International Journal of Wavelets, Multiresolution and Information Processing Vol. 4, No. 1 (2006) 105–118 c  World Scientific Publishing Company WAVELET FUSION: A TOOL TO BREAK THE LIMITS ON LMMSE IMAGE SUPER-RESOLUTION S. E. EL-KHAMY Department of Electrical Engineering, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt elkhamy@ieee.org M. M. HADHOUD Department of Information Technology, Faculty of Computers and Information, Menoufia University 32511, Shebin Elkom, Egypt mmhadhoud@yahoo.com M. I. DESSOUKY, B. M. SALAM and F. E. ABD EL-SAMIE * Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University 32952, Menouf, Egypt * fathi sayed@yahoo.com Received 11 August 2004 Revised 28 July 2005 This paper presents a wavelet-based computationally efficient implementation of the Lin- ear Minimum Mean Square Error (LMMSE) algorithm in image super-resolution. The image super-resolution reconstruction problem is well-known to be an ill-posed inverse problem of large dimensions. The LMMSE estimator to be implemented in the image super-resolution reconstruction problem requires an inversion of a very large dimension matrix, which is practically impossible. Our suggested implementation is based on break- ing the problem into four consecutive steps, a registration step, a multi-channel LMMSE restoration step, a wavelet-based image fusion step and an LMMSE image interpolation step. The objective of the wavelet fusion step is to integrate the data obtained from each observation into a single image, which is then interpolated to give a high-resolution image. The paper explains the implementation of each step. The proposed implementa- tion has succeeded in obtaining a high-resolution image from multiple degraded obser- vations with a high PSNR. The computation time of the suggested implementation is small when compared to traditional iterative image super-resolution algorithms. Keywords : Wavelet fusion; LMMSE super-resolution; multi-channel restoration; LMMSE interpolation. AMS Subject Classification: 22E46, 53C35, 57S20 105