Image Reconstruction from Gabor Magnitudes

We present an analysis of the representation of images as the magnitudes of their transform with complex-valued Gabor wavelets. Such a representation is very useful for image understanding purposes and serves as a model for an early stage of human visual processing. We show that if the sampling of the wavelet transform is appropriate then the reconstruction from the magnitudes is unique up to the sign for almost all images. We also present an iterative reconstruction algorithm derived from the ideas of the proof, which yields very good reconstruction up to the sign and minor numerical errors in the very low frequencies.

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