A New Design in Iterative Image Deblurring for Improved Robustness and Performance.

In many applications, image deblurring is a pre-requisite to improve the sharpness of an image before it can be further processed. Iterative methods are widely used for deblurring images but care must be taken to ensure that the iterative process is robust, meaning that the process does not diverge and reaches the solution reasonably fast, two goals that sometimes compete against each other. In practice, it remains challenging to choose parameters for the iterative process to be robust. We propose a new approach consisting of relaxed initialization and pixel-wise updates of the step size for iterative methods to achieve robustness. The first novel design of the approach is to modify the initialization of existing iterative methods to stop a noise term from being propagated throughout the iterative process. The second novel design is the introduction of a vectorized step size that is adaptively determined through the iteration to achieve higher stability and accuracy in the whole iterative process. The vectorized step size aims to update each pixel of an image individually, instead of updating all the pixels by the same factor. In this work, we implemented the above designs based on the Landweber method to test and demonstrate the new approach. Test results showed that the new approach can deblur images from noisy observations and achieve a low mean squared error with a more robust performance.