Under optimal filtering effect of multiple image filter algorithm selection

Chen Jun Luo Weiping

Abstract： In order to improve the noise reduction effect of mixed noise， a combined filtering algorithm is proposed， which first uses the median and mean filter for mixed noise. The salt and pepper， Gaussian noise are processed， and the improved threshold algorithm is used to restore the image details. Aiming at the difficulty of selecting threshold parameters and denoising effect in the denoising process of traditional threshold image filter， the traditional threshold filtering algorithm is improved and an optimal threshold parameter selection algorithm is proposed. The experimental results show that the peak signal-to-noise ratio （PSNR） of the combined filtering algorithm is improved by 6.415% compared with the median filtering； compared with the mean filtering algorithm， the PSNR of the combined filtering algorithm is increased by 6.796%； Compared with the hard threshold filtering algorithm， the PSNR of the combined filtering algorithm is increased by 1.564% and 1.034%， respectively.

0 Introduction

One of the main influencing factors of image quality is image noise.The presence of noise affects visual effects and subsequent processing of images. Therefore， image denoising has important practical significance[1]. The mean filter， median filter， Wiener filter， etc. can only play a significant filtering effect on a single noise， and can not remove the mixed noise； the Fourier transform has certain limitations； in the wavelet transform， the threshold parameter selection is difficult. Aiming at these problems， this paper compares the denoising effects of different filters based on the experimental results， proposes a combined filter filtering algorithm， and improves the traditional soft-hard threshold algorithm. An optimal threshold parameter selection algorithm is proposed to solve the simple problem. The mixed noise problem that the filter cannot solve improves the image noise filtering effect.

1 Principles of Common Filtering Algorithms and Defects

1.1The principle of median filtering algorithm and its defect

The value is taken as the new pixel value. This is a nonlinear signal processing technique based on the principle of sorting statistics to eliminate isolated noise points.Suppose it is sorted as：

Then， a new pixel value Y can be calculated according to the formula （1）.

The defect of median filtering is that only the pollution points randomly appearing in the picture can be processed by data sorting， and the points in the image that are not contaminated by noise are replaced by the contaminated points， and all the contaminated points in the image of random size cannot be processed.

1.2 Mean filtering principle and its defect

The basic principle of the mean filtering is to replace the individual pixel values in the original image with the average value， which can be expressed by the formula （2）：

Where f（ x，y） represents the image with noise， g（ x，y） represents the image after the mean filtering， and M is the number of pixels in the template including the current pixel.

The mean filter can remove the noise of uniform distribution and Gaussian distribution， and the suppression of Gaussian noise is better. However， the effect on the salt and pepper noise is not large， because the noise is reduced and the overall image content is also blurred， and the noise still exists.

2 Wavelet Transform Principle and Its Defects

Wavelet transform has the characteristics of high resolution at low frequency and low resolution at high frequency. The image is filtered by wavelet transform， and the original image is decomposed into a series of approximate components and detail components. The decomposed image is mainly composed of low frequency part. To characterize， and the detail part is characterized by the high frequency part， and then use the certain threshold to process the detail component， after wavelet reconstruction to get the smooth signal [2].

A noise-containing image x（t） is provided in relation to the original image s（t） as Equation（3）， where n（t） is the added noise.

For the discrete wavelet transform of x（t）， we can get the formula （4）：

The wavelet coefficient of the noisy image on the jth layer is ωx（j，k）， the wavelet coefficient of the original image on the jth layer is ωs（j，k）， and ωn（j，k） is the noise image at the jth The wavelet coefficient on the layer； j is the maximum number of decomposition layers of the wavelet transform； the length of the image is N. When ωj，k is less than a certain threshold， it is discarded， because ωj，k is mainly caused by noise， and ωj，k≈vj，k； when ωj，k is greater than a certain threshold， the wavelet coefficient is mainly Determined by the image， it can be considered as ωj， k≈μj， k. The most commonly used soft and hard threshold functions are as follows：

The soft threshold function is given by equation （5）：

The hard threshold function is given by equation （6）：

Where sgn（） is a symbolic function， is the threshold λ， and σ is the standard deviation of the noise. The estimated value of the standard deviation is ，it is estimated by the wavelet coefficients on the smallest scale， where median（| ω1， k|） represents the intermediate value of the first layer wavelet transform coefficients ω1， k amplitude.

The defect of the soft threshold function is that the wavelet coefficients in the wavelet domain are subjected to constant value compression for the wavelet coefficients larger than the threshold， which is inconsistent with the trend that the noise components gradually decrease with the increase of the wavelet coefficients； and the hard threshold function is only in the whole wavelet domain. The wavelet coefficients smaller than the threshold are processed， and the wavelet coefficients larger than the threshold are not processed， but in actual cases， the noise also exists in the wavelet coefficients larger than the threshold， and the processing is inevitably affected by the accuracy of signal reconstruction. Therefore， for the defects of the soft and hard threshold methods， a new improved threshold function is proposed.

3 Improved threshold function

The improved threshold function， such as equation （7）， is a flexible choice between soft and hard thresholds.

Where λ1 is the general threshold， λ2 = αλ1 （0 < α ≤ 1）. The improved threshold function selection factor is between the hard threshold and the soft threshold function. By controlling the variable r， the amplitude of the wavelet coefficient reduction can be adjusted， but the characteristic parameter α cannot be determined effectively， and it is necessary to repeatedly test according to the actual situation to determine an appropriate value. Aiming at this defect， this paper proposes the optimal soft threshold denoising method under the condition of wavelet entropy from the relationship of signal entropy. The algorithm of parameter α is as follows：

①Calculate the wavelet transform of the image contaminated by noise； select the appropriate wavelet and wavelet decomposition layer to obtain the corresponding wavelet decomposition coefficient ωj，k；

②Run the new threshold function for the wavelet coefficient ωj，k obtained by decomposition （7） performing threshold processing to obtain wavelet coefficient estimates μj， k， and then obtaining the filtered noise wavelet coefficient estimates vj， k by equation （8）， respectively；

③According to the principle of maximum entropy of discrete random variables， for different parameters α， the wavelet entropy Ws and the wavelet entropy Wn of the filtered noise are calculated according to formula （9） and formula （10）， and then calculated according to W=Ws Wn. The sum of wavelet entropies. When the sum of the wavelet entropies is the largest， α is obtained as the optimal parameter value， and the formula （7） at this time is the optimal threshold function.

4 Results and analysis

Compare the effect diagrams processed by various methods， as shown in Figure. It can be seen from the experimental phenomena that the improved filtering function combined with the median and mean filtering is better than the single filter processing effect， and the improved threshold combination is included. The noise image processing effect is also superior to the traditional soft and hard threshold function and the median and mean combination.

The commonly used image objective quality evaluation standard is to objectively evaluate the peak signal-to-noise ratio （PSNR） and root mean square error （RMSE） of the image after denoising [3]. In order to verify the denoising effect， the calculated Table is a comparison of the PSNR and RMSE values processed by different methods. It can be seen that the noise-reduced image processed by this method has the highest PSNR value and the lowest RMSE value.

5 Conclusions

This combined filtering algorithm using improved threshold function combined with median and mean filtering is effective in visually and objectively evaluating the standard PSNR and RMSE， which is significantly better than the filtering effect of a single filter. The Gaussian and salt-and-salt noise in the mixed noise is removed， which compensates for the defect that the single filter cannot remove the mixed noise， and can achieve the maximum reduction of the image details to the greatest extent， and has practical feasibility and use value.

References：

[1]Yu Hao. Research on digital image processing method and implementation based on MATLAB[J]. Electronic World， 2017（09）：160.

[2]Zeng Xiangli， Fu Yan， Qing Huaping. A data denoising method based on wavelet transform [J]. Computer Applications， 2005， 25（9）： 2140-2142.

[3]Zhong Jianjun， Song Jian， by Chang Xi， et al. Threshold-based wavelet denoising method based on signal-to-noise ratio evaluation [J]. Journal of Tsinghua University （Natural Science Edition）， 2014， 54（ 2） ： 259-263.

[4]He Yiming， Zhang Gangbing， Qian Xianyi. Algorithm of Salt and Pepper Noise Based on Neighborhood Mean[J].Journal of Nanjing University of Science andTechnology，2011 ，35（12）：764-767.

The first author： Chen Jun（1992-）， male， master. Research direction for the Electronic Science and technology. Corresponding author： Luo Weiping（1967-）， female， professor. Disciplinary direction for the detection technology and intelligent control， signal and information processing， research areas for digital textile equipment.