Generalized cross-validation as a stopping rule for the Richardson-Lucy algorithm
✍ Scribed by Stanley J. Reeves
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 488 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0899-9457
No coin nor oath required. For personal study only.
✦ Synopsis
The Richardson-Lucy (R-L) algorithm has been widely used to restore degraded astronomical images. This algorithm is nothing more than the expectation-maximization (EM) algorithm applied to Poisson data. The R-L method is iterative in nature and converges to a (possibly local) maximum of the likelihood function. Unfortunately, because of the ill-conditioned nature of the problem, this maximum likelihood estimate may actually be a very poor restoration. One way to prevent degradation of the restoration is to stop the iteration before it reaches convergence. A number of methods have been proposed for determining the optimal stopping point-the point that provides the best trade-off between restoring the image and amplifying the noise. Cross-validation (CV) has recently been proposed as an advantageous method for determining the optimal stopping point. We propose a different form of CV based on generalized cross-validation (GCV) that overcomes some of the difficulties of CV. We derive a GCV-based criterion for the R-L algorithm that can be efficiently evaluated at each iteration. We present examples displaying the power of the stopping rule and discuss the abilities and shortcomings of the method.