Super-Resolution Image Restoration from Blurred Low-Resolution Images

In this paper, we study the problem of reconstructing a high-resolution image from several blurred low-resolution image frames. The image frames consist of decimated, blurred and noisy versions of the high-resolution image. The high-resolution image is modeled as a Markov random field (MRF), and a maximum a posteriori (MAP) estimation technique is used for the restoration. We show that with the periodic boundary condition, the high-resolution image can be restored efficiently by using fast Fourier transforms. We also apply the preconditioned conjugate gradient method to restore the high-resolution image. Computer simulations are given to illustrate the effectiveness of the proposed method.Research supported in part by Hong Kong Research Grants Council Grant Nos. HKU 7130/02P, 7046/03P, 7035/04P and HKU CRCG Grant No. 10205775.Michael K. Ng is a Professor of the Mathematics Department, Hong Kong Baptist University, and is Adjunct Research Fellow in the E-Business Technology Institute at the University of Hong Kong. Michael was a Research Fellow (1995–1997) of Computer Sciences Laboratory, Australian National University, and an Assistant/Associate Professor (1997–2005) of the Mathematics Department, the University of Hong Kong before joining Hong Kong Baptist University in 2005. Michael was one of the finalists and honourable mention of Householder Award IX, in 1996 at Switzerland, and he obtained an excellent young researcher’s presentation at Nanjing International Conference on Optimization and Numerical Algebra, 1999. In 2001, he has been selected as one of the recipients of the Outstanding Young Researcher Award of the University of Hong Kong. Michael has published and edited several books, and published extensively in international journals and conferences, and has organized and served in many international conferences. Now he serves on the editorial boards of SIAM Journal on Scientific Computing, Numerical Linear Algebra with Applications, Multidimensional Systems and Signal Processing, International Journal of Computational Science and Engineering, Numerical Mathematics, A journal of Chinese Universities (English Series), and several special issues of the international journals.Andy C. Yau received the undergraduate (1998–2001) from the Chinese University of Hong Kong, and the M.Phil degree (2002–2004) from the University of Hong Kong. He is a PhD student of the University of Hong Kong. His research area is image processing and scientific computing.