Some new methods for restoring images of faint objects

Abstract

New methods are reviewed for forming images of faint objects. Camera data are modeled as a doubly stochastic Poisson process to account for quantum limitations and apparent jitter from propagation of light through weak turbulence, camera vibration, and tracking errors. The new methods fall into two categories depending on the model that can be assumed for the jitter. An approach that generalizes the Richardson-Lucy iteration for image restoration from quantum-limited data is obtained via statistical estimation theory when a stochastic model for the jitter is available. Faint-object (i.e., quantum-limited) and bright-object alternatives to the phase retrieval methods of Fienup for second-order correlation data and of Weigelt for third-order correlation data are obtained when the jitter is assumed to be piecewise constant during snapshots of the object.