Image representation by zero and sine-wave crossings

Abstract

Signal representation by its points of crossing of a reference signal is considered with emphasis on applications to images. Some results that are elaborated for the representation of one-dimensional signals by their sine-wave crossings are extended and applied to images. The issue of the stability of the reconstruction algorithms is examined through derivation of bounds on the mean-square error caused by inaccuracies in the determination of crossing locations and by the effect of out-of-band energy. These bounds highlight the dependence of the reconstruction error on major parameters of the underlying signal and the reference sine wave. Computational results on images reconstructed from their sine-wave crossings support the theoretical results and indicate that the bounds are tight. The representation of signals by their crossings of a reference signal is further examined in the context of a general framework of unique representation wherein the signal is modeled as a sample path of an ergodic band-limited random process. The idea of a scheme for signal representation that is almost stable in a probabilistic Sence is introduced and discussed.