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Abstract：Over the years,the actual theory of wavelet has been developed rapidly.Because it has good time-frequency characteristics,it has received the attention of many scholars,and it has also used many fields.The system adds three different types of noise to the image,and simultaneously uses the wavelet wavelet transform to perform noise processing.By observing the experimental phenomenon,the noise processing of the wavelet transform has great advantages.
Keywords：wavelet transform;image denoising;comparative analysis
本文引用格式：ZHOU Xiu-mei等.Research on Performance Analysis of Wavelet Denoising System[J].教育现代化，2019，6（46）：227-229.
0Preface
During the acquisition or transmission process,images may generate a series of different types of noise due to external and internal reasons,that is,information that may be mixed or unnecessary with respect to the original image information.In this study,image processing is used to compare the popular wavelet transform technology,and Gaussian noise,salt and pepper noise,and uniform noise are denoised,so that the performance of wavelet system transformation and the evaluation of image information processing are performed.
1wavelet removal design method
1.1Comparison of Wavelet Transform and Fourier Transform
Fourier transform is one of the most basic methods of frequency domain analysis.The Fourier transform is as shown in the following figure.It can process some signals relative to stationary,but has a disadvantage when it is to obtain the frequency domain related information of the signal.In time,it is necessary to know all the time domain information of the signal.On the contrary,if the time domaininformation is obtained from the frequency domain,all the information in the frequency domain must be known,so there are obvious disadvantages in the non-stationary information processing.
F(w)f(t)e dt(F o u r i e r p o s i t i v e transformation formula)
f(t)1F(w)e j 2ft dw（I n v e r s e F o u r i e r transform）
The wave transform provides a time-frequency window that can be modulated.The width of the window changes with frequency.When the frequency increases,the width of the time window narrows to improve the resolution.The average amplitude of the wavelet over the entire time range is zero,with a finite duration and abrupt frequency and amplitude,which can be irregular,or asymmetric.
The difference between wavelet t ransform and Fourier transform is that its time-frequency window can be changed,and the width of the window can change with frequency.Thus,some column correlation characteristics of the wavelet transform are obtained:when processing the low frequency signal,the window function increases the resolution by widening the window function width.When processing the high frequency signal,the window function narrows the width by adjusting the window function to improve the resolution.The wavelet transform formula is as follows:
1.2Haar wavelet transform
The Haar wavelet transform is one of the simplest methods of wavelet transform.Because of its simplicity,the computational analysis is extremely fast and it also has orthogonality.The required high frequency signal can be obtained by performing two or more compressions on the haar.The basic expressions are as follows:
1.3Daubechies Wavelet transform
Daubechies is a series of binary orthogonal wavelets.The order of the vanishing matrix and the band division effect change with the order of the wavelet.The higher the order,the larger the order of the vanishing matrix,and the better the partitioning effect.The expression is as follows:
1.4Coiflet Wavelet transform
An orthogonal wavelet satisfies the following conditions:
The biorthogonal wavelet has a good peak-to-noise ratio,has high vanishing momentum,and is used for image compression.
2Simulation test
2.1Add noise to the image
In order to judge the effect of wavelet denoising and the effect of wavelets using different shrinking methods on different noise processing,firstly,the simulation program is written by MATLAB compiling software based on window7 and above.Select a picture with bright colors,and add Gaussian noise,salt and pepper noise,and mean noise to the picture.The picture after adding noise is shown below:
Gaussian noise means that the amplitude value probability obeys the Gaussian distribution, and the power spectrum obeys the uniformly distributed noise. The salt and pepper noise refers to a pulse typenoise with random white spots or black spots. The uniform noise refers to a spectrum that is constant. The power spectrum is constant, the mathematicalexpectation is a constant noise, and their three noises are very well represented.
2.2Use haar wavelet denoising effect diagram
The next step is to input the noise effect map of the previous step into the wavelet denoising system with the contraction method haar.The observed effect diagram is as follows:
Eva l u a ti o n o f p i c tu re p e rfo rman c e indicators Evaluating the quality of a picture's filtering is usually measured by the peak signal-to-noise ratio and the structural similarity index.
（1）The mean error of the peak signal to noise
ratio is defined as:
The peak signal to noise ratio is defined as:
In the formula,MAX represents the maximum value of the color of the image point.This simulation experiment uses 8-bit representation.
（2）SSIM structural similarity is an indicator
that measures the similarity between two different pictures.The expression is as follows:
Through the processing of the haar wavelet denoising in the previous step,the evaluation indexes of the image renderings after adding noise are as follows:
It can be seen from the performance index of the image in the above table and the effect diagram after wavelet denoising that for the wavelet variation using the same shrinking method,the effect of processing Gaussian noise is better than other noises.
2.5Different shrinking methods for image
processing with Gaussian noise Through the analysis of the previous indicator and effect diagram,for the wavelet transform transformation,the effect of processing the image with Gaussian noise is better.Next,the Gaussian noise image with the same amplitude will be processed,and the wavelet transform with different shrinkage methods will be used.The decomposition level is 2,and the effect diagram is as follows:
3.Simulation result analysis
By performing the above experimental processing on multiple graphs,it can be found that wavelet transform denoising has a very good effect on processing image processing with Gaussian noise,because different shrinking methods are used when processing the same Gaussian noise image with different shrinking methods.The characteristics of the processing are slightly different,but in general,the haar wavelet is very simple and runs very fast,and the desired high-frequency part signal can be obtained by the compression method,so it is not very In the case of harsh picture quality,haar wavelet has good denoising,small time complexity and more efficient operation.
4 Conclusion
This paper expounds the classical algorithmbased on wavelet t ransform as the theoretical basis. Through the simulation experiment and image performance index evaluation,the images with different noises are processed.It is concluded that the wavelet transform denoising processing Gaussian noise is better,but for different shrinking methods.The wavelet transform is the same method for Gaussian noise.The haar wavelet transform has the characteristics of small time complexity,high operating efficiency and excellent processing effect.Therefore,it is the preferred method for processing Gaussian white noise and has guiding significance for practical applications.
references
[1]Paul S.Addison,The Illustrated Wavelet Transform Handbook, Institute of Physics,2002,ISBN 0-7503-0692-0
[2]Ingrid Daubechies,Ten Lectures on Wavelets,Society for Industrial and Applied Mathematics,1992,ISBN 0-89871-274-2
[3]P.P.Viadyanathan,Multirate Systems and Filter Banks,Prentice Hall,1993,ISBN 0-13-605718-7
[4]A Wavelet Tour of Signal Processing,Third Edition:The Sparse Way,by S.Malla
[5]Coiflet wavelet transform applied to inspect power system disturbance-generated signals.Shyh-Jier Huang,and Cheng-Tao Hsieh.2002.
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