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11 September 2015 Geometric multi-resolution analysis and data-driven convolutions
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Abstract
We introduce a procedure for learning discrete convolutional operators for generic datasets which recovers the standard block convolutional operators when applied to sets of natural images. They key observation is that the standard block convolutional operators on images are intuitive because humans naturally understand the grid structure of the self-evident functions over images spaces (pixels). This procedure first constructs a Geometric Multi-Resolution Analysis (GMRA) on the set of variables giving rise to a dataset, and then leverages the details of this data structure to identify subsets of variables upon which convolutional operators are supported, as well as a space of functions that can be shared coherently amongst these supports.
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Nate Strawn "Geometric multi-resolution analysis and data-driven convolutions", Proc. SPIE 9597, Wavelets and Sparsity XVI, 95971D (11 September 2015); https://doi.org/10.1117/12.2187654
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