4,060 research outputs found
A fast patch-dictionary method for whole image recovery
Various algorithms have been proposed for dictionary learning. Among those
for image processing, many use image patches to form dictionaries. This paper
focuses on whole-image recovery from corrupted linear measurements. We address
the open issue of representing an image by overlapping patches: the overlapping
leads to an excessive number of dictionary coefficients to determine. With very
few exceptions, this issue has limited the applications of image-patch methods
to the local kind of tasks such as denoising, inpainting, cartoon-texture
decomposition, super-resolution, and image deblurring, for which one can
process a few patches at a time. Our focus is global imaging tasks such as
compressive sensing and medical image recovery, where the whole image is
encoded together, making it either impossible or very ineffective to update a
few patches at a time.
Our strategy is to divide the sparse recovery into multiple subproblems, each
of which handles a subset of non-overlapping patches, and then the results of
the subproblems are averaged to yield the final recovery. This simple strategy
is surprisingly effective in terms of both quality and speed. In addition, we
accelerate computation of the learned dictionary by applying a recent block
proximal-gradient method, which not only has a lower per-iteration complexity
but also takes fewer iterations to converge, compared to the current
state-of-the-art. We also establish that our algorithm globally converges to a
stationary point. Numerical results on synthetic data demonstrate that our
algorithm can recover a more faithful dictionary than two state-of-the-art
methods.
Combining our whole-image recovery and dictionary-learning methods, we
numerically simulate image inpainting, compressive sensing recovery, and
deblurring. Our recovery is more faithful than those of a total variation
method and a method based on overlapping patches
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
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