. In this thesis, we consider an image deblurring model and discuss several optimization methods for the box-constrained minimization problems. Furthermore, we compare the complexity of them. Among them, a new gradient based approach, ISTA, is noteworthy. However, gradient based algorithms are known to converge quite slowly. Hence we present a two-step algorithm, FISTA, which preserves the computational simplicity of ISTA, but global convergence rate is significantly better. Numerical experiments for each methods are also included.