

Paper: 
Statistical Image Analysis: Deconvolution Done Correctly 
Volume: 
217, Imaging at Radio Through Submillimeter Wavelengths 
Page: 
224 
Authors: 
Rydbeck, G. 
Abstract: 
The basic concepts necessary for a statistical approach to image analysis are discussed. It is demonstrated that ones knowledge of an observed image can be described by an ensemble of possible true imagages. To see how this ensemble is obtained, assume first that observations are corrupted by a known type of noise and made with a certain telescope beam and that they result in a map of intensities. Assume now that it is possible to define, in a general sense, an unbiased ensemble of {all possible} intensity maps. One may call this the prior ensemble of maps. Pick randomly a set of maps from the infinte series of maps in the prior ensemble. Then observe all these maps as above. If the set is large enough a subset will have observed pixel intensities which are equal to the actual observed pixel intensities. This subset is the ensemble of possible 'true' map intensities as constrained by the observations. >From this subset one may then form pixel mean intensities and their variance. A solution to the difficult and well known problem of defining the unbiased prior ensemble is suggested, and the resulting approximate equations for solving the pixel mean image intensities are given The power of the equations is tested on simulated observations of model distribution. It is seen, as expected, that spectral structure help improve resolution. Finally maps resulting from application of the method to observed CO emission from the galaxies M51 and CIRCINUS are shown. 



