Local regularity-based interpolation

Abstract : 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 recognition. In some applications, one dispose of several low resolution overlapping signals [1]. In more general situations, a single signal is available for superresolution. 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 minimum 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 class of similar signals [2, 4]. This type of approach could be called "contextual". Both "class-based" and "contextual" approaches use a "model" for interpolation: The "class-based model" is that the signal belongs to an abstract class characterized by a certain mathematical property. The "contextual model" is that the signal will behave locally under a change of resolution in way "similar" to other signals in a given set, for which a high resolution version is known. Both types of techniques have some drawbacks. Roughly speaking, class-based methods generally lead to overly smooth signals, while contextual-based ones, on the contrary, tend to generate spurious details.
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Communication dans un congrès
WAVELET X, Part of SPIE's Symposium on Optical Science and Technology, Aug 2003, San Diego, United States. 5207, 2003
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Pierrick Legrand, Jacques Lévy Véhel. Local regularity-based interpolation. WAVELET X, Part of SPIE's Symposium on Optical Science and Technology, Aug 2003, San Diego, United States. 5207, 2003. 〈inria-00576479〉

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