A statistical interpretation of non-local means

Thacker, Neil A.; Manjón, José V.; Bromiley, Paul A.

doi:10.1049/cp:20080317

Cited by 8 publications

(6 citation statements)

References 7 publications

(10 reference statements)

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“…Nonetheless, statistical arguments have also been developed to explore the validity of denoising algorithms. The statistical validity of NL-means is discussed in [141], [83] and [57] (where a Bayesian interpretation is proposed) or [151] where a bias of NL-means is corrected. [137] gives "a probabilistic interpretation and analysis of the method viewed as a random walk on the patch space".…”

Section: Miscellaneous "Patch Based" Considerations and Applicationsmentioning

confidence: 99%

Secrets of image denoising cuisine

Lebrun¹,

Colom²,

Buades³

et al. 2012

Acta Numerica

174

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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Section: Miscellaneous "Patch Based" Considerations and Applicationsmentioning

confidence: 99%

Secrets of image denoising cuisine

Lebrun¹,

Colom²,

Buades³

et al. 2012

Acta Numerica

174

108

View full text Add to dashboard Cite

show abstract

“…In this way, (5) can be interpreted as the standard quantitative χ 2 test to measure the similarity of the two samples [8]. The statistical interpretation of the exponential function used in (3) is not straightforward [8], although may be possible to relate it to Gaussian kernels used in probability density estimation. Nevertheless, this exponential function gives a larger weight to a pixel with a smaller patch difference ( Fig.…”

Section: Problems With the Nlm Weight Functionmentioning

confidence: 99%

Probabilistic Non-Local Means

Tracey

Natarajan

et al. 2013

IEEE Signal Process. Lett.

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In this paper, we propose a so-called probabilistic non-local means (PNLM) method for image denoising. Our main contributions are: 1) we point out defects of the weight function used in the classic NLM; 2) we successfully derive all theoretical statistics of patch-wise differences for Gaussian noise; and 3) we employ this prior information and formulate the probabilistic weights truly reflecting the similarity between two noisy patches. The probabilistic nature of the new weight function also provides a theoretical basis to choose thresholds rejecting dissimilar patches for fast computations. Our simulation results indicate the PNLM outperforms the classic NLM and many NLM recent variants in terms of peak signal noise ratio (PSNR) and structural similarity (SSIM) index. Encouraging improvements are also found when we replace the NLM weights with the probabilistic weights in tested NLM variants.

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“…Here, D i,j is interpreted as the standard χ 2 test to measure patch similarity (Thacker et al ., ). Comparing Equations 5 and 7, it is obvious that they are somewhat similar, but the measure of the patch similarity in the latter one is statistically rigorous.…”

Section: Methodsmentioning

confidence: 97%

Improving dimensional measurement from noisy atomic force microscopy images by non‐local means filtering

Chen

2015

Scanning

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Quantitative evaluation of dimensional parameters from noisy atomic force microscopy (AFM) images was investigated. Non-local means (NLM) denoising was adopted to reduce noise and maintain fine image structures. Major tuning parameters in NLM filtering, such as the patch size and the window size, were optimized on simulated surface structures. The ability of dimensional evaluation from noisy data was demonstrated to be improved by almost 15 times. Finally, NLM filtering with optimal settings was applied on experimental AFM images, which were scanned on a patterned few-layer graphene specimen. Evaluations of the step height and the pattern size were verified to be much more accurate and robust. Such a data processing method can enhance the AFM dimensional measurements, particularly when the noise-level is reached.

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A statistical interpretation of non-local means

Cited by 8 publications

References 7 publications

Secrets of image denoising cuisine

Secrets of image denoising cuisine

Probabilistic Non-Local Means

Improving dimensional measurement from noisy atomic force microscopy images by non‐local means filtering

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