Convexly constrained linear inverse problems: Iterative least-squares and regularization

In this paper, we consider regularization of ill-posed linear inverse problems when accompanied by convex and closed constraints. After briefly discussing the well posedness of the inverse problem, we present three new iterative algorithms. First, an iterative method to compute the minimum norm least-squares solution is presented, and its strong convergence is proved. The second algorithm computes a Tikhonov-regularized solution for a given regularization parameter. Last, we present a stopping rule to obtain a regularization scheme for the linear operator. Asymptotic properties of the rule are studied. Constrained Laplace inversion is used to illustrate the use of the proposed stopping rule.