Suboptimality of nonlocal means on images with sharp edges

Maleki, Arian; Narayan, Manjari; Baraniuk, Richard G.

doi:10.1109/allerton.2011.6120182

Cited by 8 publications

(36 citation statements)

References 10 publications

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“…Note that, in order to streamline the proofs, we take a continuous-variable analysis approach in this paper, in contrast to our approach in [41]. The moral of the story is compatible with [41], however. Table 1 Minimax risk decay rates of several classical image denoising algorithms; recall that according to Theorem 1, for α = 2 the optimal minimax rate is σ 4/3 .…”

Section: Minimax Analysis Frameworkmentioning

confidence: 83%

“…The proof is similar to the proof of Theorem 5 in [41]; we consider the function f h (t 1 , t 2 ) for h(t 1 ) = 1/2 and prove that the bias of the NLM on (t 1 , t 2 ) ∈ Q δ n is Θ(1) for any choice of the threshold parameter. However, in the continuous setting considered here, the steps are more challenging.…”

Section: Appendix B Minimax Risk Of Nlmmentioning

confidence: 89%

“…Nevertheless, we repeat the proof here for the sake of completeness and since our continuous framework is slightly different from the discrete framework in [4]. See [41] for the generalization of this result.…”

Section: Appendix a Minimax Risk Of The Mean Filtermentioning

confidence: 91%

“…As we will see in Section 3, n 2 → ∞ as σ → 0, and hence the effect of 4 The analysis framework used in [4] and [41] is discrete rather than continuous. Therefore, for the sake of completeness we establish the results for the mean filter and NLM in Appendices A and B, respectively.…”

Section: Nonlocal Means Denoisingmentioning

confidence: 98%

“…1) [41]. 1 Indeed, NLM's theoretical performance is more or less equivalent to wavelet thresholding, which was shown to be suboptimal in [17].…”

Section: Introductionmentioning

confidence: 98%

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Anisotropic nonlocal means denoising

Maleki

Narayan

Baraniuk

2013

Applied and Computational Harmonic Analysis

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It has recently been proved that the popular nonlocal means (NLM) denoising algorithm does not optimally denoise images with sharp edges. Its weakness lies in the isotropic nature of the neighborhoods it uses to set its smoothing weights. In response, in this paper we introduce several theoretical and practical anisotropic nonlocal means (ANLM) algorithms and prove that they are near minimax optimal for edge-dominated images from the Horizon class. On real-world test images, an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin.

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Section: Minimax Analysis Frameworkmentioning

confidence: 83%

Section: Appendix B Minimax Risk Of Nlmmentioning

confidence: 89%

Section: Appendix a Minimax Risk Of The Mean Filtermentioning

confidence: 91%

Section: Nonlocal Means Denoisingmentioning

confidence: 98%

“…1) [41]. 1 Indeed, NLM's theoretical performance is more or less equivalent to wavelet thresholding, which was shown to be suboptimal in [17].…”

Section: Introductionmentioning

confidence: 98%

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Anisotropic nonlocal means denoising

Maleki

Narayan

Baraniuk

2013

Applied and Computational Harmonic Analysis

Self Cite

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Block compressive sensing of image and video with nonlocal Lagrangian multiplier and patch-based sparse representation

Chien

Dinh

Jeon

et al. 2017

Signal Processing: Image Communication

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Although block compressive sensing (BCS) makes it tractable to sense large-sized images and video, its recovery performance has yet to be significantly improved because its recovered images or video usually suffer from blurred edges, loss of details, and high-frequency oscillatory artifacts, especially at a low subrate. This paper addresses these problems by designing a modified total variation technique that employs multi-block gradient processing, a denoised Lagrangian multiplier, and patch-based sparse representation. In the case of video, the proposed recovery method is able to exploit both spatial and temporal similarities. Simulation results confirm the improved performance of the proposed method for compressive sensing of images and video in terms of both objective and subjective qualities.

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Secrets of image denoising cuisine

Lebrun¹,

Colom²,

Buades³

et al. 2012

Acta Numerica

178

108

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Digital images are matrices of equally spaced pixels, each containing a photon count. This photon count is a stochastic process due to the quantum nature of light. It follows that all images are noisy. Ever since digital images have existed, numerical methods have been proposed to improve the signal-to-noise ratio. Such ‘denoising’ methods require a noise model and an image model. It is relatively easy to obtain a noise model. As will be explained in the present paper, it is even possible to estimate it from a single noisy image.

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Suboptimality of nonlocal means on images with sharp edges

Cited by 8 publications

References 10 publications

Anisotropic nonlocal means denoising

Anisotropic nonlocal means denoising

Block compressive sensing of image and video with nonlocal Lagrangian multiplier and patch-based sparse representation

Secrets of image denoising cuisine

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