A GENERAL BAYESIAN IMAGE RECONSTRUCTION ALGORITHM WITH ENTROPY PRIOR. PRELIMINARY APPLICATION TO HST DATA

Abstract

ABSTRACT This paper describes a general Bayesian iterative algorithm with entropy prior for image reconstruction. It solves the cases of both pure Poisson data and Poisson data with Gaussian readout noise. The algorithm maintains positivity of the solution; it includes case-specific prior information (default map) and flatfield corrections; it removes background and can be acclerated to be faster than the Richardson-Lucy algorithm. In order to determine the hyperparameter that balances the entropy and likelihood terms in the Bayesian approach, we have used a likeliehood cross-validation technique. Cross-validation is more robust than other methods because it is less demanding in terms of the knowledge of exact data characteristics and of the point spread function. We have used the algorithm to reconstruct successfully images obtained in different space and ground based imaging situations. It has been possible to recover most of the original intended capabilities of the Hubble Space Telescope Wide Field and Planetary Camera and Faint Object Camera from images obtained in their present state. Semi-real situations for the future Wide Field Planetary Camera 2 show that even after the repair of the spherical aberration problem, image reconstruction can play a key role in improving the resolution of the cameras, well beyond the design of the Hubble instruments. We also show that ground based images can be reconstructed successfully with the algorithm. A technique which consists of dividing the CCD observations into two frames, with one half the exposure time each, emerges as a recommended procedure for the utilization of the described algorithms. We have compared our technique with two commonly used reconstruction algorithms: the Richardson-Lucy and the Cambridge Maximum Entropy algorithms.