Abstract

Imaging at low-light levels relies on intensity measurements that have a signal-to-noise ratio of $\sqrt{N}$, if N photons are detected at a pixel. Usually, a simple time integration to improve the SNR is not possible because the object being imaged or the measurement system is moving; this results in a loss of high spatial frequency information and possible blur. Examples of imaging techniques are described along with the usual techniques for dealing with the photon-limited data, poor SNR, and blur. Correlation based methods (recovery from Fourier magnitude or bispectral data) provide a solution to some of these problems, in principle, and are outlined. Spectral estimation techniques to restore high spatial frequencies or missing phase information can further improve these images but are very noise sensitive in general. New methods are described that are either explicitly or implicitly regularized and permit reliable image restoration; they are based on minimum norm estimators that can incorporate prior knowledge about the object, if available. Both linear and nonlinear estimators can be defined and the role of the prior knowledge is quite different in the two cases.

© 1991 Optical Society of America