A Newton algorithm for convex constrained reconstruction

A quadratically convergent iterative algorithm (Newton algorithm) for signal recovery from linear measurements is presented. Prior information is expressed as a convex set and the signal is constrained to lie in this set. Central to the Newton algorithm is the derivative of the nonlinear projection operator onto a convex set. A new general mathematical result for the existence and construction of the derivative of the projection operator is obtained for a class of convex sets. This result is then used to give the Newton algorithm for the signal recovery problem. The algorithm is demonstrated in a medical imaging application.<>