Preconditioning Strategies for a Nonnegatively Constrained
Steepest Descent Algorithm
J. Bardsley and J. Nagy
A class of ill-posed inverse problems that arises in astronomical
imaging is considered. An iterative steepest descent method for
regular least squares problems which constrains the solution to be
nonnegative is presented. A careful consideration of the noise
statistics that arise from the use of a CCD camera for data
generation motivates the extension of this algorithm for use on
weighted least squares problems. Preconditioning strategies are
examined for both algorithms, and it is shown that in order to
preserve noise statistics, preconditioners must be highly
structured. Examples from astronomical imaging are used to
illustrate behavior of the methods.