Superresolution imaging : models and algorithms

Abstract

In this thesis, two types of super-resolution imaging models were presented: a linear type model using Laplacian matrix as a regularization, and a non-linear type model using total variation (TV) term as a regularization. In the literatures, two types of imaging systems are usually considered: a near imaging and a far imaging. In the near imaging system, the blurring from optical devices is considered, whereas in the far imaging system, the blurring from the environmental factors is considered. In this thesis, two new models called field models, which generalize both of the above imaging systems, were presented. In these new models, the high-resolution restored image was obtained by using a maximum-a-posteriori (MAP) estimation technique with a Gaussian prior. The linearity of this model comes from the use of the Laplacian matrix in the regularization. In the first medium model, the observed low-resolution images were assumed to be first blurred by the environmental factors, then downsampled, and finally blurred by the optical devices. In the second medium model, the observed low-resolution images were assumed to be blurred by the environmental factors, then blurred by the optical devices, and finally downsampled. The observed images were all assumed to contain noises. The periodic boundary condition and the zero boundary condition were considered in the blurring matrix. By using a suitable trigonometric transforms to simplify the coefficient matrix, the Neumann boundary condition, which gives better results than these boundary conditions, can be also considered in all these four models which are Laplacian-based models. For the TV-based model, a unified super-resolution model was presented. The idea is based on that missing pixels of the observed images can be found if they are mapped into the high-resolution image grid and the total variation (TV) inpainting technique is used to find them. So roughly speaking, a super-resolution imaging model was combined with a TV inpainting model. Furthermore, an extra missing region such as scratches in observed images was allowed in this model. Several observation models, which have been considered by some other researchers, were included by this unified model. The non-linearity comes from the TV regularization. A fast algorithm based on the fixed-point iterations and preconditioning technique with factorized sparse inverse preconditioner (FSIP) was developed to solve the problem. The proposed algorithm is faster than the time marching scheme commonly used to solve the TV type regularization problem. Furthermore, the TV super-resolution model was modified to obtain a super-resolution image by using a sequence of zoomed images. Numerical results were presented to illustrate the proposed algorithm in different models. They reveal that high quality of the super-resolution images can be obtained by the proposed models.