| Abstract: |
| Finding a good representation for a given data set is often providing the key to solving a variety of signal processing problems. We propose to explore
the design of a data adaptive representation with low redundancy that also incorporates multi-
scale structure via minimizing a jointly weighted $l^1$ functional that induces scale separation and
fast coefficient decay. Given a dataset of elements that share structural similarities, we
aim at obtaining a tight frame with low redundancy and predefined scaling properties, yet without
the explicitly required self-similar structure.
We replace the task of finding a representation inducing joint sparsity within the given dataset by the task of finding a system that provides an $l^1$ -optimal weighted sparsity, which is further shown to be suitable for many classical image analysis and recovery tasks.
The efficiency of the acquired representations are illustrated with digital removal of the cracks on Monet`s paintings, identifying the leading geometric features of a dataset qualitatively better than SVD and more. |
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