CN109242799A - A kind of Wavelet noise-eliminating method of variable threshold value - Google Patents
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Abstract
The present invention discloses a kind of Wavelet noise-eliminating method of variable threshold value, including five steps.Step 1 inputs original image and corresponding Gaussian noise is added；Step 2 selects wavelet basis function and determines the number of plies O of wavelet decomposition: decomposing to obtain first layer low frequency coefficient A1, horizontal and vertical high frequency coefficient H1 and V1, diagonal high frequency coefficient D1 to noise image S；A1 is decomposed to obtain second layer low frequency coefficient A2, horizontal and vertical high frequency coefficient H2 and V2, diagonal high frequency coefficient D2；A2 is decomposed to obtain third layer low frequency coefficient A3, horizontal and vertical high frequency coefficient H3 and V3 and diagonal high frequency coefficient D3；Successively decompose O layers；Step 3: choosing the wavelet threshold closed and with straight lineWavelet coefficient is handled for the wavelet threshold function of asymptote；Step 4 carries out wavelet reconstruction to the wavelet coefficient after threshold value quantizing；Step 5, the image after output denoising.The present invention can improve the precision of wavelet transform process noise signal, effectively promote the denoising effect of image, obtain high quality and denoise image.
Description
Technical field
The present invention relates to the denoising field of Digital Image Processing more particularly to a kind of Wavelet noise-eliminating methods of variable threshold value.
Background technique
Image vulnerable to the influence of noise, and leads to image quality decrease in formation, record, processing and transmission process,
So that image is thickened, or even flood characteristics of image, this is to works such as subsequent image region segmentation, target identification, edge extractings
Bring difficulty.Therefore, before handling image, removal noise is a crucial pretreatment link.In order to obtain
Quality digital image, it is necessary to carry out noise reduction process to image, holding raw information integrality is (i.e. main special as far as possible
Sign) while, and information useless in signal can be removed.So noise reduction process is always the hot spot of image procossing.
Wavelet Denoising Method is generally divided into three classes, and the first kind is to carry out image denoising using wavelet modulus maxima method；The
Two classes are after making wavelet transformation to noisy acoustical signal, big according to correlation by calculating the correlation of wavelet coefficient between adjacent ruler
Small to accept or reject to wavelet coefficient, finally reconstruct obtains denoised signal；Third class is threshold denoising, it is according to after wavelet transformation
The distribution of the wavelet coefficient of signal and noise is different, carries out what different processing was realized to wavelet coefficient.Wherein wavelet threshold denoising
Method operand is small, realizes simply, is used widely.
Patent " DR image de-noising method and system based on wavelet transformation " (patent No.: 102663695A), using improvement
Soft-threshold function image is handled, wavelet reconstruction obtains the high frequency coefficient and low frequency coefficient of first layer, to first layer height
Frequency coefficient uses hard threshold function to be handled again, then reconstructs again.This method organically combines soft, hard threshold function one
It rises, achieves preferable denoising effect, improve the signal-to-noise ratio of image, but still not can solve soft, hard threshold function itself
Disadvantage.
The present invention is compared with " DR image de-noising method and system based on wavelet transformation ", advantage are as follows:
(1) wavelet threshold function of the invention is with straight lineFor asymptote, solves hard threshold function in threshold
The problem of being worth the constant deviation bring edge blurry at point between discontinuous and soft-threshold function.
(2) wavelet threshold proposed by the present invention has adaptivity, meets noise letter of the picture signal in decomposable process
Number constantly reduce and picture signal the characteristics of constantly increasing.In Decomposition order i=1, as global threshold, with decomposition layer
Several increase threshold values is constantly reducing.
(3) wavelet threshold proposed by the present invention can be according to the different update thresholds that can be adaptive of the picture breakdown number of plies
Value, is allowed to the characteristics of adapting to each layer of wavelet conversion coefficient.
The purpose of the present invention is to provide a kind of wavelet threshold and wavelet threshold functions, can improve wavelet transform process noise
The precision of signal effectively promotes the denoising effect of image, obtains high quality and denoises image.
Summary of the invention
To solve the deficiencies in the prior art, the purpose of the present invention is to provide a kind of Wavelet noise-eliminating method of variable threshold value, with
Improve the denoising effect of image.
The present invention relates to a kind of Wavelet noise-eliminating methods of variable threshold value, which is characterized in that specifically follows the steps below:
Step 1 inputs original image and corresponding Gaussian noise is added；
Step 2, select a wavelet basis function appropriate and determine wavelet decomposition number of plies O, then to noisy image into
O layers of wavelet decomposition of row:
(a) noise image S is decomposed to obtain first layer low frequency coefficient A1, first layer horizontal high-frequent coefficient H1, first
Layer vertical high frequency coefficient V1, the diagonal high frequency coefficient D1 of first layer；
(b) first layer low frequency coefficient A1 is decomposed to obtain second layer low frequency coefficient A2, second layer horizontal high-frequent coefficient
H2, second layer vertical high frequency coefficient V2, the diagonal high frequency coefficient D2 of the second layer；
(c) second layer low frequency coefficient A2 is decomposed to obtain third layer low frequency coefficient A3, third layer horizontal high-frequent coefficient
H3, third layer vertical high frequency coefficient V3 and the diagonal high frequency coefficient D3 of third layer；
(d) the O layer wavelet decomposition number of plies until reaching requirement is successively decomposed to the low frequency coefficient of current layer；
Step 3: the threshold value quantizing of wavelet coefficient, chooses suitable wavelet threshold and wavelet threshold function to wavelet coefficient
It is handled；
Step 4, wavelet coefficient reconstruct carry out wavelet reconstruction to the wavelet coefficient after threshold value quantizing；
Step 5, the image after output denoising.
Further, the Wavelet noise-eliminating method of a kind of variable threshold value according to claim 1, which is characterized in that described
In step 3, the threshold value quantizing of wavelet coefficient, choose suitable wavelet threshold and wavelet threshold function to wavelet coefficient at
Reason, wavelet threshold function is,
M is positive number in formula (1),For treated wavelet coefficient, WL, kFor wavelet coefficient, T is wavelet threshold
Further, the Wavelet noise-eliminating method of a kind of variable threshold value, which is characterized in that in the step 3, small echo
The threshold value quantizing of coefficient, chooses suitable wavelet threshold and wavelet threshold function handles wavelet coefficient, wavelet threshold letter
Number is with straight lineFor asymptote.
Further, the Wavelet noise-eliminating method of a kind of variable threshold value, which is characterized in that in the step 3, small echo
The threshold value quantizing of coefficient, chooses suitable wavelet threshold and wavelet threshold function handles wavelet coefficient, wavelet threshold T
For,
I is the number of plies of current decomposition in formula (2), and σ is signal variance, and M*N is the size of i-th layer of high frequency coefficient, threshold value energy
It is enough to reduce with the increase of Decomposition order, meet the variation of noise signal and picture signal in wavelet decomposition real process.
Further, the Wavelet noise-eliminating method of a kind of variable threshold value, which is characterized in that in the step 3, small echo
In threshold function table, when 50≤m≤60, can obtain best image denoising effect.
The present invention achieves following technical effect compared with the existing technology:
(1) wavelet threshold function of the invention is with straight lineIt is for asymptote and continuous at threshold point ± T, no
Hard threshold function discontinuous disadvantage at threshold point is addressed only, soft-threshold function can also be solvedAnd Wj,kBetween have
The problem of having constant deviation and bring edge blurry.Will be proven below the wavelet threshold function of formula (1) withFor gradually
Inlet wire.
Work as WL, k→T+And WL, k→T-When,Work as WL, k→-T+And WL, k→-T+WhenSo after improving
Threshold function table it is continuous at threshold point ± T, solve figure of the hard threshold function after the place threshold point ± T discontinuously causes to denoise
As there is the pseudo- vision distortions phenomenon such as Gibbs' effect and ring.
IfWherein m, T are constant
Cause are as follows:
So function f (x) is that can to obtain the wavelet threshold function of formula (1) using y=x as asymptote be with straight lineFor asymptote.Solve soft-threshold function treated wavelet coefficient and original wavelet coefficient there are it is constant partially
The problem of difference, so that the effect that image is handled in terms of edge details is more further.
(2) wavelet threshold function of the invention is continuous at threshold point ± T, solves hard threshold function in threshold point ± T
Place discontinuously causes the image after denoising the pseudo- vision distortions phenomenon such as Gibbs' effect and ring occur.
(3) wavelet threshold proposed by the present invention has adaptivity, meets noise letter of the picture signal in decomposable process
Number constantly reduce and picture signal the characteristics of constantly increasing.
(4) wavelet threshold proposed by the present invention can solve traditional global threshold problem, the ln (e+2 in formula (2)(1-i)- 1) it is equivalent to a contraction factor, in Decomposition order i=1, as global threshold, with the increase of Decomposition order
Threshold value is constantly reducing.
(5) wavelet threshold proposed by the present invention can be according to the different update thresholds that can be adaptive of the picture breakdown number of plies
Value, is allowed to the characteristics of adapting to each layer of wavelet conversion coefficient.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the invention
Example, for those of ordinary skill in the art, without any creative labor, can also be according to these attached drawings
Obtain other attached drawings.
Fig. 1 is small echo hard threshold function image；
Fig. 2 is wavelet soft-threshold functional image；
Fig. 3 is threshold function table image of the invention；
Fig. 4 is a kind of Wavelet noise-eliminating method flow chart of variable threshold value；
Fig. 5 is wavelet decomposition process schematic；
Fig. 6 is wavelet coefficient threshold quantization flow figure；
Fig. 7 is denoising result of the distinct methods to the Lena image addition Gaussian noise of σ=10；
Fig. 8 is denoising result of the distinct methods to the Lena image addition Gaussian noise of σ=20；
Fig. 9 is denoising result of the distinct methods to the Lena image addition Gaussian noise of σ=30；
Wherein, S is noise image；A1, A2, A3 are respectively first, second and third layer of low frequency coefficient；G1, G2, G3 are respectively
One, two, three layers of high frequency coefficient；G11, G22, G33 are respectively first, second and third layer of high frequency coefficient after threshold value quantizing；It is each
The high frequency coefficient G of layer includes horizontal, vertical and diagonal high frequency coefficient H, V and D.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Fig. 1 and Fig. 2 is hard, the soft-threshold function figure of small echo respectively, when being used for image denoising, because hard threshold function exists
It is discontinuous at threshold point, so that the image of reconstruct will appear the vision distortions such as pseudo- Gibbs' effect, ring.And soft-threshold letter
For the small echo signal of number treated small echo signal and original image there are constant deviation, accuracy decline when leading to reconstruct makes image
Edge blurry.In order to improve the above problem, the present invention devises the threshold function table of Fig. 3.
As shown in figure 4, the present invention discloses a kind of Wavelet noise-eliminating method of variable threshold value, including five steps.
Step S1 inputs original image and corresponding Gaussian noise is added；
Step S2 selects wavelet basis function and determines the number of plies O of wavelet decomposition: according to the wavelet decomposition figure of Fig. 5 to noise
Image S decomposes to obtain first layer low frequency coefficient A1, horizontal and vertical high frequency coefficient H1 and V1, diagonal high frequency coefficient D1；Again to A1
Decomposition obtains second layer low frequency coefficient A2, horizontal and vertical high frequency coefficient H2 and V2, diagonal high frequency coefficient D2；A2 is decomposed again
To third layer low frequency coefficient A3, horizontal and vertical high frequency coefficient H3 and V3 and diagonal high frequency coefficient D3；Successively decompose O layers；
Step S3, the wavelet threshold closed is chosen and with straight lineFor asymptote wavelet threshold function to small echo
Coefficient is handled；
Step S4, according to the wavelet coefficient threshold quantization flow figure of Fig. 6 to threshold value quantizing, then to the wavelet systems after quantization
Number carries out wavelet reconstruction；
Step S5, the image after output denoising.
Further, the Wavelet noise-eliminating method of a kind of variable threshold value according to claim 1, which is characterized in that described
In step 3, the threshold value quantizing of wavelet coefficient, choose suitable wavelet threshold and wavelet threshold function to wavelet coefficient at
Reason, wavelet threshold function is,
Wherein m is positive number,For treated wavelet coefficient, WL, kFor wavelet coefficient, T is wavelet threshold.
Further, the Wavelet noise-eliminating method of a kind of variable threshold value, which is characterized in that in the step 3, small echo
The threshold value quantizing of coefficient, chooses suitable wavelet threshold and wavelet threshold function handles wavelet coefficient, wavelet threshold letter
Number is with straight lineFor asymptote.
Further, the Wavelet noise-eliminating method of a kind of variable threshold value, which is characterized in that in the step 3, small echo
The threshold value quantizing of coefficient, chooses suitable wavelet threshold and wavelet threshold function handles wavelet coefficient, wavelet threshold T
For,
Wherein i is the number of plies of current decomposition, and σ is signal variance, and M*N is the size of i-th layer of high frequency coefficient, and threshold value can be with
The increase of Decomposition order and reduce, meet the variation of noise signal and picture signal in wavelet decomposition real process.
Further, the Wavelet noise-eliminating method of a kind of variable threshold value, which is characterized in that in the step 3, small echo
In threshold function table, when 50≤m≤60, can obtain best image denoising effect.
In order to verify effectiveness of the invention, l-G simulation test has been carried out.
Experiment programs in the environment of MATLAB 2018a, is being configured to intel (R) Core (TM) i5-5200U
It is run on the PC of CPU2.19GHz.The number of plies value N=3 of wavelet decomposition in experimentation, the m=58 in modus ponens (1).
σ=10, σ=20 are added in the standard Lena image that resolution ratio is 512 × 512, after the Gaussian noise of σ=30, point
It Cai Yong not hard threshold function, soft-threshold function, soft and hard threshold function combination (patent " the image denoising side DR based on wavelet transformation
Method and system ", the patent No.: 102663695A) and method proposed by the present invention denoised, the effect after denoising such as Fig. 7, Fig. 8
With shown in Fig. 9, it is clear that the present invention can preferably protect the marginal information of image while denoising.With Y-PSNR (PSNR)
The effect of denoising is measured, denoising result is as shown in table 1.
1 denoising result of table compares
Can be seen that denoising method of the invention from 1 test result of table can obtain better PSNR.
The foregoing is merely one embodiment of the present of invention, are not intended to limit the scope of the present invention.It is all
Any modification, equivalent replacement, improvement and so within the spirit and principles in the present invention, are all contained in protection scope of the present invention
It is interior.
Claims (5)
1. a kind of Wavelet noise-eliminating method of variable threshold value, which is characterized in that specifically follow the steps below:
Step 1 inputs original image and corresponding Gaussian noise is added；
Step 2 selects a wavelet basis function appropriate and determines the number of plies O of wavelet decomposition, then carries out O to noisy image
Layer wavelet decomposition:
(a) it is decomposed to obtain first layer low frequency coefficient A1, first layer horizontal high-frequent coefficient H1, first layer to noise image S to hang down
Straight high frequency coefficient V1, the diagonal high frequency coefficient D1 of first layer；
(b) first layer low frequency coefficient A1 is decomposed to obtain second layer low frequency coefficient A2, second layer horizontal high-frequent coefficient H2,
Two layers of vertical high frequency coefficient V2, the diagonal high frequency coefficient D2 of the second layer；
(c) second layer low frequency coefficient A2 is decomposed to obtain third layer low frequency coefficient A3, third layer horizontal high-frequent coefficient H3,
Three layers of vertical high frequency coefficient V3 and third layer diagonal coefficient D3；
(d) the O layer wavelet decomposition number of plies until reaching requirement is successively decomposed to the low frequency coefficient of current layer；
Step 3: the threshold value quantizing of wavelet coefficient, chooses suitable wavelet threshold and wavelet threshold function and carries out to wavelet coefficient
Processing；
Step 4, wavelet coefficient reconstruct carry out wavelet reconstruction to the wavelet coefficient after threshold value quantizing；
Step 5, the image after output denoising.
2. a kind of Wavelet noise-eliminating method of variable threshold value according to claim 1, which is characterized in that small in the step 3
The threshold value quantizing of wave system number, chooses suitable wavelet threshold and wavelet threshold function handles wavelet coefficient, wavelet threshold
Function is,
M is positive number in formula (1),For treated wavelet coefficient, WL, kFor wavelet coefficient, T is wavelet threshold.
3. a kind of Wavelet noise-eliminating method of variable threshold value according to claim 1, which is characterized in that small in the step 3
The threshold value quantizing of wave system number, chooses suitable wavelet threshold and wavelet threshold function handles wavelet coefficient, wavelet threshold
Function is with straight lineFor asymptote.
4. a kind of Wavelet noise-eliminating method of variable threshold value according to claim 1, which is characterized in that small in the step 3
The threshold value quantizing of wave system number, chooses suitable wavelet threshold and wavelet threshold function handles wavelet coefficient, wavelet threshold T
For,
I is the number of plies of current decomposition in formula (2), and σ is signal variance, and M*N is the size of i-th layer of high frequency coefficient, and threshold value can be with
The increase of Decomposition order and reduce, meet the variation of noise signal and picture signal in wavelet decomposition real process.
5. a kind of Wavelet noise-eliminating method of variable threshold value according to claim 1, which is characterized in that small in the step 3
In wave threshold function table, when 50≤m≤60, can obtain best image denoising effect.
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| CN113239751A (en) * | 2021-04-27 | 2021-08-10 | 电子科技大学 | Wavelet threshold denoising method based on weighting factor |
| CN113628627A (en) * | 2021-08-11 | 2021-11-09 | 广东电网有限责任公司广州供电局 | Electric power industry customer service quality inspection system based on structured voice analysis |
| CN113628627B (en) * | 2021-08-11 | 2022-06-14 | 广东电网有限责任公司广州供电局 | Electric power industry customer service quality inspection system based on structured voice analysis |
| CN114841213A (en) * | 2022-05-19 | 2022-08-02 | 东南大学 | Silicon micro-resonance type accelerometer noise reduction method based on improved wavelet threshold function |
| CN115147316A (en) * | 2022-08-06 | 2022-10-04 | 南阳师范学院 | Computer image high-efficiency compression method and system |
| CN115147316B (en) * | 2022-08-06 | 2023-04-04 | 南阳师范学院 | Computer image efficient compression method and system |
| CN117520752A (en) * | 2024-01-05 | 2024-02-06 | 梁山公用水务有限公司 | Hydraulic engineering information management method based on big data |
| CN117520752B (en) * | 2024-01-05 | 2024-04-12 | 梁山公用水务有限公司 | Hydraulic engineering information management method based on big data |
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