The duality of two recent image interpolation methods

The problem of determining unknown sets of n pixels in N×N images, band-limited in the sense that all but r<N² harmonics of their DFT vanish, has captured the attention of many authors. We show that two recently proposed approaches to this problem, which originally seem to arise out of quite distinct ideas, are in fact closely related and the dual of each other. The impact of this result is the following: it clarifies the connections between two apparently unrelated methods, providing a unified way of looking at them, and makes some results originally developed for one of the methods available for both. It also opens new possibilities for obtaining “best-possible” formulations of the image interpolation problem, of minimum dimension, and comparable stability