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

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 x m matrices provides the computation framework of the method. The method has been tested by reconstructing an image represented by an r x 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.