Distributed Coding of Shifts Using the DFT Phase

In this paper we consider the problem of image encoding with side information at the decoder, where the side information is an integer shifted version of the image at the encoder. The encoder is asked to send the shift of its own image with respect to the side information which is only available at the decoder. We propose a solution based on the encoding of the phase sign of the DFT coefficients, taken at exponentially spaced positions. We first introduce the method under ideal hypothesis, i.e. noiseless conditions without border effects, giving a theoretical foundation to the technique. Then, we consider the more realistic case of noisy images with border effects, showing the effectiveness of the proposed method.