On a mathematical theory of coded exposure

Abstract

This paper proposes a mathematical model and formalism to study coded exposure (flutter shutter) cameras. The model includes the Poisson photon (shot) noise as well as any additive (readout) noise of finite variance. This is an improvement compared to our previous work that only considered the Poisson noise. Closed formulae for the mean square error and signal to noise ratio of the coded exposure method are given. These formulae take into account for the whole imaging chain, i.e., the Poisson photon (shot) noise, any additive (readout) noise of finite variance as well as the deconvolution and are valid for any exposure code. Our formalism allows us to provide a curve that gives an absolute upper bound for the gain of any coded exposure camera in function of the temporal sampling of the code. The gain is to be understood in terms of mean square error (or equivalently in terms of signal to noise ratio), with respect to a snapshot (a standard camera).