Two New Methods for Retrieving an Image from Noisy, Incomplete Data and Comparison with the Cambridge Maxent Package

Abstract

We consider two new methods for retrieving an image from noisy, incomplete data, based on the principle of maximum entropy. The image is reconstructed by either placing grains one at a time into image pixels, or transferring them between randomly chosen pairs of pixels on the basis of certain deterministic rules. The performance of the methods is tested for an application in x-ray astronomy and compared with that of the Cambridge MaxEnt package. We also demonstrate the application of the Cambridge MaxEnt package to a real problem in x-ray astronomy.

We propose here two simple and effective methods for retrieving an image from noisy, incomplete data, based on the principle of maximum entropy. The essence of the methods is to allocate trial grains one at a time to image pixels or to transfer them between randomly chosen pairs of image pixels on the basis of deterministic rules. We term them the ‘grain allocation method’ (GAM) (Frieden, 1974) and the ‘grain transfer method’ (GTM). The methods are based on an idea first used by Frieden (1974) in processing strongly blurred images.

We first describe the methods and investigate their performance in analyzing images from a proposed astronomical 1-d imaging instrument. The results are compared with those obtained using the Cambridge MaxEnt package (Skilling and Bryan, 1983). Second, we consider retrieval of images from real data, obtained by the TTM instrument, a 2-d coded mask x-ray telescope (Skinner, 1988) on the Kvant module of the Mir space station. This is the first application of the MaxEnt package to processing images from coded mask x-ray telescopes.