A New Poisson Noise Filter Based on Weights Optimization

Jin, Qiyu; Grama, Ion; Liu, Quansheng

doi:10.1007/s10915-013-9743-7

Cited by 11 publications

(15 citation statements)

References 36 publications

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“…For removing the non-Gaussian noise, such as Poisson noise and the mixture of Gaussian noise and impulse noise, and for the case where the different parts of the image are corrupted by different Gaussian noises, the proposed QOWNLMF is not suitable if it is implemented directly. However, it can be adapted to construct new quaternion filters for removing such kind of noises, by using ideas from Jin et al [47,48]. This will be done in our next works.…”

Section: Discussionmentioning

confidence: 99%

Removing Gaussian noise for colour images by quaternion representation and optimisation of weights in non‐local means filter

Chen

Liu

Sun

et al. 2014

IET Image Processing

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Section: Discussionmentioning

confidence: 99%

Removing Gaussian noise for colour images by quaternion representation and optimisation of weights in non‐local means filter

Chen

Liu

Sun

et al. 2014

IET Image Processing

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“…In this paper, we introduce the notion of Reliable Weight to measure the probability for a pixel to be noise-free, in an image with the presence of a random impulse noise. Combining Reliable Weight with the technique of the Optimal Weights Filter [25,26], we get an efficient filter for removing randomvalued impulse noise. Under suitable assumptions we prove the convergence of the filter.…”

Section: Computational Complexitymentioning

confidence: 99%

Removing random-valued impulse noise with reliable weight

Jin¹,

Bai²,

Grama³

et al. 2020

Inverse Problems &Amp; Imaging

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In this paper, we present a patch based weighted means filter for removing an impulse noise by adapting the fundamental idea of the non-local means filter to the random-valued impulse noise. Our approach is to give a weight to a pixel in order to evaluate the probability that the pixel is contaminated by the impulse noise, which we call Reliable Weight of the pixel. With the help of the Reliable Weights we introduce the similarity function to measure the similarity among patches of the image contaminated by a random impulse noise. It turns out that the similarity function has significant anti impulse noise interference ability. We then incorporate the Reliable Weights and the similarity function into a filter designed to remove the random impulse noise. Under suitable conditions, we establish two convergence theorems to demonstrate that our method is feasible. Simulation results confirm that our filter is competitive compared to recently proposed methods.2010 Mathematics Subject Classification. Primary: 62H35. 2(1 − p) 2 .By Hypothesis 1, λ → 0 in probability, so thatin probability. On the other hand, since the observed image v is bounded, say by V max , we have ∆v (t) 2 = (v(x 0 + t) − v(x + t)) 2 ≤ V 2 max for each t, so that R

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“…Let pixel

x_{q}

from the set

{bold-italicB}_{q}

be the centre pixel of the denoised image piece

{\hat{bold-italicf}}_{q}

(whose size is

\sqrt{M^{'}} \times \sqrt{M^{'}}

pixels,

\sqrt{M^{'}} = 2 \times m + 1

). In the merging procedure, each pixel

x \in I

is first assigned the following weight [38]:

κ_{q, m} ()(, x) = ({, \begin{aligned} \sum_{s = {(∥∥, x - x_{q})}_{\infty}}^{m} \frac{1}{m {false(2 s + 1 false)}^{2}} if x \neq x_{q} and x \in B_{q}, \\ \sum_{s = 1}^{m} \frac{1}{m {false(2 s + 1 false)}^{2}} if x = x_{q}, \\ 0 if x \in I normal∖ {bold-italicB}_{q}, \end{aligned})

where

∥ ∙ ∥_{\infty}

denotes supremum norm. Then, the full‐size estimate

\hat{f}

is obtained as follows [48]:

\hat{f} false(x false) = <...>

…”

Section: New Approach: Poisson Pwpcamentioning

confidence: 99%

“…variable‐stabilising transformation (VST), multiscale VST, conditional variance stabilisation, or Fisz transform [2–19]) and, then, to use methods that assume signal‐independent noise [20–23]. Other approaches to the SNR improvement have also been proposed such as maximum‐likelihood estimation [24–32], plug‐and‐play scheme [33], deep convolutional denoising [34] Kullback–Leibler divergence [35–37], optimal weights filtering [38] based on non‐local means approach [20], or non‐local principal component analysis (NLPCA) [39].…”

Section: Introductionmentioning

confidence: 99%

Poisson image denoising by piecewise principal component analysis and its application in single‐particle X‐ray diffraction imaging

Jin

Miyashita

Tama

et al. 2018

IET Image Processing

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This article describes an improved method for Poisson image denoising that is based on a state-of-the-art Poisson denoising approach known as Non-Local Principal Component Analysis (NLPCA). The new method is referred to as PieceWise Principal Component Analysis (PWPCA). In PWPCA, the given image is first split into pieces, then NLPCA is run on each image piece, and finally, the entire image is reconstituted by a weighted combination of the NLPCA-processed image pieces. Using standard test images with Poisson noise, we show that PWPCA restores images more effectively than state-of-the-art Poisson denoising approaches. In addition, and to the best of our knowledge, we show a first application of such approaches to singleparticle X-ray free-electron laser (XFEL) data. We show that the resolution of 3D reconstruction from XFEL diffraction images is improved when the data are preprocessed with PWPCA. XFELs are currently under rapid development to allow high-resolution biomolecular structure determination at near-physiological conditions. Data analysis methods developments follow these technological advances and are expected to have high impact in structural biology and drug design. This article contributes to these developments. As little experimental single-particle XFEL data is available still, the XFEL experiments shown here were performed with simulated data.

show abstract

A New Poisson Noise Filter Based on Weights Optimization

Cited by 11 publications

References 36 publications

Removing Gaussian noise for colour images by quaternion representation and optimisation of weights in non‐local means filter

Removing Gaussian noise for colour images by quaternion representation and optimisation of weights in non‐local means filter

Removing random-valued impulse noise with reliable weight

Poisson image denoising by piecewise principal component analysis and its application in single‐particle X‐ray diffraction imaging

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