The Linear Vector Space Theory of Unfolding

Abstract

Abstract : The problem of unfolding a spectrum is treated by the methods of linear vector space theory. For a system with a finite number of measurements consisting of the outputs from detectors with known responses, some part of the unknown spectrum cannot be inferred. One may approximate the unknown spectrum with a finite expansion in terms of some arbitrary set of functions w sub n (E). The relationships between the various solutions obtained by using different sets of w sub n (E) functions are explored, and it is shown that the solution obtained by allowing the w sub n (E) to be the response functions themselves displays some unique and desirable properties. Among these properties is an insensitivity to small errors in the measured outputs from the detectors and in the analytic response functions used to describe the true detector responses. (Author)