Inverse Problems in Astronomy

In many research fields the basic properties of a system have to be deduced from remotely sensed observations rather than from first-hand on the spot measurements. These remotely sensed data are often difficult to interpret physically because they emerge as severely filtered convolutions of the original source function. The central 'inverse' problem is to transform these data, through integral inversion techniques, into stable and physically meaningful representations of the source. This book gives a general mathematical introduction to the subject and illustrates it with examples and applications in astronomy. The authors outline the classical theory of itegral inversion and illustrate why classical techniques fail, then go on to describe and compare a variety of non-classical techniques. Methods such as regularisation, employing smoothing constraints and the use of a priori information such as non-negativity are carefully explained and applied to contemporary research problems in astronomy. Finally, the way to develop an optimal overall strategy is discussed. This is the first book to address all aspects of inverse problems, from how they occur to their analytic formulation and practical numerical treatments. Enough mathematical detail is incorporated for the text to be self contained. As such it will primarily be of interest to postgraduate and research astronomers and physicists, and to applied mathematicians. Other workers in passive observational studies such as meteorology, and areas of economics and sociology will find chapters on theory and strategy useful. Attention is also drawn to implications of inverse theory for a central tenet in the philosophy of science, namely falsifiability of hypotheses.