CN112819728A - Method for removing radiation image Poisson noise based on shear wave - Google Patents
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Abstract
The invention discloses a method for removing radiation image Poisson noise based on shear wave, which is mainly used for medical images and images of large container inspection systems aiming at the Poisson noise caused by statistical fluctuation of a radiation imaging system, and can also provide reference for other Poisson noise images. The method utilizes ansscombe transformation to convert Poisson distribution noise into approximate Gaussian distribution noise, and utilizes the multi-scale and multi-resolution characteristics of shear waves to decompose noise images in multiple directions to obtain high-frequency and low-frequency coefficients. Removing coefficients with absolute values smaller than a threshold value by threshold denoising, and then obtaining a final poisson noise radiation image by shear wave reconstruction and ansscombe correction inverse transformation. The method can better remove the Poisson noise and simultaneously can keep the detail information of the image edge.
Description
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to a method for removing poisson noise of a radiation image based on shear waves.
Background
Radiation imaging utilizes the difference of the absorption capacity of an object to rays, so that the internal condition of the object can be observed, and the radiation imaging system has wide application in the aspects of medical treatment, safety inspection, nondestructive inspection and the like. The noise of the radiation image can affect the definition of the image, the detail information is covered, the accuracy of human eyes and intelligent identification is reduced, the misjudgment risk is increased, and therefore the removal of the radiation image noise is very necessary. When the radiation dose is low or the scanned object is goods with large mass and thickness, such as medical images and scanned images of large container inspection equipment, the main noise source is statistical fluctuation, and the noise follows Poisson distribution. Such noise is related to the intensity of the radiation, where a large intensity of radiation causes a weak poisson noise due to statistical fluctuations, and a weak intensity of radiation causes a strong poisson noise due to statistical fluctuations. At present, a denoising method mainly aims at gaussian noise, but the gaussian noise is irrelevant to a signal, so that the difference between a poisson noise and a gaussian noise removing method is large, and the poisson noise removing method cannot be directly applied to removing the gaussian noise.
At present, wavelet transformation is widely applied to the aspect of removing image noise, and most of the wavelet transformation aims at Gaussian noise, the patent application publication numbers are 201811274460.8 'a wavelet domain value denoising method based on Gaussian kernel function', 201811094442.1 'a variable threshold wavelet denoising method' adopt wavelet transformation to remove Gaussian noise, and the patent application publication numbers are 201910633659.3 'a fuzzy image restoration method under Poisson noise' and 201811508716.7 'a pixel level threshold self-adaptive Poisson denoising method' utilize wavelet transformation to remove Poisson noise. However, wavelet transform has only limited directionality and edge discontinuity affects the series expansion, so its advantages cannot be directly generalized to higher dimensions, shear wave transform is very effective in providing optimal sparse representation for multidimensional data, shows advantages in various image processing applications, and is able to retain detailed information. In addition, the stable variance transformation can convert the Poisson noise related to the signal into Gaussian noise unrelated to the signal, so that the stable variance transformation and the shear wave transformation are effectively combined, the Poisson noise can be better denoised, and a satisfactory effect can be obtained.
Disclosure of Invention
In view of the above problems of the prior art, the present invention is directed to removing poisson noise of a radiation image and retaining image edge detail information.
In order to achieve the purpose, the invention adopts the following technical scheme: a method for removing radiation image Poisson noise based on shear waves comprises the following steps:
step 1, carrying out nonlinear ansscombe transformation on a radiation image containing Poisson noise, converting the Poisson noise into approximate Gaussian noise, decorrelating the noise and a signal, and transforming the rear difference to be approximately 1;
step 2, adopting tightly-supported shear wave decomposition on the approximate Gaussian noise radiation image obtained in the step 1, adopting scale matrix parameters to measure the degree of anisotropy, obtaining a plurality of high-frequency sub-bands and a low-frequency sub-band through measuring the direction of the shear matrix, and extracting shear wave coefficients of different sub-band images;
step 3, estimating the noise standard variance sigma for different sub-band images respectively, and then obtaining the threshold value T of each sub-band image coefficient by adopting the minimum maximum principle:
wherein n is the signal length; after the threshold values of different sub-band image coefficients are determined, threshold value denoising is carried out on the shear wave coefficient in the step 2, the shear wave coefficient larger than the threshold value is reserved, and the shear wave coefficient smaller than the threshold value is removed;
step 4, shear wave reconstruction is carried out by utilizing the shear wave coefficient subjected to denoising in the step 3, and a radiation image with Gaussian noise removed is obtained;
and 5, performing Anscombe correction inverse transformation on the radiation image with the approximate Gaussian noise removed in the step 4:
and y is an image subjected to shear wave denoising, and a radiation image finally subjected to Poisson noise removal is obtained.
Preferably, in step 1, the image to be denoised is converted into a gray image, and Anscombe transformation is performed on each pixel point to obtain a radiation image converted into gaussian noise.
Preferably, the number of decomposition layers used in step 2 to support the shear wave decomposition is 5, and the window function is dmaxflat 4.
Preferably, in step 3, a hard threshold function is used to improve the denoising effect, so that the shear wave coefficient f with an absolute value smaller than a threshold valuedSetting zero, keeping the shear wave coefficient f with absolute value greater than or equal to thresholdd。
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in:
1) the invention adopts stable variance transformation Anscombe transformation to convert the Poisson noise into approximate Gaussian noise, which solves the problem that most of the prior denoising technologies only aim at the Gaussian noise. The shear wave has the characteristics of multi-scale and multi-resolution, overcomes the defect that the wavelet transformation cannot well express anisotropic information, and can better capture detailed information;
2) the method has better denoising effect than that of denoising methods widely used in non-subsampled shear wave transformation NSST, fast curvelet transformation FDCT, stationary wavelet transformation SWT and the like. Meanwhile, parameters such as the number of layers of decomposition of the shear wave, a threshold value, a threshold function and the like are optimized and selected, so that a better denoising effect is obtained;
3) the invention can better remove the Poisson noise of the radiation image caused by statistical fluctuation, simultaneously retain the detail information of the image, and is beneficial to human eye observation and intelligent identification.
Drawings
FIG. 1 is a flow chart of a method for removing Poisson noise from a radiation image based on shear waves according to the present invention;
FIG. 2 is a diagram of the effect of a median filtering noise reduction method;
FIG. 3 is a diagram of the effect of the wavelet denoising method;
FIG. 4 is an effect diagram of a method for removing Poisson noise from a radiation image based on shear waves according to the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It is to be noted that, unless otherwise specified, technical or scientific terms used herein shall have the ordinary meaning as understood by those skilled in the art to which the invention pertains.
The invention will be further explained with reference to the drawings.
As shown in fig. 1, a method for removing poisson noise of a radiation image based on shear waves includes the following steps:
step 1: performing ansscombe transformation on the radiation image containing the Poisson noise;
the poisson noise is signal-dependent, is multiplicative noise, and is not additive noise of gaussian noise, so the method for removing gaussian noise cannot be directly applied to poisson noise. The method can convert the Poisson noise into the Gaussian noise through variance stabilization transformation, one of the methods which are most applied in the variance stabilization transformation is Anscombe transformation, and the Anscombe transformation can convert the Poisson noise into the noise which is approximately in Gaussian distribution, so that the denoising can be completed by adopting a method for removing the Gaussian noise after the transformation. g is subject to Poisson distribution, wherein the read image needs to be grayed, each gray value is transformed, g is a gray image pixel matrix, y (g) is obtained after Anscombe transformation,
step 2: decomposing the ansombe transformed y (g) with a precision tightly-supported shear wave;
the shear wave is developed from wavelets, and has the advantages of effective sparse representation, multi-resolution, multi-scale, multi-direction, translation invariance and edge information maintenance, so that the accurate tight support shear wave multi-scale multi-resolution is adopted for decomposition, and the detail information of the image can be kept after denoising.
α＝(αj)jFor each dimension j, αj∈(0,2)，c＝(c1,c2)∈(R+)2The shear wave system is defined as follows,
Φ(φ；α,c1)＝{φm＝φ(·-c1m):m∈Z2} (3)
wherein the parameters of the scale matrix are used to measure the degree of anisotropy, for which the scale matrix is defined as,
the direction being through the shear matrix SkOr
The change is made to the state of the mobile terminal,
the number of decomposition layers in the decomposition process is 5 and the window function is dmaxflat 4.
And step 3: denoising by using a threshold;
after the shear wave decomposition, the signals are concentrated in the shear wave coefficient with larger amplitude, and the noise has smaller amplitude, so that the threshold value is selected for denoising. The selection of the threshold is a relatively large challenge, a larger threshold may shrink signal characteristics, resulting in over-smoothing or difficulty in distinguishing the signal, and a smaller threshold may leave noise information. The standard deviation is calculated for each layer of sub-band images, the minimum maximum principle threshold is selected as the threshold, the minimum mean square deviation extreme value is generated by utilizing the estimation quantity in statistics to obtain the threshold, n is the signal length, sigma is the noise standard deviation, and the expression of the threshold T is as follows:
because the hard threshold function can better retain the edge information, the hard threshold function is selected for denoising, the coefficient with the absolute value of the coefficient larger than or equal to the threshold is retained, and the coefficient with the absolute value smaller than the threshold is set to be zero. Threshold value T, shear wave coefficient fdCoefficient after treatment is
The expression is as follows:
and 4, step 4: reconstructing shear waves;
shear wave reconstruction is carried out by utilizing the shear wave coefficient obtained after denoising, a conjugate gradient method based on the frame property of the shear wave is adopted,
the expression for the reconstruction is as follows,
and 5: performing Anscombe inverse transformation;
after reconstruction through shear waves, an image Anscombe needs to be inversely transformed, and algebraic inverse transformation is carried out
However, since the Anscombe transform is nonlinear, the result obtained by the equation (17) is biased, and therefore, a certain correction needs to be performed on the inverse transform, and the inverse transform is approximately unbiased, so that the radiation image can be better restored after the correction, y is an image denoised by the shear wave, and the inverse transform of the correction is expressed as follows,
aiming at large container inspection equipment, due to the fact that the cargo mass and the cargo thickness are large, the main noise is Poisson noise, and in order to verify the effect of the method, the method is compared with other common denoising methods. The radiation image containing the Poisson noise is processed by respectively adopting the commonly used median filtering, wavelet denoising and denoising methods, the most commonly used peak signal-to-noise ratio is taken as a quantitative measurement standard, the peak signal-to-noise ratio is the ratio of the maximum possible power of a signal to the noise power, the larger the peak signal-to-noise ratio is, the better the denoising effect is, and the obtained result is as follows:
the radiation images of the large container after median filtering and wavelet denoising are respectively shown in fig. 2 and fig. 3, the peak signal-to-noise ratios calculated by the two methods are 28.9845dB and 27.1344dB respectively, the denoising effect graph of the invention is shown in fig. 4, and the peak signal-to-noise ratio calculated by the method of the invention is 32.3031 dB. After median filtering and wavelet denoising, noise can be obviously seen, the edge is unclear, the effect is not ideal, and the peak signal-to-noise ratio is obviously lower than that of the method. Therefore, the invention can be widely applied to various fields of radiation images with Poisson noise.
According to the invention, through the combination of the Anscombe transformation and the shear wave transformation, the Poisson noise can be converted into approximate Gaussian noise, then the Gaussian noise is removed by adopting the shear wave transformation and threshold denoising, and the denoised image Anscombe is subjected to inverse modification transformation to obtain a final denoised radiation image. The method has a good denoising effect on Poisson noise, particularly on low-dose rays and object radiation images with large mass and thickness, and can retain detailed information.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements made to the technical solution of the present invention by those skilled in the art without departing from the spirit of the present invention shall fall within the protection scope defined by the claims of the present invention.
Claims (4)
1. A method for removing radiation image Poisson noise based on shear waves is characterized by comprising the following steps:
step 1, carrying out nonlinear ansscombe transformation on a radiation image containing Poisson noise, converting the Poisson noise into approximate Gaussian noise, decorrelating the noise and a signal, and transforming the rear difference to be approximately 1;
step 2, adopting tightly-supported shear wave decomposition on the approximate Gaussian noise radiation image obtained in the step 1, adopting scale matrix parameters to measure the degree of anisotropy, obtaining a plurality of high-frequency sub-bands and a low-frequency sub-band through measuring the direction of the shear matrix, and extracting shear wave coefficients of different sub-band images;
step 3, estimating the noise standard variance sigma for different sub-band images respectively, and then obtaining the threshold value T of each sub-band image coefficient by adopting the minimum maximum principle:
wherein n is the signal length;
after the threshold values of different sub-band image coefficients are determined, threshold value denoising is carried out on the shear wave coefficient in the step 2, the shear wave coefficient larger than the threshold value is reserved, and the shear wave coefficient smaller than the threshold value is removed;
step 4, shear wave reconstruction is carried out by utilizing the shear wave coefficient subjected to denoising in the step 3, and a radiation image with Gaussian noise removed is obtained;
and 5, performing Anscombe correction inverse transformation on the radiation image with the approximate Gaussian noise removed in the step 4:
and y is an image subjected to shear wave denoising, and a radiation image finally subjected to Poisson noise removal is obtained.
2. The method for removing poisson noise of a radiation image based on shear waves as claimed in claim 1, wherein in the step 1, the image to be denoised is converted into a gray image, and Anscombe transformation is performed on each pixel point to obtain the radiation image converted into gaussian noise.
3. The method for removing poisson noise from radiation images based on shear waves as claimed in claim 1, wherein the number of layers for tight-support shear wave decomposition used in step 2 is 5, and the window function is dmaxflat 4.
4. The method for removing poisson noise from radiation image based on shear wave as claimed in claim 1, wherein in said step 3, a hard threshold function is used to improve the de-noising effect, so that the shear wave coefficient f with absolute value less than the threshold valuedSetting zero, keeping the shear wave coefficient f with absolute value greater than or equal to thresholdd。
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| CN109472756A (en) * | 2018-11-15 | 2019-03-15 | 昆明理工大学 | Image de-noising method based on shearing wave conversion and with directionality local Wiener filtering |
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| CN109472756A (en) * | 2018-11-15 | 2019-03-15 | 昆明理工大学 | Image de-noising method based on shearing wave conversion and with directionality local Wiener filtering |
| CN109961411A (en) * | 2019-03-12 | 2019-07-02 | 浙江工业大学之江学院 | Non-lower sampling shears wave conversion medicine CT image denoising method |
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