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Representation learning via Cauchy Convolutional Sparse Coding

Mayo, Perla, Karakus, Oktay ORCID:, Holmes, Robin and Achim, Alin 2021. Representation learning via Cauchy Convolutional Sparse Coding. IEEE Access 9 , pp. 100447-100459. 10.1109/ACCESS.2021.3096643

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In representation learning, Convolutional Sparse Coding (CSC) enables unsupervised learning of features by jointly optimising both an ℓ2 -norm fidelity term and a sparsity enforcing penalty. This work investigates using a regularisation term derived from an assumed Cauchy prior for the coefficients of the feature maps of a CSC generative model. The sparsity penalty term resulting from this prior is solved via its proximal operator, which is then applied iteratively, element-wise, on the coefficients of the feature maps to optimise the CSC cost function. The performance of the proposed Iterative Cauchy Thresholding (ICT) algorithm in reconstructing natural images is compared against algorithms based on minimising standard penalty functions via soft and hard thresholding as well as against the Iterative Log-Thresholding (ILT) method. ICT outperforms the Iterative Hard Thresholding (IHT), Iterative Soft Thresholding (IST), and ILT algorithms in most of our reconstruction experiments across various datasets, with an average Peak Signal to Noise Ratio (PSNR) of up to 11.30 dB, 7.04 dB, and 7.74 dB over IST, IHT, and ILT respectively. The source code for the implementation of the proposed approach is publicly available at

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Additional Information: This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see
Publisher: Institute of Electrical and Electronics Engineers
ISSN: 2169-3536
Date of First Compliant Deposit: 14 September 2021
Date of Acceptance: 7 July 2021
Last Modified: 02 May 2023 12:08

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