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Image enhancement using deep-learning fully connected neural network mean filter

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Abstract

Improving the quality of a noisy image is important for image applications. Many novel schemes pay great efforts in the removal of impulse noise. Most of them restore noisy pixels only by using the neighboring noise-free pixels, but the relationship between a noisy image and its noise-free one, which denotes the clean image not corrupted by noise, is ignored. So the reconstruction quality cannot be further improved. In this study, we employ a deep-learning fully connected neural network (FCNN) to select top N candidates of neighboring un-corrupted pixels for the restoration of a center noisy pixel in an analysis window. Hence, the mean value of the gray levels of these top N pixels is computed and employed to replace the noisy pixel, yielding the noisy pixel being restored. The experimental results reveal that the proposed deep-learning FCNN mean filter can remove impulse noise effectively in corrupted images with different noise densities.

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Abbreviations

\(\varPsi_{i,j}\) :

Feature vector of the FCNN

\(\eta_{i,j}\) :

Noise-free flag

\(r_{i,j}\) :

Spatial distance

\(\, k_{i,j}\) :

Similarity measure

\(\, \sigma_{i,j}\) :

Pixel deviation

\(x_{i,j}\) :

Noisy pixel

\(d_{i,j}\) :

The gray-level distance

\(N_{\text{ne}}\) :

The number of non-extreme pixel

\(\, \tilde{x}_{i,j}\) :

Non-corrupted pixel

\(l_{i,j}^{*}\) :

The optimum position index of the neighboring noise-free pixel

\(s_{i,j}\) :

The pixel in the noise-free image

\(\hat{l}_{i,j}\) :

The recognized index of neighboring pixel

\(\tilde{s}_{i,j}\) :

The recognized pixel of the FCNN in an analysis window

\(\hat{s}_{i,j}\) :

Denoised pixel

\(\tilde{x}_{\text{Top}\,i}\) :

The top i recognized results of the FCNN

N :

The number of noise-free pixels among top i recognized results

\(N_{s}\) :

The desired number of neighboring noise-free pixels recognized by the FCNN in an analysis window

\(F_{\text{Top}\,i}\) :

The noise-free flag of the top ith neighboring pixel

\(s_{\text{max} }\) :

The maximum value of the gray level

\(\varepsilon\) :

The mean square error (MSE) between the noise-free image and the enhanced one

Q :

The number of columns in an image

P :

The number of rows in an image

\(\mu_{{s_{\text{m}} }}\) :

The mean of the noise-free pixels

\(\mu_{{\hat{s}_{\text{m}} }}\) :

The mean of the reconstructed pixels

\(\sigma_{{s_{\text{m}} }}\) :

The standard deviations of clean pixels

\(\sigma_{{\hat{s}_{\text{m}} }}\) :

The standard deviations of reconstructed pixels

\(\sigma_{{s_{\text{m}} \hat{s}_{\text{m}} }}\) :

The square root of the covariance of clean and reconstructed pixels

MSSIM:

Mean structural similarity index

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Acknowledgements

This work was supported by the Ministry of Science and Technology, Taiwan [Grant Number MOST 104-2221-E-468-007]. Our gratitude goes to the reviewers for their valuable comments which have improved the quality of this paper.

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Authors and Affiliations

  1. Department of Information Communication, Asia University, Taichung City, 41354, Taiwan, ROC

    Ching-Ta Lu, Ling-Ling Wang & Jun-Hong Shen

  2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung City, 40402, Taiwan, ROC

    Ching-Ta Lu & Jun-Hong Shen

  3. Department of Digital Media Design, Asia University, Taichung City, 41354, Taiwan, ROC

    Jia-An Lin

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Lu, CT., Wang, LL., Shen, JH. et al. Image enhancement using deep-learning fully connected neural network mean filter. J Supercomput 77, 3144–3164 (2021). https://doi.org/10.1007/s11227-020-03389-6

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