Donald C. Wells

Restoring with maximum entropy. III. Poisson sources and backgrounds

The maximum entropy (ME) restoring formalism has previously been derived under the assumptions of (i) zero background and (ii) additive noise in the image. However, the noise in the signals from many modern image detectors is actually Poisson, i.e., dominated by single-photon statistics. Hence, the noise is no longer additive. Particularly in astronomy, it is often accurate to model the image as being composed of two fundamental Poisson features: (i) a component due to a smoothly varying background image, such as caused by interstellar dust, plus (ii) a superimposed component due to an unknown array of point and line sources (stars, galactic arms, etc.). The latter is termed the “foreground image” since it contains the principal object information sought by the viewer. We include in the background all physical backgrounds, such as the night sky, as well as the mathematical background formed by lower-frequency components of the principal image structure. The role played by the background, which may be separately and easily estimated since it is smooth, is to pointwise modify the known noise statistics in the foreground image according to how strong the background is. Given the estimated background, a maximum-likelihood restoring formula was derived for the foreground image. We applied this approach to some one-dimensional simulations and to some real astronomical imagery. Results are consistent with the maximum-likelihood and Poisson hypotheses: i.e., where the background is high and consequently contributes much noise to the observed image, a restored star is broader and smoother than where the background is low. This nonisoplanatic behavior is desirable since it permits extra resolution only where the noise is sufficiently low to reliably permit it.

Nonlinear Image Restoration: What We Have Learned

The first nonlinear image restoration algorithms were devised a little more than a decade ago. The subsequent development of this subject by a number of research workers has produced a rich and fascinating literature. But because much of it is located in unfamiliar journals and publications, many astronomical newcomers to the field may be unaware of this work. It has been known since the discovery of the nonlinear image restoration techniques that they have pronounced performance advantages over linear restoration techniques in astronomical applications, and many of the published examples of nonlinear restorations of imagery have involved astronomical data. The new image detector systems appearing in optical astronomy, particularly CCDs, produce images of a quality that fully justifies the employment of sophisticated algorithms for the extraction of the maximum amount of information from the data. This review of the literature has been prepared in the hope that it will encourage new astronomical workers to enter into it.

Interactive Image Analysis for Astronomers

During the last five years, ground-based astronomers have seeh some remarkable changes in the image data available to us for scientific analysis. Our image intensifiers have been greatly improved, and new photographic emulsions (Kodak IIIa-J and IIIa-F) with higher detective quantum efficiency and greater storage capacity have been introduced. Precise microdensitometers with digital output and adequate speed have become commercially available, so that we are now able to convert essentially all of the information from a photographic emnulsion into digital form. Integrating digital television cameras and silicon diode arrays with excellent sensitivity and good cosmetic quality are now replacing photographic plates in many ground-based astronomical observations. Meanwhile, radio astronomers have devised their own scheme–aperture synthesis–for recording radio-wavelength digital pictures of the sky. But improvements in digital image-handling technology are needed if we are to fully exploit the scientific research possibilities created by these new detector systems. One step in this direction is the Interactive Picture Processing System (IPPS) developed at the Kitt Peak National Observatory.

DIVISION XII / COMMISSION 5 / WORKING GROUP FITS DATA FORMAT

The Working Group FITS (WG-FITS) is the international control authority for the Flexible Image Transport System (FITS) data format. The WG-FITS was formed in 1988 by a formal resolution of the IAU XX General Assembly in Baltimore (MD, USA), 1988, to maintain the existing FITS standards and to approve future extensions to FITS.

DIVISION XII / COMMISSON 5 / WORKING GROUP: FITS

The business meeting began with a brief review of the current rules and procedures of the WG, which are documented on the WG web page. Four regional FITS committees have been established by the WG, covering North American, Europe, Japan, and Australian/New Zealand, to provide advice to the WG on pending proposals. While it is recognized that this committee structure might need to be revised to provide representation to other regions, the current system is working well, and there were no motions to make any changes at this time.

The Mode Filter: A Nonlinear Image Processing Operator

The estimation of the low spatial frequency background signals in astronomical digital imagery is a fundamental problem of all the photometric techniques used with such imagery. This problem is particularly acute when numerous foreground sources (stars, galaxies, etc.) are present, because the statistical distribution of background pixel values is skewed. All linear lowpass filters (e.g., the running mean) produce biased estimates in this situation, and the result is biased photometry of the foreground sources, which can produce subtle errors in luminosity functions and other results derived from the photometry (e.g., the apparent number of faint sources may be inversely related to the number of bright sources). These problems can be mostly avoided in many situations by estimating the mode of the skewed distribution rather than the mean. This paper describes a lowpass-filter program which computes an estimate of the mode of the image values in a region around each pixel of an image.