CN108596863A - A kind of Poisson image de-noising method based on optimum linear prediction - Google Patents
A kind of Poisson image de-noising method based on optimum linear prediction Download PDFInfo
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- CN108596863A CN108596863A CN201810619397.0A CN201810619397A CN108596863A CN 108596863 A CN108596863 A CN 108596863A CN 201810619397 A CN201810619397 A CN 201810619397A CN 108596863 A CN108596863 A CN 108596863A
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Abstract
A kind of Poisson image de-noising method based on optimum linear prediction proposed in the present invention, main contents include：Optimum linear prediction and Poisson image denoising based on patch, process are first to obtain guiding estimated value with existing Poisson denoising methodThen input picture is divided intoThe patch of a overlapping, then each patch is by after with neighbouring patch joint denoising, obtain corresponding net patch (not by the patch of noise pollution), the net image after denoising is finally rebuild using net patch (not by the image of noise pollution), it repeats L times, using the denoising image obtained every time as guiding estimated value next time.It is excessively complicated that the present invention solves the problems, such as that previous Poisson image de-noising method calculates, and can preferably optimize the initial denoising image obtained by several state-of-the-art methods, and algorithm is simple, computation complexity is low.
Description
Technical field
The present invention relates to image processing fields, more particularly, to a kind of Poisson image denoising based on optimum linear prediction
Method.
Background technology
Noise is an extremely important problem in image procossing, its each ring to the input of image, acquisition, processing
Section and final output result can all generate certain influence, and Poisson image de-noising method can be applied in aircraft remote sensing and be defended
In star remote sensing technology, denoising is carried out to remote sensing images, improves the quality of image；It can also apply in biomedical engineering side
Face carries out denoising to the image of microscope photographing, more accurately carries out bio-medical analysis such as chromosome analysis, cancer cell
Identification etc.；In terms of communication engineering, Poisson image de-noising method can be equally used for the image that processing receives, and improve communication matter
Amount.However, previous Poisson image de-noising method has calculating excessively complexity.
A kind of Poisson image de-noising method based on optimum linear prediction is proposed in the present invention, is first gone with existing Poisson
Method for de-noising obtains guiding estimated valueThen input picture is divided intoThe patch of a overlapping, then each patch is logical
It crosses with after neighbouring patch joint denoising, obtaining corresponding net patch (not by the patch of noise pollution), is finally mended using net
Fourth rebuild denoising after net image (not by the image of noise pollution), repeat L times, using the denoising image obtained every time as
Guiding estimated value next time.The present invention can preferably optimize the initial denoising image obtained by several state-of-the-art methods,
And algorithm is simple, and computation complexity is low.
Invention content
Excessively complicated problem is calculated for previous Poisson image de-noising method, the purpose of the present invention is to provide one kind
Poisson image de-noising method based on optimum linear prediction first obtains guiding estimated value with existing Poisson denoising methodThen
Input picture is divided intoThe patch of a overlapping, then each patch is by after with neighbouring patch joint denoising,
Corresponding net patch (not by the patch of noise pollution) is obtained, the net image finally rebuild after denoising using net patch (is not had
By the image of noise pollution), it repeats L times, using the denoising image obtained every time as guiding estimated value next time.
To solve the above problems, the present invention provides a kind of Poisson image de-noising method based on optimum linear prediction, master
The content is wanted to include：
(1) optimum linear prediction；
(2) the Poisson image denoising based on patch；
Wherein, the optimum linear prediction, include mainly the functional form of optimum linear prediction (BLP), characteristic and
The BLP of Poisson observation.
Further, the functional form refers to indicating that random vector and B indicate certainty matrix using a, then estimates
Unknown probability density function random vector X ∈ RnIt is the random vector Y ∈ R observedmLinear function：
Wherein B and a is a fixed matrix and vector respectively；Enable μyAnd μxThe respectively mean value of stochastic variable Y and X, is based on
The optimal selection of BLP theorems, B and a at least mean-square error (MMSE) is：
The optimal value of B and a is as above.
Further, the characteristic, refer to BLP be it is a kind of independently of stochastic variable be distributed except prediction technique, only
It is related with vector with covariance matrix；In the case of Gaussian noise, BLP is equivalent to using multivariate Gaussian distribution and covariance
It is predicted.
Further, it is Poisson random vector that the BLP of Poisson observation, which is instruction Y, its potential expectation value isI.e. for m=n, have：
WhereinPoisson condition is distributed, it is expected that method can obtain covariance matrix using iteration
∑xy=∑xx；The mean value and variance of Poisson distribution are equal, therefore by considering diagonal element, it is expected that method can using iteration
To obtain ∑xxAnd ∑yyBetween relationship, finally, the BLP of the X estimated by Poisson observation Y is：
The calculation formula of X is as above.
Wherein, the Poisson image denoising based on patch refers to being first image segmentationA overlapping
Patch, then each patch is by after with neighbouring patch joint denoising, obtaining corresponding net patch (not by noise pollution
Patch), the net image (not by the image of noise pollution) after denoising then is rebuild using net patch, is repeated L times, using each
The denoising image of acquisition is as guiding estimated value next time.
Further, the joint denoising refers to usingIt indicates the reference patch of guiding estimated value, usesIndicate adjacent
The set of nearly patch, calculates the average value mu of sample from patch setxWith covariance matrix ∑xx, using acquisition average value and
Covariance matrix removes y by BLPrIn all patches noise after, allow the patch of denoising to return to original position, calculate overlapping
Partial average value.
Further, the set of the neighbouring patch refers to input picture withCentered on, size be N × N window
Set of the upper excentric Euclidean plane apart from nearest k patch compositions.
Further, the average value and covariance matrix refer to assuming that neighbouring patch has same covariance square
Battle array ∑xx, then to μxAnd ∑xxEstimation really calculate sample average value and variance；Have in known variance additional zero flat
When mean value additive white Gaussian, still it is possible to obtain μ from patchxAnd ∑xx；It is obtained by a ready-made Poisson denoising method
After the initial estimation for obtaining net image, μ can be obtained by initial estimation imagexAnd ∑xx。
Further, the variance, refer to Poisson observation in, variance depend on the potential net value of image (not by
The numerical value of noise pollution), and the potential net value of image is unknown.
Description of the drawings
Fig. 1 is a kind of system flow chart of the Poisson image de-noising method based on optimum linear prediction of the present invention.
Fig. 2 is a kind of design sketch of the Poisson image de-noising method based on optimum linear prediction of the present invention.
Specific implementation mode
It should be noted that in the absence of conflict, the features in the embodiments and the embodiments of the present application can phase
It mutually combines, invention is further described in detail in the following with reference to the drawings and specific embodiments.
Fig. 1 is a kind of system flow chart of the Poisson image de-noising method based on optimum linear prediction of the present invention.Main packet
Include optimum linear prediction and the Poisson image denoising based on patch.
Wherein, optimum linear prediction includes mainly functional form, characteristic and the Poisson observation of optimum linear prediction (BLP)
BLP.
Further, the functional form refers to indicating that random vector and B indicate certainty matrix using a, then estimates
Unknown probability density function random vector X ∈ RnIt is the random vector Y ∈ R observedmLinear function：
Wherein B and a is a fixed matrix and vector respectively；Enable μyAnd μxThe respectively mean value of stochastic variable Y and X, is based on
The optimal selection of BLP theorems, B and a at least mean-square error (MMSE) is：
The optimal value of B and a is as above.
Further, the characteristic, refer to BLP be it is a kind of independently of stochastic variable be distributed except prediction technique, only
It is related with vector with covariance matrix；In the case of Gaussian noise, BLP is equivalent to using multivariate Gaussian distribution and covariance
It is predicted.
Further, it is Poisson random vector that the BLP of Poisson observation, which is instruction Y, its potential expectation value isI.e. for m=n, have：
WhereinPoisson condition is distributed, it is expected that method can obtain covariance matrix using iteration
∑xy=∑xx；The mean value and variance of Poisson distribution are equal, therefore by considering diagonal element, it is expected that method can using iteration
To obtain ∑xxAnd ∑yyBetween relationship, finally, the BLP of the X estimated by Poisson observation Y is：
The calculation formula of X is as above.
Wherein, the Poisson image denoising based on patch refers to being first image segmentationThe patch of a overlapping, connects
Each patch by after with neighbouring patch joint denoising, obtaining corresponding net patch (not by the patch of noise pollution),
Then the net image (not by the image of noise pollution) after denoising is rebuild using net patch, repeats L times, utilizes what is obtained every time
Denoising image is as guiding estimated value next time.
Further, the joint denoising refers to usingIt indicates the reference patch of guiding estimated value, usesIndicate neighbouring
The set of patch calculates the average value mu of sample from patch setxWith covariance matrix ∑xx, the average value using acquisition and association
Variance matrix removes y by BLPrIn all patches noise after, allow the patch of denoising to return to original position, calculate overlapping portion
The average value divided.
Further, the set of the neighbouring patch refers to input picture withCentered on, size be N × N window
Set of the upper excentric Euclidean plane apart from nearest k patch compositions.
Further, the average value and covariance matrix refer to assuming that neighbouring patch has same covariance square
Battle array ∑xx, then to μxAnd ∑xxEstimation really calculate sample average value and variance；Have in known variance additional zero flat
When mean value additive white Gaussian, still it is possible to obtain μ from patchxAnd ∑xx；It is obtained by a ready-made Poisson denoising method
After the initial estimation for obtaining net image, μ can be obtained by initial estimation imagexAnd ∑xx。
Further, the variance, refer to Poisson observation in, variance depend on the potential net value of image (not by
The numerical value of noise pollution), and the potential net value of image is unknown.
Fig. 2 is a kind of design sketch of the Poisson image de-noising method based on optimum linear prediction of the present invention.(a) is that do not have in figure
There is the original image of denoising；(b) it is to be based on a kind of existing Poisson image de-noising method --- Nonlinear Principal Component Analysis method
(NLPCA) image after noise is removed；(c) it is after combining a kind of existing Poisson image de-noising method and present invention removal noise
Image, can be intuitive to see that the denoising effect of (c) is better, the Y-PSNR (PSNR) of (c) is also than (b) simultaneously
It is higher by 0.8, shows that the present invention can preferably optimize the initial denoising image obtained by several state-of-the-art methods.
For those skilled in the art, the present invention is not limited to the details of above-described embodiment, in the essence without departing substantially from the present invention
In the case of refreshing and range, the present invention can be realized in other specific forms.In addition, those skilled in the art can be to this hair
Bright to carry out various modification and variations without departing from the spirit and scope of the present invention, these improvements and modifications also should be regarded as the present invention's
Protection domain.Therefore, the following claims are intended to be interpreted as including preferred embodiment and falls into all changes of the scope of the invention
More and change.
Claims (10)
1. a kind of Poisson image de-noising method based on optimum linear prediction, which is characterized in that include mainly optimum linear prediction
(1)；Poisson image denoising (two) based on patch.
2. based on the optimum linear prediction (one) described in claims 1, which is characterized in that include mainly optimum linear prediction
(BLP) functional form, characteristic and the BLP of Poisson observation.
3. based on the functional form described in claims 2, which is characterized in that indicate that random vector and B indicate certainty using a
Matrix, then the random vector X ∈ R for the unknown probability density function estimatednIt is the random vector Y ∈ R observedmLinear function：
Wherein B and a is a fixed matrix and vector respectively；Enable μyAnd μxThe respectively mean value of stochastic variable Y and X is based on BLP
The optimal selection of theorem, B and a at least mean-square error (MMSE) is：
The optimal value of B and a is as above.
4. based on the characteristic described in claims 2, which is characterized in that BLP be it is a kind of independently of stochastic variable be distributed except
Prediction technique, it is only related with vector with covariance matrix；In the case of Gaussian noise, BLP is equivalent to use multivariate Gaussian
Distribution and covariance are predicted.
5. the BLP based on the Poisson observation described in claims 2, which is characterized in that it is Poisson random vector to enable Y, it dives
It is in desired valueI.e. for m=n, have：
WhereinPoisson condition is distributed, it is expected that method can obtain covariance matrix ∑ using iterationxy=
∑xx；The mean value and variance of Poisson distribution are equal, therefore by considering diagonal element, it is expected that method can obtain using iteration
∑xxAnd ∑yyBetween relationship, finally, the BLP of the X estimated by Poisson observation Y is：
The calculation formula of X is as above.
6. based on the Poisson image denoising (two) based on patch described in claims 1, which is characterized in that first image segmentation
ForThe patch of a overlapping, then each patch is by after with neighbouring patch joint denoising, obtaining corresponding net patch
(not by the patch of noise pollution) then rebuilds the net image after denoising (not by the figure of noise pollution using net patch
Picture), it repeats L times, using the denoising image obtained every time as guiding estimated value next time.
7. based on the joint denoising described in claims 6, which is characterized in that useIt indicates the reference patch of guiding estimated value, usesThe set for indicating neighbouring patch, calculates the average value mu of sample from patch setxWith covariance matrix ∑xx, utilize acquisition
Average value and covariance matrix are removed by BLPIn all patches noise after, allow the patch of denoising to return to original position,
Calculate the average value of lap.
8. the set based on the neighbouring patch described in claims 7, which is characterized in that input picture withCentered on, size be
Set of the excentric Euclidean plane apart from nearest k patch compositions on the window of N × N.
9. based on average value and covariance matrix described in claims 7, which is characterized in that assuming that neighbouring patch has equally
Covariance matrix ∑xx, then to μxAnd ∑xxEstimation really calculate sample average value and variance；Have in known variance
When additional zero mean additive white Gaussian, still it is possible to obtain μ from patchxAnd ∑xx；Pass through a ready-made Poisson
After denoising method obtains the initial estimation of net image, μ can be obtained by initial estimation imagexAnd ∑xx。
10. based on the variance described in claims 9, which is characterized in that in Poisson observation, it is potential that variance depends on image
Net value (not by the numerical value of noise pollution), and the potential net value of image is unknown.
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104969257A (en) * | 2012-12-06 | 2015-10-07 | 日本电气株式会社 | Image processing device and image processing method |
| CN107123094A (en) * | 2017-03-23 | 2017-09-01 | 四川精目科技有限公司 | A kind of mixing Poisson, the video denoising method of gaussian sum impulsive noise |
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Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104969257A (en) * | 2012-12-06 | 2015-10-07 | 日本电气株式会社 | Image processing device and image processing method |
| CN107123094A (en) * | 2017-03-23 | 2017-09-01 | 四川精目科技有限公司 | A kind of mixing Poisson, the video denoising method of gaussian sum impulsive noise |
Non-Patent Citations (1)
| Title |
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| MILAD NIKNEJAD: "Poisson Image Denoising Using Best Linear Prediction: A Post-processing Framework", 《ARXIV:1803.00389V1》 * |
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