Two iterative methods for reverse image filtering

We consider the problem of recovering an original image x from its filtered version y = f ( x ) , assuming that the internal structure of the filter f ( · ) is unknown to us (i.e., we can only query the filter as a black-box and, for example, cannot invert it). We present two new iterative methods to attack the problem, analyze, and evaluate them on various smoothing and edge-preserving image filters.