The active-set method for nonnegative regularization of linear ill-posed problems

In this work, we analyze the behavior of the active-set method for the nonnegative regularization of discrete ill-posed problems. In many applications, the solution of a linear ill-posed problem is known to be nonnegative. Standard Tikhonov regularization often provides an approximated solution with negative entries. We apply the activeset method to find a nonnegative approximate solution of the linear system starting from the Tikhonov regularized one. Our numerical experiments show that the activeset method is effective in reducing the oscillations in the Tikhonov regularized solution and in providing a nonnegative regularized solution of the original linear system. 2005 Elsevier Inc. All rights reserved.