TWO-LEVEL METHOD FOR IMAGE DEBLURRING PROBLEM

This proposal is for 18-month project submitted under the "KFUPM Internal Research Grant. The proposed research will focus on the efficient and robust numerical technique which remove blurry and noise from digital images. Image deblurring model with computationally expensive regularization such as total fractional-order variation (TFOV) and mean curvature (MC) are used to improve the quality of the deblurred images. These models are very efficient in preserving edges and removing staircase effect and other nice properties. However, the associated Euler-Lagrange equations involve dense matrices or high order derivatives which complicate developing an efficient numerical algorithm. In this research work, we present an efficient and robust Two-Level method to overcome these difficulties. The Two-Level method started by reducing the problem to one small, non-linear system on image with small number of pixels (Level-I) and one less expensive linear system with large number of pixels (Level-II). The derivation of the optimal regularization parameters will be studied. Numerical experiments on several images will also provide to demonstrate the efficiency of the Two-Level method. This study will require writing a Matlab computer code, and testing it on different digital images. It is expected that this research will be of significance to the researches in the area of digital images such as medical images technologies and in the area of image processing in general. Upon the completion of this research, the expected outcomes are algorithms, Matlab codes, and manuscript to be submitted for journal publication in addition to the research technical report.