Uniform motion blur in Poissonian noise: blur/noise tradeoff

In this paper we consider the restoration of images corrupted by both uniform motion blur and Poissonian noise. We formulate an image formation model that explicitly takes into account the length of the blur point-spread function and the noise level as functions of the exposure time. Further, we present an analysis of the achievable restoration performance by showing how the root mean squared error varies with respect to the exposure time. It turns out that the worst situations are represented by either too short or too long exposure times. In between there exists an optimal exposure time that maximizes the restoration performance, balancing the amount of blur and noise in the observation. We justify such result through a mathematical analysis of the signal-to-noise ratio in Fourier domain; this study is then validated by deblurring synthetic data as well as camera raw data.