(eng): Finding a point in the intersection of two closed convex sets is a common problem in image processing and other areas. Projections onto convex sets (POCS) is a standard algorithm for finding such a point. Dykstra’s projection algorithm is a well known alternative that finds the point in the intersection closest to a given point. Yet another lesser known alternative is the alternating direction method of multipliers (ADMM) that can be used for both purposes. In this paper we discuss the differences in the convergence of these algorithms in image processing problems. The ADMM applied to finding an arbitrary point in the intersection is much faster than POCS and any algorithm for finding the nearest point in the intersection.\n