Modified Gabor Wavelets for Image Decomposition and Perfect Reconstruction

Abstract

This article presents a scheme for image decomposition and perfect reconstruction based on Gabor wavelets. Gabor functions have been used extensively in areas related to the human visual system due to their localization in space and bandlimited properties. However, since the standard two-sided Gabor functions are not orthogonal and lead to nearly singular Gabor matrices, they have been used in the decomposition, feature extraction, and tracking of images rather than in image reconstruction. In an attempt to reduce the singularity of the Gabor matrix and produce reliable image reconstruction, in this article, the authors used single-sided Gabor functions. Their experiments revealed that the modified Gabor functions can accomplish perfect reconstruction.