Conjugate Gradient Methods For Super-resolution Image Reconstruction Problems

This thesis consists of two chapters. The main contents are as follows.In chapter 1, we give some introductory materials. The developing of the construction of high-resolution and super-resolution images from multiple un-dersample, shifted, degraded frames with subpixel displacement is introduced. Some related symbols, conceptions and theorems are given. Two iteration methods conjugate gradient (CG) method and preconditioned conjugate gra-dient(PCG) method are also introduced. We also introduce some background of this thesis, list some important results.In Chapter 2, we consider using CGE method (i.e. CG with early stop criterion) to solve the super-resolution image reconstruction problem. The PCG method with cosine transform preconditioner is efficient for solving many cases of the super-resolution image reconstruction problem, while it is inefficient when there are two low-resolution images taken from sensors with diagonal subpixel displacement (diagonal sensors). In this thesis, we discuss the use of the CGE method to the super-resolution image reconstruction problem. Numerical results are given to show that the early stop method is very efficient for the case of diagonal sensors.