Image Representation by the Magnitude of the Discrete Gabor Wavelet Transform

We present an analytical analysis of the representation of images as the magnitudes of their transform with complex-valued Gabor wavelets. Although reconstruction of the image is difficult such a representation is very useful for image understanding purposes. We show that if the sampling of the linear wavelet transform is appropriate then the representation by the nonlinearity introduced by the magnitude is unique up to the sign for almost all images. Finally, numerical experiments with a phase retrieval algorithm show that recognizable versions of the original image can be reconstructed from the magnitudes. Keywords— Gabor wavelets, feature extraction, phase retrieval, Gabor magnitudes, DFT, interpolation, image coding, visual cortex.