ON THE DANGER OF APPLYING STATISTICAL RECONSTRUCTION METHODS IN THE CASE OF MISSING PHASE INFORMATION J.C. Dainty, M.A. Fiddy and A.H. Greenaway Department of Physics, Queen Elizabeth College, Campden Hill Road, London W8 7AH, U.K. Departement d'Astrophysique, Universite de Nice, Pare Valrose, 06034 Nice Cedex, FRANCE. I. INTRODUCTION The use of entropy as a basis for object/image reconstruction proT cedures is not new , but with the appearance of new, faster algorithms the actual use of these algorithms for the reconstruction of objects from 'real' data is likely to increase. The purpose of this contribution is not to discourage such applic- ations, but to illustrate that, under certain circumstances, there is a need for caution in interpreting the results obtained from such algorithms. Specifically, we shall show that the application of statistical methods to problems of object reconstruction, in situations where only the modulus of the object Fourier transform is known, could lead to wholly false con- clusions. Indeed, we shall primarily be concerned here with situations for which there is no 'aovveot' solution. In such situations it is point- less to speak of 'safe' object reconstruction algorithms. The important point here is that the user of a statistically based 'object reconstruct- ion algorithm' may be totally ignorant of whether or not he is working in this regime. The problem thus formulated, i.e. the reconstruction of an object from its autocorrelation, is the so-called phase problem, which occurs in fields as diverse as electron microscopy, radio and optical astronomy and X-ray diffraction. It has long been recognised that, in general, the solution to such problems cannot be unique. In all cases it is nec- essary to provide additional information, such as the phase of the object Fourier transform, in order to resolve the inherent ambiguities associated with this problem. The key point to this paper, is that to speak of 'safe' reconstruct- ion procedures, one must show that the problem posed has a unique solution. If one can show that this is indeed the case, any algorithm which yields a solution consistent with the defined problem will give the correct solution. In this sense all such algorithms may be regarded as 'safe'. 95 C. van Schooneveld fed.), Image Formation from Coherence Functions in Astronomy, 95-101. Copyright © 1979 by D. Reidel Publishing Company use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0252921100074789 Downloaded from https://www.cambridge.org/core. IP address: 207.90.37.89, on 12 Jun 2019 at 11:16:02, subject to the Cambridge Core terms of