Blur Models Suitable for Representation by

Hierarchical Structured Matrices in Image Reconstruction

Collaborative Research Experience for Undergraduates

We have received funding from the CDC and CRA-W to complete a project in the 2011-2012 academic year. We are very grateful to the CDC and CRA-W for this opportunity. Here is some information about our project.

Project Objective:

Restoration of blurred images is a continuous research topic now in days.  Satellite images are affected by atmospheric turbulence and noise.  Blurred images are represented by the matrix equation Ax=b, where A is the blur matrix, x is the restored image and b is the distorted blurred image.    Our research objective is finding blur operators that can be represented by hierarchical structured matrices or HSM. Once blur operators have been found, they will be rewritten in hierarchical structured matrices. Iterative techniques are sometimes better to use, due to the high cost with direct inverse methods. These structured matrices are used as an approximate and basis for preconditioned iterative methods.