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arXiv:1202.6429cs.CV

Stable image reconstruction using total variation minimization

Deanna Needell, Rachel Ward

Abstract

This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization. In particular, we show that from O(slog(N)) nonadaptive linear measurements, an image can be reconstructed to within the best s-term approximation of its gradient up to a logarithmic factor, and this factor can be removed by taking slightly more measurements. Along the way, we prove a strengthened Sobolev inequality for functions lying in the null space of suitably incoherent matrices.

arXiv comments
25 pages
Journal reference
DOI
Subjects
cs.CVComputer Vision and Pattern Recognition cs.ITInformation Theory math.NANumerical Analysis

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Linked by 3 identifiable commenters in 4 comments across 4 threads, from Sep 2013 to Mar 2024.

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Discussed in comments4 threads

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    • Specific modern technical issues with the original scan are: Lena contains about 250,000 pixels, some 32 times smaller than a picture snapped with an iPhone 6. And then there’s a quality problem: The most commonly used version of the image is a scan of a printed page. The…

      defrostView on HNParent context

  2. Finding Lena Forsen, the Patron Saint of JPEGs 1 comment

    • I feel that whenever Lena is mentioned, we should also give a shoutout to the researchers who were fed up with her and decided to use Fabio instead. https://arxiv.org/abs/1202.6429 What do you guys (yes, guys) think about making Fabio the standard image instead?

      jordighView on HNParent context

  3. What convolutional neural networks look at when they see nudity 1 comment
  4. The Rest of the Lenna Story 1 comment

    • Two female image processing researchers recently used a picture of Fabio as a test image in a paper of theirs: http://arxiv.org/abs/1202.6429 (Additional discussion at http://www.kitware.com/blog/home/post/246) Personally, I'm all for the use of amusing (arousing?) test images…

      idbfsView on HNParent context

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