INVERSE PROBLEMS IN X-RAY AND GAMMA-RAY ASTRONOMICAL IMAGING

Imaging with mirrors is difficult at high photon energies, and this has led to the development by x- and gamma-ray astronomers of a variety of alternative approaches to forming images. Most of these involve 'coding' the sky brightness distribution, such that a single bright point source at a given position produces a complex but characteristic signature on the detector. The mathematical description of the imaging process, and the advantages and disadvantages of focusing and non-focusing approaches are discussed. The problem of image reconstruction in the focusing case is similar to that in familiar optical imaging applications, though complicated by variations in point spread function with position and energy. We therefore concentrate on the inversion of coded images, which are more characteristic of high-energy astronomy. The design of the coding process, which is crucial to achieving good imaging performance, is discussed, as are techniques for image reconstruction in the case of 'perfect coding', and a variety of remedies for making the best use of imperfectly coded data.