Image reconstruction from zeros of the z-transform

A new method for reconstructing a compact pixellated image from the zeros of its z-transform is presented. Particular zeros are chosen from the infinity which form the zero sheet of the z-transform in order to construct samples (spaced according to the Nyquist criterion) in complex Fourier space. Inverse discrete Fourier transformation and division by a known exponential weighting function reconstructs the image to within an arbitrary multiplicative complex constant. The method allows greater flexibility in the use of the zero sheet in deconvolution and phase retrieval than is possible with methods which use only the Fourier components at real spatial frequencies. Images as large as 64×64 pixels have been successfully reconstructed using the technique; it is equally applicable to both real and complex images. The computational complexity of the method is O(N³)