Iterative Algorithms With Fast Convergence-Rates In Nonlinear Image-Restoration

In this paper, the applications of the iterative Gauss-Newton (GN) approach in nonlinear image restoration are considered. The convergence properties of a general class of nonlinear iterative algorithm are studied through the Global Convergence Theorem (GCT). The iterative GN algorithm for the solution of the least-squares optimization problem is presented. The computational complexity of this algorithm is enormous, making its implementation very difficult in practical applications. Structural modifications are introduced, which drastically reduce the computational complexity while preserving the convergence rate of the GN algorithm. With the structural modifications, the GN algorithm becomes particularly useful in nonlinear optimization problems. The convergence properties of the algorithms introduced are readily derived, on the basis of the generalized analysis and the GCT. The applications of these algorithms on practical problems, is demonstrated through an example.