Local regularity-based interpolation

Description of the work and motivation A ubiquitous problem in signal processing is to obtain data sampled with the best possible resolution. At the acquisition step, the resolution is limited by various factors such as the physical properties of the captors or the cost. It is therefore desirable to seek methods which would allow to increase the resolution after acquisition. This is useful for instance in medical imaging or target recog-nition. In some applications, one dispose of several low resolution overlapping signals [1]. In more general situations, a single signal is available for superres-olution. Interpolation then requires that the available data be supplemented by some a priori information. Two types of methods have been explored: In the rst, "class-based " one, the signal is assumed to belong to some class, with conditions expressed mainly in the time or frequency domain [3, 5, 10]. This puts constraints on the interpolation, which is usually obtained as the mini-mum of a cost-function. The second type of approaches hypothesizes that the information needed to improve the resolution is local and is present in a clas