Image Decomposition and Reconstruction using Two-Dimensional Complex-Valued Gabor Wavelets

This paper presents a scheme for image decomposition and reconstruction, using complex 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 and feature extraction 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 paper, we show that a single-sided Gabor function can accomplish both, with the reconstruction residual error being very small (PSNR of at least 300 dB).