CN109242798A - A kind of Poisson denoising method based on three cross-talk network representations - Google Patents
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Abstract
The present invention provides a kind of Poisson denoising methods based on three cross-talk network representations, the following steps are included: step (a): the input picture that pixel value is all 1 is added after process of convolution with by the noisy image of two convolution operators, obtains intermediate processed images 1；Step (b): by intermediate processed images 1 after one without normalization layers of batch of resnet resume module, intermediate processed images 2 are obtained；Step (c): after further using two convolution to step (b), the figure for being 1 with pixel value is added, and obtains final result；The present invention inherits and extends the structure and advantage of traditional variance stabilizing transformation scheme, by the method for network design and supervised learning, is mapped using three sub- network processes Nonlinear Learnings, widening for network substantially increases denoising performance；Compared with traditional iterated denoising method, the present invention has better denoising performance, and especially image recovery effects are more superior in the case where low signal-to-noise ratio.
Description
Technical field
The present invention relates to optoelectronic device technology field, specially a kind of Poisson denoising side based on three cross-talk network representations
Method.
Background technique
Image denoising is the basic problem in image procossing, and target is to estimate ideal image from noisy observed image,
Usually this is an ill posed indirect problem, and lot of documents conducts in-depth research the problem, but is primarily directed to
Additive white Gaussian noise, however in optical quantum counter imaging system, such as CCD solid-state photo detector array, astronomical imaging, meter
X-ray imaging (CR), fluorescent confocal micro-imaging etc. are calculated, the image of acquisition suffers from the pollution of quantum noise.
Since light has quantum special efficacy, reaching the quantum numbers of photo detector surfaces, there are statistic fluctuations, therefore, image
Monitoring have graininess, this graininess cause picture contrast become smaller and the covering to image detail information, we
To it is this because light quantum and caused by measuring uncertainty become image poisson noise.In the case where photon limitation, lead to
Poisson noise can often be generated.In the application such as biomedical imaging, night vision and astronomy, the signal degradation as caused by poisson noise
It is a kind of common phenomenon.Therefore, poisson noise is particularly important for subsequent processings such as the classification and identification of image.But with additivity height
This noise is different, and poisson noise is a kind of multiplicative noise, be unsatisfactory for simple additive principle and noise intensity and variance be signal according to
Bad.Noise signal depends on image itself, i.e., feature relevant to signal.Specifically, it is assumed that f is the obedience pool observed
The image polluted by noise of pine distribution, then discrete probabilistic are as follows:
Wherein noise-free picture u represents the average value of distribution, and i represents pixel value.Generally, the signal-to-noise ratio of each pixel
(i.e. peak value) isTherefore, in the image observed, lower signal strength means stronger noise.Making an uproar in image
Acoustical power is usually measured by the maximum value of image, referred to as peak value.
Statistically, the big pixel of brightness is more interfered, therefore removing poisson noise is a difficult task.It goes
Except a classical way of poisson noise is to carry out variance stabilizing transformation, example in airspace or transform domain (such as small echo) to observation data
Such as Anscombe, HaarFisz, CVS are converted, and each data are approximate homoscedastic Gaussian Profile after transformation, to be converted into
General Gauss Denoising Problems.Such as Wiener filtering, the wavelet threshold contraction of many algorithms can be applied to the problem, most afterwards through anti-VS
Transformation can get final denoising data.But, data are just progressive only when number of photons gradually becomes more, after VS transformation tends to be high
This distribution, is not particularly suited for low light quantity subnumber situation, and such as X-Ray, Gamma ray data, while VS is transformed to nonlinear transformation,
It is unfavorable for the performance of analysis and optimization Denoising Algorithm.
Practical application needs more efficiently Poisson denoising method, without carrying out variance stabilizing transformation pretreatment, Neng Gouzhi
Connect analysis Poisson data.The wavelet conversion coefficient of noisy image grasp with the threshold value that poisson noise statistical property is adapted
Make, can avoid variance stabilizing transformation.For this purpose, being directed to the statistical property of poisson noise, Kolaczyk is had modified originally for Gauss
The wavelet coefficient threshold strategy of noise, but be not still very effectively under low number of photons situation.Subsequent Kolaczyk is proposed
Another algorithm can preset false detection rate, to Haar by assumed statistical inspection (hypothesis-testing) strategy
Wavelet coefficient consistency (importance) is differentiated, and carries out corresponding threshold operation.Further by this method be extended to it is double just
Haar small echo is handed over, more smooth denoising image can be formed.Another kind of method is that pool is handled under multiple dimensioned Bayesian frame
Loose noise.The advantages of Bayesian method is to utilize simultaneously during denoising in combination with the priori knowledge about ideal image
Multiscale analysis can simplify Denoising Problems, obtain the approval of scholars.
Above method has its saving grace, but generally existing shortcoming is to handle under low signal-to-noise ratio well
Image restore.
Summary of the invention
The purpose of the present invention is to provide a kind of Poisson denoising methods based on three cross-talk network representations, to solve above-mentioned back
The problem of being proposed in scape technology.
To achieve the above object, the invention provides the following technical scheme: a kind of Poisson based on three cross-talk network representations is gone
Method for de-noising, comprising the following steps:
Step (a): pixel value be all 1 input picture after process of convolution with the noisy figure by two convolution operators
As being added, intermediate processed images 1 are obtained；
Step (b): intermediate processed images 1 are passed through at the resnet module without normalization layers of batch
After reason, intermediate processed images 2 are obtained；
Step (c): after further using two convolution to step (b), the figure for being 1 with pixel value is added, and is most terminated
Fruit.
Further, the step (a) are as follows:
If output of the noisy image f of input after a convolution operatorAre as follows:
Wherein, w is the weight to be learnt, and b is biasing, d1, d2The number of filter respectively output and input, in network
Training under study weight and biasing have a great impact to the result of experiment；Therefore the output g of sub-network 1 can be expressed approximately
Are as follows:
G=Conv (1)+Conv (Conv (f))
Wherein, Conv (1) is that pixel value is all the output of 1 image after a convolutional layer, and Conv (Conv (f)) is
Output of the noisy image after two continuous convolutional layers.The Anscombe transformation of sub-network 1 main analog, will have Poisson
The stochastic variable of distribution is converted into the stochastic variable with approximate test Gaussian Profile, facilitates subsequent be further processed.
Further, the step (b) are as follows:
Non-linear very strong due to poisson noise, the forward transform of the first step and the denoising of second step are simultaneously inaccurate, can only
Approximation is realized.Therefore, the design of subnet 2 is not intended to remove pure Gaussian noise, but an approximate Gauss denoises.Therefore it needs
Whole process is assisted using more flexible operation operator, therefore there is no use in the residual error learning network of sub-network two
Normalization layers of batch, this idea has obtained experimental verification in other networks；
The thought of residual error study is utilized in sub-network 2, if the Feature Mapping of the input g of network is F (g), it is just like following table
It reaches:
F (g)=w2σ(w1g)
Wherein, F (g) is the compound function being made of convolution operator and ReLU activation primitive, and σ represents nonlinear function
ReLU, ReLU unit are essential a part in the active coating and network of network, after being usually arranged on convolutional layer.
The output of sub-network 2 is H (g), function representation are as follows:
H (g)=F (g, { wi})+g
This residual error function is easier to optimize and can solve the degenerate problem of depth network, and the network number of plies can be made to add significantly
It is deep.
Further, the step (c) are as follows:
Sub-network 3 simulates the inverse transformation of Anscombe transformation, returns it to that variance is stable and denoising data were to originally
Range is echoed with 1 phase of sub-network；
Output=Conv (1)+Conv (Conv (H (g)))
Wherein Conv (Conv (H (g))) be sub-network 2 output after two continuous convolutional layers as a result, in this way
Continuous convolution operation can not only improve the recovery effects of image, more training process can be made more stable.
Compared with prior art, the beneficial effects of the present invention are:
The present invention combines variance stabilizing transformation structure with convolutional neural networks, and it is non-to propose a kind of new Poisson denoising
Iterative algorithm.Combination learning strategy and two stages incremental learning strategy is utilized, to the reasonability of variance stabilizing transformation scheme
It is studied with intensity.The structure and advantage for inheriting and extending traditional variance stabilizing transformation scheme, by network design and
The method of supervised learning is mapped using three sub- network processes Nonlinear Learnings.Widening for network substantially increases denoising performance.
Compared with traditional iterated denoising method, the present invention has better denoising performance, the especially following figure the low signal-to-noise ratio the case where
As recovery effects are more superior.
Detailed description of the invention
Fig. 1 is the flow chart of inventive algorithm step；
Fig. 2 is present invention training frame diagram；
Fig. 3 is the denoising result figure under the present invention is 0.1 in peak value；It (a) is original image；It (b) is noise pattern；(c)(d)
It (e) is respectively Poisson-NL, NLPCA and the reconstruction result map of this algorithm；
Fig. 4 is the denoising result figure under the present invention is 2 in peak value；It (a) is original image；It (b) is noise pattern；(c)(d)
It (e) is respectively Poisson-NL, NLPCA and the reconstruction result map of this algorithm.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is described in further detail.The specific embodiments are only for explaining the present invention technical solution described herein, and
It is not limited to the present invention.
It is described as follows in conjunction with specific steps of the attached drawing 1 to the method for the present invention.
Step (a): being the image containing poisson noise having been observed that based on f known to variance stabilizing transformation, it is assumed that there are one
A transformation Φ can make Φ f become sparse and obey Poisson distribution, then can approximately be described by Taylor's formula are as follows:
Wherein, O (Φ fi) indicate the remainder of Taylor's formula, i.e. actual function value and polynomial deviation.For intuitive,
If we simulate Φ transformation, g using convolution operatoriThe sum of some convolution algorithms can be approximately expressed as.Therefore,
We approach non-linear squares radical operator with convolution algorithm.For stable purpose in sub-network 1, we utilize convolutional layer
And summation operation is approximately promoted aforesaid equation, it may be assumed that
For specific, output of the input picture after a convolution operatorAre as follows:
Wherein, w is the weight to be learnt, and b is biasing, d1, d2The number of filter respectively output and input, in network
Training under study weight and biasing have a great impact to the result of experiment.
Conv (1) is that pixel value is all the output of 1 image after convolution operation, and Conv (f) be that input contains Poisson
Output of the image of noise after convolution operation.Pixel value is all 1 image and the image difference containing poisson noise of input
It is added to after convolution operation together, the processing of sub-network 1 is the key that be different from traditional Poisson denoising network.Many institute's weeks
To know, traditional forward direction Anscombe transformation can only accurately handle the biggish Poisson data of peak value, and in the case where peak value is small
Recovery effects are bad, and the Φ transformation trained in the present invention is definite existing and can be well to any peak value
Input signal is handled.It is noted that stabilization process becomes more inaccurate when peak value reduces, need more complicated
Structure.Therefore, when low signal-to-noise ratio in peak value less than 20, sub-network 1 uses two continuous convolutional layer (i.e. Conv
(Conv (f))) performance is improved, not only make image recovery effects more outstanding, also becomes more stable entire training process,
That is:
G=Conv (1)+Conv (Conv (f))
The Anscombe transformation of sub-network 1 main analog, converting the stochastic variable with Poisson distribution to has approximation
The stochastic variable of standard gaussian distribution, facilitates subsequent be further processed.
Step (b): the Feature Mapping of input g of sub-network 2 is set as F (g), it has following expression:
F (g)=w2σ(w1g)
Wherein, F (g) is the compound function being made of convolution operator and ReLU activation primitive, and w is the power to be learnt
Weight, σ represent nonlinear function ReLU, and ReLU unit is essential a part in the active coating and network of network, usually
After being arranged on convolutional layer, by ReLU realize it is sparse after model can preferably excavate correlated characteristic, be fitted training data.
The output of sub-network 2 is H (g), function representation are as follows:
H (g)=F (g, { wi})+g
This residual error function is easier to optimize and can solve the degenerate problem of depth network, and the network number of plies can be made to add significantly
It is deep.
It is non-linear extremely strong due to poisson noise, so output data is not pure after the forward transform of sub-network 1
Pure Gaussian distributed, but approximate homoscedastic Gaussian Profile, so needing in the part of sub-network 2 using more flexible
Operator assist whole process.Therefore, from existing some different, subnets that using residual error learn to carry out the algorithm of Gauss denoising
The residual block of network 2 is only provided with convolutional layer and ReLU layers, and there is no the operation for using batch normalization, Yi Xieke
The experiment leaned on also demonstrates that normalization layers of batch are not necessarily in fact.
In network training process, the parameter of each layer is instructed together with the parameter of sub-network 1 and sub-network 3 in sub-network 2
Experienced, experiments have shown that the denoising effect of joint training in this way is more preferable than two separated step training effects.
Step (c): sub-network 3 simulates the inverse transformation of Anscombe transformation, returns it to variance stabilization and denoising data
To original range, echoed with 1 phase of sub-network；
Output=Conv (1)+Conv (Conv (H (g)))
Wherein, Conv (Conv (H (g))) be sub-network 2 output after two continuous convolutional layers as a result, in this way
Continuous convolution operation can not only improve the recovery effects of image, more training process can be made more stable.
There is a kind of trend in recent years, i.e. the network of expansion filter size and the number of channel there are image recovery tasks very much
Benefit, therefore foundation channel number is each arranged to 128 in three cross-talk networks, such setting has not only been widened network and has been improved again
The efficiency of training.
So far, the training of network all terminates.Technical solution of the present invention is using different peak factors to the side proposed
The performance of method is assessed.The standard value of various parameters is respectively set as follows in experimentation: convolution kernel size is 7 × 7, filtering
Device number is 128, and test image size is 256 × 256, sliding step 14, and network depth is 5 layers, and momentum 0.9 is learned
Habit rate is initially set to 0.1, and weight decays to 10-4, this model is trained using Caffe frame, passes through NVIDIA Titan
X GPU is realized.The quality of reconstruction image is measured by using Y-PSNR (PSNR).
In summary result and analysis, a kind of Poisson denoising side based on three cross-talk network representations proposed by the invention
Method, can guarantee can remove poisson noise in each peak value well, and especially in low peak, effect is more significant, and
And algorithm complexity is low, is adapted to deep neural network, this makes the present invention that can preferably be applied in practice.
The above only expresses the preferred embodiment of the present invention, and the description thereof is more specific and detailed, but can not be because
This and be interpreted as limitations on the scope of the patent of the present invention.It should be pointed out that for those of ordinary skill in the art,
Under the premise of not departing from present inventive concept, several deformations can also be made, improves and substitutes, these belong to protection of the invention
Range.Therefore, the scope of protection of the patent of the invention shall be subject to the appended claims.
Claims (4)
1. a kind of Poisson denoising method based on three cross-talk network representations, it is characterised in that: the following steps are included:
Step (a): pixel value be all 1 input picture after process of convolution with the noisy image phase by two convolution operators
Add, obtains intermediate processed images 1；
Step (b): by intermediate processed images 1 after one without normalization layers of batch of resnet resume module,
Obtain intermediate processed images 2；
Step (c): after further using two convolution to step (b), the figure for being 1 with pixel value is added, and obtains final result.
2. a kind of Poisson denoising method based on three cross-talk network representations according to claim 1, it is characterised in that: described
Step (a) are as follows:
If output of the noisy image f of input after a convolution operatorAre as follows:
Wherein, w is the weight to be learnt, and b is biasing, d1, d2The number of filter respectively output and input, in the instruction of network
Practice lower study weight and biasing has a great impact to the result of experiment；Therefore the output g of sub-network 1 can be expressed approximately are as follows:
G=Conv (1)+Conv (Conv (f))
Wherein, Conv (1) is that pixel value is all the output of 1 image after a convolutional layer, and Conv (Conv (f)) is noisy
Output of the image after two continuous convolutional layers.The Anscombe transformation of sub-network 1 main analog, will have Poisson distribution
Stochastic variable be converted into the stochastic variable with approximate test Gaussian Profile, facilitate subsequent be further processed.
3. a kind of Poisson denoising method based on three cross-talk network representations according to claim 1, it is characterised in that: described
Step (b) are as follows:
Non-linear very strong due to poisson noise, the forward transform of the first step and the denoising of second step are simultaneously inaccurate, can only be approximate
It realizes.Therefore, the design of subnet 2 is not intended to remove pure Gaussian noise, but an approximate Gauss denoises.Therefore it needs to make
Whole process is assisted with more flexible operation operator, therefore there is no use batch in the residual error learning network of sub-network two
Normalization layers, this idea has obtained experimental verification in other networks；
The thought of residual error study is utilized in sub-network 2, if the Feature Mapping of the input g of network is F (g), it has following expression:
F (g)=w2σ(w1g)
Wherein, F (g) is the compound function being made of convolution operator and ReLU activation primitive, and σ represents nonlinear function
ReLU, ReLU unit are essential a part in the active coating and network of network, after being usually arranged on convolutional layer.
The output of sub-network 2 is H (g), function representation are as follows:
H (g)=F (g, { wi))+g
This residual error function is easier to optimize and can solve the degenerate problem of depth network, and the network number of plies can be made to deepen significantly.
4. a kind of Poisson denoising method based on three cross-talk network representations according to claim 1, it is characterised in that: described
Step (c) are as follows:
Sub-network 3 simulates the inverse transformation of Anscombe transformation, returns it to that variance is stable and denoising data are to original range,
It is echoed with 1 phase of sub-network；
Output=Conv (1)+Conv (Conv (H (g)))
Wherein Conv (Conv (H (g))) be sub-network 2 output after two continuous convolutional layers as a result, such connect
Continuous convolution operation can not only improve the recovery effects of image, more training process can be made more stable.
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| CN109978778A (en) * | 2019-03-06 | 2019-07-05 | 浙江工业大学 | Convolutional neural networks medicine CT image denoising method based on residual error study |
| CN113111720A (en) * | 2021-03-17 | 2021-07-13 | 浙江工业大学 | Electromagnetic modulation signal denoising method and system based on deep learning |
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| CN106875361A (en) * | 2017-02-17 | 2017-06-20 | 深圳市唯特视科技有限公司 | A kind of method that poisson noise is removed based on depth convolutional neural networks |
| CN108280811A (en) * | 2018-01-23 | 2018-07-13 | 哈尔滨工业大学深圳研究生院 | A kind of image de-noising method and system based on neural network |
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| CN106875361A (en) * | 2017-02-17 | 2017-06-20 | 深圳市唯特视科技有限公司 | A kind of method that poisson noise is removed based on depth convolutional neural networks |
| CN108280811A (en) * | 2018-01-23 | 2018-07-13 | 哈尔滨工业大学深圳研究生院 | A kind of image de-noising method and system based on neural network |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109978778A (en) * | 2019-03-06 | 2019-07-05 | 浙江工业大学 | Convolutional neural networks medicine CT image denoising method based on residual error study |
| CN113111720A (en) * | 2021-03-17 | 2021-07-13 | 浙江工业大学 | Electromagnetic modulation signal denoising method and system based on deep learning |
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