Accelerating the convergence of POCS algorithms by exponential prediction

The convergence of projection on convex sets (POCS) algorithms is monotonic and exponential near the point of convergence, so it is reasonable to predict the limit point using a simple exponential regression. For circumstances where the convergence of each coordinate direction is, in fact, monotonic, this results in a significant acceleration of POCS. However, as we show, the convergence in the coordinates is not monotonic at points sufficiently far from the limit point. We develop an algorithm which takes direction changes into account. An example of POCS on bandlimited reconstruction is presented.