Reconstruction of two-dimensional signals from level crossings

Recent results indicate that reconstruction of two-dimensional signals from crossings of one level requires, in theory and practice, extreme accuracy in positions of the samples. The representation of signals with one-level crossings can be viewed as a tradeoff between bandwidth and dynamic range, in the sense that if the available bandwidth is sufficient to preserve the level crossings accurately, then the dynamic range requirements are significantly reduced. On the other hand, representation of signals by their samples at the Nyquist rate can be considered as requiring relatively small bandwidth and large dynamic range, because, at least in theory, amplitude information at prespecified points is needed, to infinite precision. An overview of existing results in zero crossing representation is presented, and a number of new results on sampling schemes for reconstruction from multiple-level threshold crossing are developed. The quantization characteristics of these sampling schemes appear to lie between those of Nyquist sampling and one-level crossing representations, thus bridging the gap between explicit Nyquist sampling and implicit one-level crossing sampling strategies.>