The Landweber iteration and projection onto convex sets

Iterative signal reconstruction and restoration have made considerable use of variations of the Landweber iteration and, more recently, of projection onto convex sets. For circulant systems, the Landweber iteration with a special step size is shown to be equivalent to a variation of the projection method. Based on experimental evidence, it is conjectured that the projection technique has a better convergence rate. Additionally, the projection method makes it easier to combine other a priori information with the basic iteration.