Estimating the CramerRao Bound for Restored Astronomical Observations
Abstract
This work addresses the problem of assigning confidence intervals to estimated photometry data obtained from astronomical observations. The proposed solution is to estimate the CramerRao bound, which is an analytical expression that describes the minimum obtainable mean square error associated with a given estimate of a parameter. This Letter presents a compact and simple form for the bound associated with a linear estimator such as a Wiener filter estimator. A prescription for estimating the variance associated with each element in a restored object was developed using an analytical model for observed data corrupted by either Poisson or Gaussian noise. Both one and twodimensional examples are presented.
 Publication:

The Astrophysical Journal
 Pub Date:
 February 1995
 DOI:
 10.1086/187740
 Bibcode:
 1995ApJ...439L..43Z
 Keywords:

 Astronomical Photometry;
 Error Analysis;
 Image Processing;
 Imaging Techniques;
 Mean Square Values;
 Statistical Analysis;
 Confidence Limits;
 Estimates;
 Image Reconstruction;
 Random Noise;
 Variance (Statistics);
 Wiener Filtering;
 Astrophysics;
 GALAXIES: PHOTOMETRY;
 METHODS: STATISTICAL;
 STARS: IMAGING;
 TECHNIQUES: IMAGE PROCESSING