SURE-Based Non-Local Means

Ville, Dimitri Van De; Kocher, Michel

doi:10.1109/lsp.2009.2027669

Cited by 224 publications

(150 citation statements)

References 18 publications

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“…In this way, the optimal shrinkage parameters can be easily and efficiently computed from the SURE map of an initially denoised image, and allows a better estimation of the clean image without rerunning NLM denoising. Although in experiment we report the best scores by exhaustively searching the h space, one may simply use the empirical optimal h ≈ |P|σ 2 /2 in [6] instead. Performance scores 8 of using these empirical h are close to reported ones.…”

Section: Discussionmentioning

confidence: 99%

“…Specifically, the NLM patches P used in simulations vary from 3×3 to 7×7, the search region is fixed at 15×15, and the bandwidth parameter h is chosen from 5% to 200% of |P|σ 2 . The quality of each denoised image is evaluated by using the PSNR [6] and the SSIM [11]. The best scores over all hs for each method under different parameter combinations are given in Table I (methods with best scores are underlined).…”

Section: Methodsmentioning

confidence: 99%

“…The NLM-SURE estimator [6] is a powerful tool predicting the denoising risk without knowing the clean image. Since it can be obtained along with the computation of x, it has been extensively used in parameter selections.…”

Section: Preliminarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…[6] derived the closed-form of NLM-SURE and used the SURE to pick the proper bandwidth parameter. Although [6] gave an empirical choice of the bandwidth parameter, the optimal choice (also dependent on image content) still requires looping over NLM for many times. [1] introduced the multi-patch NLM to overcome the denoising artifacts by combining results of using various patch shapes and sizes.…”

Section: Introductionmentioning

confidence: 99%

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Fast blockwise SURE shrinkage for image denoising

Tracey

Natarajan

et al. 2014

Signal Processing

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In this letter, we investigate the shrinkage problem for the non-local means (NLM) image denoising.In particular, we derive the closed-form of the optimal blockwise shrinkage for NLM that minimizes the Stein's unbiased risk estimator (SURE). We also propose a constant complexity algorithm allowing fast blockwise shrinkage. Simulation results show that the proposed blockwise shrinkage method improves NLM performance in attaining higher peak signal noise ratio (PSNR) and structural similarity index Index TermsImage Denoising, Non-Local Means, Adaptive Algorithm, Shrinkage Estimator, Stein's Unbiased Risk EstimatorBrian Tracey and Joseph P. Noonan are with the department of electrical and computer engineering, Tufts university, 161 College Ave, Medford, MA 02155; e-mail: ywu03@ece.tufts.edu. Premkumar Natarajan is with the Raytheon BBN technologies, 10 Moulton St., Cambridge, MA 02138. Yue Wu was with the department of electrical and computer engineering at Tufts university, but is now with the Raytheon BBN technologies.

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Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Preliminarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fast blockwise SURE shrinkage for image denoising

Tracey

Natarajan

et al. 2014

Signal Processing

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Image denoising for real‐time MRI

Klosowski

Frahm

2016

Magnetic Resonance in Med

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Low Complexity Regularization of Linear Inverse Problems

Vaiter

Peyré

Fadili

2015

Sampling Theory, a Renaissance

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Inverse problems and regularization theory is a central theme in imaging sciences, statistics and machine learning. The goal is to reconstruct an unknown vector from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown vector is to solve a convex optimization problem that enforces some prior knowledge about its structure. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of ℓ 2 -stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem.

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SURE-Based Non-Local Means

Cited by 224 publications

References 18 publications

Fast blockwise SURE shrinkage for image denoising

Fast blockwise SURE shrinkage for image denoising

Image denoising for real‐time MRI

Low Complexity Regularization of Linear Inverse Problems

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