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Dictionary Learning Based on Sparse Distribution Tomography

P. Pad, F. Salehi, E. Celis, P. Thiran, M. Unser

Proceedings of the Thirty-Fourth International Conference on Machine Learning (ICML'17), Sydney, Commonwealth of Australia, August 6-11, 2017, pp. 2731-2740.


We propose a new statistical dictionary learning algorithm for sparse signals that is based on an α-stable innovation model. The parameters of the underlying model—that is, the atoms of the dictionary, the sparsity index α and the dispersion of the transform-domain coefficients—are recovered using a new type of probability distribution tomography. Specifically, we drive our estimator with a series of random projections of the data, which results in an efficient algorithm. Moreover, since the projections are achieved using linear combinations, we can invoke the generalized central limit theorem to justify the use of our method for sparse signals that are not necessarily α-stable. We evaluate our algorithm by performing two types of experiments: image in-painting and image denoising. In both cases, we find that our approach is competitive with state-of-the-art dictionary learning techniques.

Beyond the algorithm itself, two aspects of this study are interesting in their own right. The first is our statistical formulation of the problem, which unifies the topics of dictionary learning and independent component analysis. The second is a generalization of a classical theorem about isometries of ℓp-norms that constitutes the foundation of our approach.

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AUTHOR="Pad, P. and Salehi, F. and Celis, E. and Thiran, P. and Unser,
	M.",
TITLE="Dictionary Learning Based on Sparse Distribution Tomography",
BOOKTITLE="Proceedings of the Thirty-Fourth International Conference on
	Machine Learning ({ICML'17})",
YEAR="2017",
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pages="2731--2740",
address="Sydney, Commonwealth of Australia",
month="August 6-11,",
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© 2017 The Authors. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from The Authors. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
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