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In this paper we introduce a new unified framework for multi-scale detail manipulation of graph signals. The key to this unification is to model any kind of data as signals defined on appropriate weighted graphs. Graph signals are represented as the sum of successive layers, each capturing a given scale of detail. Detail layers are obtained through a series of regularization procedures based on total...
The classical super-resolution (SR) setting starts with a set of low-resolution (LR) images related by subpixel shifts and tries to reconstruct a single high-resolution (HR) image. In some cases, partial observations about the HR image are also available. Trying to complete the missing HR data without any reference to LR ones is an inpainting (or completion) problem. In this paper, we consider the...
A new hierarchical representation of general discrete data sets living on graphs is proposed. The approach takes advantage of recent works on graph regularization. The different levels of the hierarchy are discovered as the regularization process is performed. The role of the merging criterion that is common to hierarchical representations is greatly reduced due to the regularization step. This yields...
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