Image reconstruction from zero crossings

This study is concerned with the information in zero crossings (ZC) of images. Logan's conditions, specifying when a one-dimensional signal may be recovered (within a multiplicative constant) from its ZC, are extended for various cases of two-dimensional signals. An algorithm is implemented in reconstruction of context-free band-pass images. It is also successfully applied in reconstruction of contextual images by first dissecting the image into appropriate bandpass-band-limited two-dimensional signals. In almost all cases of spectrum confined to less than an octave in one dimension, the reconstruction algorithm converges, whereas it does not converge for any signal exceeding one octave in bandwidth. This paper substantiates the proposition that images are well represented by the partial information confined to ZC.