Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 750352, 14 pages
Research Article

Digital Image Reconstruction in the Spectral Domain Utilizing the Moore-Penrose Inverse

1Hellenic Transmission System Operator, 18545 Piraeus, Greece
2General Department of Mathematics, Technological Education Institute of Piraeus, 12244 Athens, Greece
3Department of Statistics, Athens University of Economics and Business, 76 Patission Str., 10434 Athens, Greece

Received 17 October 2009; Accepted 19 April 2010

Academic Editor: Panos Liatsis

Copyright © 2010 Spiros Chountasis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The field of image restoration has seen a tremendous growth in interest over the last two decades. The recovery of an original image from degraded observations is a crucial method and finds application in several scientific areas including medical imaging and diagnosis, military surveillance, satellite and astronomical imaging, and remote sensing. The proposed approach presented in this work employs Fourier coefficients for moment-based image analysis. The main contributions of the presented technique, are that the image is first analyzed in orthogonal basis matrix formulation increasing the selectivity on image components, and then transmitted in the spectral domain. After the transmission has taken place, at the receiving end the image is transformed back and reconstructed from a set of its geometrical moments. The calculation of the Moore-Penrose inverse of r×m matrices provides the computation framework of the method. The method has been tested by reconstructing an image represented by an r×m matrix after the removal of blur caused by uniform linear motions. The noise during the transmission process is another issue that is considered in the current work.