NDLI: An Iterative Linear Expansion of Thresholds for <formula formulatype=inline> <tex Notation=TeX>$ell_{1}$</tex></formula>-Based Image Restoration

Content Provider	IEEE Xplore Digital Library
Author	Hanjie Pan Blu, T.
Copyright Year	1992
Abstract	This paper proposes a novel algorithmic framework to solve image restoration problems under sparsity assumptions. As usual, the reconstructed image is the minimum of an objective functional that consists of a data fidelity term and an ℓ₁ regularization. However, instead of estimating the reconstructed image that minimizes the objective functional directly, we focus on the restoration process that maps the degraded measurements to the reconstruction. Our idea amounts to parameterize the process as a linear combination of few elementary thresholding functions (LET) and to solve the linear weighting coefficients by minimizing the objective functional. It is then possible to update the thresholding functions and to iterate this process ( i-LET). The key advantage of such a linear parametrization is that the problem size reduces dramatically-each time we only need to solve an optimization problem over the dimension of the linear coefficients (typically less than 10) instead of the whole image dimension. With the elementary thresholding functions satisfying certain constraints, a global convergence of the iterated LET algorithm is guaranteed. Experiments on several test images over a wide range of noise levels and different types of convolution kernels clearly indicate that the proposed framework usually outperforms state-of-the-art algorithms in terms of both the CPU time and the number of iterations.
Sponsorship	IEEE Signal Processing Society
Page Count	14
File Size	3566496
Starting Page	3715
Ending Page	3728
File Format	PDF
ISSN	10577149
Volume Number	22
Issue Number	9
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	linear expansion of thresholds (LET) Image restoration sparsity majorization minimization (MM) iterative reweighted least square (IRLS) thresholding
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Software

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