Similarity Recovery From Threshold-Based Sampling Under General Conditions

A mathematical framework for similarity recovery from threshold-based sampling based on the concept of quasiisometry is introduced. The approach leads to a unified model of threshold-based sampling schemes which comprises "send-ondelta" (SOD), "leaky integrate-and-fire" or the psychophysical Weber-Fechner law as examples and gives raise to novel sampling schemes such as "Leaky SOD." As a result, the input and the output spaces become metric spaces being linked by lower and upper bounds under general conditions which go beyond assumptions in the signal recovery context. In particular, the proposed approach allows us to estimate the signal reconstruction error by resampling the reconstructed signal and applying the quasi-isometric distance measure in the sample space.