Degree Name

Doctor of Philosophy


School of Electrical, Computer and Telecommunications Engineering


Image restoration methods attempt to remove the noise and blurring that occur during image capture with the aim of producing a more accurate representation of the original scene. First becoming popular among scientist involved in space exploration, the application of image restoration methods rapidly spread to other areas such as medical imaging, where it is used as a tool for improved patient diagnosis. Although image restoration is a mature field of research, significant progress in this field is continually being made.

The combination of unknown random noise and blurring make the image restoration problem an ill-posed inverse problem. To create a well-posed problem, it is essential to incorporate additional information about the ideal image via regularization methods. State-of-the-art regularization methods utilize nonlinear image priors. This means that the image restoration problem is most accurately expressed as a nonlinear optimization problem with inequality constraints.

It has traditionally been diffcult to solve nonlinear image restoration problems that have inequality constraints. As a result, a great deal of research has focused on developing algorithms for solving unconstrained nonlinear restoration problems. These include variable splitting, two-step, and Bregman iterative algorithms. In this thesis, the nonlinear convex image restoration problem with inequality constraints is reformulated as a variational inequality problem. The variational inequality problem is then solved using a dynamical systems approach. This approach simultaneously computes the restored image and an adaptive regularization parameter.

The proposed variational inequality approach to image restoration is also extended to perform region-based regularization. Region-based regularization methods use contextual information to calculate a spatially adaptive regularization parameter for each image region. Using the new theoretical results described in compressive sampling theory, the proposed region-based restoration method performs selective deconvolution of image coefficients. This is shown to provide improved restoration performance, suppressing noise amplification without adversely affecting the restoration of edges.

Multi-frame image restoration problems are also solved using the proposed variational inequality approach. The increased development and use of hybrid and stereo cameras has highlighted the need for effective multi-frame restoration methods. However, standard methods fail to exploit image correlations if the scene in each exposure changes. In this thesis, extended isotropic and anisotropic total variation regularizers are developed to solve this problem. Using these regularizers, a multi-frame restoration method is presented. The proposed method simultaneously restores the degraded images and calculates an adaptive regularization parameter for each image.

Finally, a bi-level programming approach to image restoration is presented. A limitation of standard restoration methods is that no attempt is made to explicitly reduce the amount of noise in the degraded image before performing image deblurring. Instead, noise is removed implicitly by the regularizer, at the cost of image fidelity. To rectify this problem, restoration methods have been developed to decouple denoising and deblurring into separate steps. In this thesis, we employ bi-level programming methods for this purpose. These methods are characterized by having separate upper-level and lower-level objective functions. By solving both objective functions, the proposed method simultaneously denoises the observed image and deblurs the resulting denoised image. This is shown to provide state-of-the-art performance.