A greedy approach to ℓ 0, ω -based convolutional sparse coding

Elad Plaut, Raja Giryes

Research output: Contribution to journalArticlepeer-review


Sparse coding techniques for image processing traditionally rely on the processing of small overlapping patches separately, followed by averaging. This has the disadvantage that the reconstructed image no longer obeys the sparsity prior used in the processing. For this purpose convolutional sparse coding has been introduced, where a shift-invariant dictionary is used and the sparsity of the recovered image is maintained. Most such strategies target the ℓ 0 “norm” or the ℓ 1 norm of the whole image, which may create an imbalanced sparsity across various regions in the image. In order to face this challenge, the ℓ 0,∞ “norm” has been proposed as an alternative that “operates locally while thinking globally.” The approaches taken for tackling the nonconvexity of these optimization problems have been using either a convex relaxation or local pursuit algorithms. In this paper, we present an efficient greedy method for sparse coding and dictionary learning, which is specifically tailored to ℓ 0,∞ and is based on matching pursuit. We demonstrate the usage of our approach in salt-and-pepper noise removal and image inpainting.

Original languageEnglish
Pages (from-to)186-210
Number of pages25
JournalSIAM Journal on Imaging Sciences
Issue number1
StatePublished - 2019


FundersFunder number
Horizon 2020 Framework Programme757497
European Research Council


    • Convolutional sparse coding
    • Global modeling
    • Greedy algorithms
    • Local processing
    • Sparse representations


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