On the Danger of Applying Statistical Reconstruction Methods in the Case of Missing Phase Information

Abstract

The use of entropy as a basis for object/image reconstruction procedures 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 applications, 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 conclusions. Indeed, we shall primarily be concerned here with situations for which there is no ‘correct’ solution. In such situations it is pointless to speak of ‘safe’ object reconstruction algorithms. The important point here is that the user of a statistically based ‘object reconstruction algorithm’ may be totally ignorant of whether or not he is working in this régime.