Gamma Radiation Image Noise Prediction Method Based on Statistical Analysis and Random Walk

The gamma radiation environment is one of the harshest operating environments for image acquisition systems, and the captured images are heavily noisy. In this paper, we improve the multi-frame difference method for the characteristics of noise and add an edge detection algorithm to segment the noise region and extract the noise quantization information. A Gaussian mixture model of the gamma radiation noise is then established by performing a specific statistical analysis of the amplitude and quantity information of the noise. The established model is combined with the random walk algorithm to generate noise and achieve the prediction of image noise under different accumulated doses. Evaluated by objective similarity matching, there is no significant difference between the predicted image noise and the actual noise in subjective perception. The ratio of similarity-matched images in the sample from the predicted noise to the actual noise reaches 0.908. To further illustrate the spillover effect of this research, in the discussion session, we used the predicted image noise as the training set input to a deep residual network for denoising. The network model was able to achieve a good denoising effect. The results show that the prediction method proposed in this paper can accomplish the prediction of gamma radiation image noise, which is beneficial to the elimination of image noise in this environment.


Introduction
With the development of nuclear technology and the industrialization process in China, nuclear and radiation technology are widely used in aerospace, electric power, industrial agriculture, and other fields to create substantial economic benefits [1]. In the process of reactor repair and maintenance, daily supervision of cobalt source devices, and emergency disposal of radiation accidents, it is imperative to provide accurate visual information for operators. Image sensors are exposed to high energy in a gamma radiation environment, which will produce accumulated dose effects and transient ionization effects, causing abnormalities in the output of the image element [2], so that the resulting image will have serious noise. When particles in the gamma radiation environment are incident on the semiconductor device, the charged particles can excite some bound electrons from the valence band to the conduction band through the ionization process, resulting in many electron-hole pairs, forming a dense ionization trail. These electron-hole pairs generated by charged particle radiation have an impact on the performance of the semiconductor device, resulting in the generation of noise in the image. In this process, the secondary electrons are small in extent and low in energy, but they are also a cause of noise generation. When the secondary electrons replace the original electrons in the image element, this will cause transient pulse currents that will macroscopically manifest as bright spots on the image [3]. If the radiation causes lattice defects or displacement damage to the sensor, resulting in In view of this situation, this paper improves the threshold selection method of the three inter-frame difference method and adds the Canny operator to detect the noise region, the amplitude and quantity information of the noise, statistical analysis, and the establishment of a Gaussian mixture model of gamma radiation noise. The established model is combined with the random walk algorithm to generate noise and finally predict the image noise under different accumulated doses. The results show that the method has a good prediction effect for gamma radiation image noise. The predicted image noise has a high similarity to the actual radiation image noise.

Noise Detection and Extraction
The image noise includes readout noise and intrinsic noise [15]. When the camera has good initial performance and a stable line connection, the intrinsic noise component is small. The image acquisition device is a branded CMOS camera with a resolution of 2560 × 1440, a frame rate of 25 fps, a minimum illumination of 0.005 Lux and an image element size of 2 µm, with a shutter range between 1/3 and 1/100,000 s.
Our team used the camera for the experimental acquisition of noise data in the II cobalt source device of the Heilongjiang Institute of Atomic Energy. The radiation dose rate at the experimental position was 6 Gy/h, the accumulated doses was 50 Gy, 100 Gy, 300 Gy, 500 Gy, and 1000 Gy. The distance between the image acquisition equipment and the center of the radiation source was 7 m, and the diameter of the radiation source was 40 cm. We selected 1600 images, each of the same accumulated doses, for a total of 8000 images.
The prerequisite for data analysis of noise in a gamma radiation environment is that the detected noise should be free of omission and complete. This meaning that the effective information should not be identified as noise. In the gamma radiation environment, the image noise has the characteristics of obvious jump and transients. The central area is usually a bright spot and the edge areas have a high contrast with the adjacent areas. The camera lens cover is closed during the image acquisition, so that there are no interfering objects in the field of view to avoid the noise in the actual image affecting the analysis results.
The three inter-frame difference method was improved by the authors of [16] by adding morphological transformations. When using this method for image noise retrieval in a gamma-radiation environment, due to the high dose of radiation, some noise will appear in the same location of the image in multiple consecutive frames. The three-frame differential algorithm will miss such noise and cause incomplete noise contour recognition and the occurrence of "hollow" or "double shadow" phenomenon [17]. Moreover, the inclusion of morphological transformations causes the edges of the noise to be blurred to ensure that the amount of noise is not missed and the contour is complete. In this paper, the three inter-frame difference method is improved and combined with the edge detection operator to perform noise location retrieval. The aim of the traditional inter-frame difference method is to acquire the dynamic target and filter out the noise, whereas in this case we aim to acquire the location of the noise, so the sum operation of the inter-frame difference is changed to an operation to extend the noise retrieval region. The thresholds for traditional inter-frame differencing are usually defined empirically, and a large or small threshold can result in incorrect retrieval of the target. This paper uses OSTU for adaptive selection of thresholds, which is calculated as follows: In this equation, w 0 is the proportion of background pixels in the image, u 0 is the average greyscale of the background pixels, w 1 is the proportion of foreground pixels in the image, u 1 is the average greyscale of the foreground pixels, and u is the average greyscale of the whole image.
The retrieval results of the improved three-frame difference method are fused with Canny, which can preserve the noise quantization information and the noise local neighborhood image. The noise segmentation and quantization extraction are divided into two steps: (1) Detecting the location of noise. To take advantage of the outlier features of noise and the characteristics of small internal differences in noise, we use the inter-difference method, and the Canny detection algorithm in parallel operation to obtain the accurate position of noise in the current image. (2) Save local information of noise. The regional position of the noise is mapped with the current image. To obtain the local contour image of the current image noise, the local external minimum rectangle of the noise contour is drawn and saved in BMP format, where the quantization information is saved to a text file in the order of the noise arrangement. Figure 1 shows the results of the extraction of real image noise in a gamma-ray environment using the algorithm elaborated in Figure 2.
average greyscale of the background pixels, 1 w is the proportion of foreground pixels in the image, 1 u is the average greyscale of the foreground pixels, and u is the average greyscale of the whole image.
The retrieval results of the improved three-frame difference method are fused with Canny, which can preserve the noise quantization information and the noise local neighborhood image.
The noise segmentation and quantization extraction are divided into two steps: (1) Detecting the location of noise. To take advantage of the outlier features of noise and the characteristics of small internal differences in noise, we use the inter-difference method, and the Canny detection algorithm in parallel operation to obtain the accurate position of noise in the current image.
(2) Save local information of noise. The regional position of the noise is mapped with the current image. To obtain the local contour image of the current image noise, the local external minimum rectangle of the noise contour is drawn and saved in BMP format, where the quantization information is saved to a text file in the order of the noise arrangement. Figure 1 shows the results of the extraction of real image noise in a gamma-ray environment using the algorithm elaborated in Figure 2.

Modeling and Prediction of Radiation Image Noise
Radiation image noise modeling and prediction consists of two parts: (1) Constructing a radiated noise model, using various functions to fit the amplitude and quantity characteristics of the noise, and evaluating the fit effect using the coefficient of determination (R-square) and root mean square error (RMSE) tests. The RMSE is also called the standard deviation of the fit of the regression system, which is obtained by squaring the mean of the "sum of squares" of the fitted data and the original data, and the smaller the value is, the closer the fitted data is to the original data, and the better the model fit [18]. (2) Image noise generation method and prediction, based on the results of statistical analysis, the

Modeling and Prediction of Radiation Image Noise
Radiation image noise modeling and prediction consists of two parts: (1) Constructing a radiated noise model, using various functions to fit the amplitude and quantity characteristics of the noise, and evaluating the fit effect using the coefficient of determination (R-square) and root mean square error (RMSE) tests. The RMSE is also called the standard deviation of the fit of the regression system, which is obtained by squaring the mean of the "sum of squares" of the fitted data and the original data, and the smaller the value is, the closer the fitted data is to the original data, and the better the model fit [18]. (2) Image noise generation method and prediction, based on the results of statistical analysis, the random walk algorithm was used to generate noise by setting parameters such as noise seed, number of walks, and range of walks, and to predict the image noise under different accumulated doses from 50 Gy to 1000 Gy.

Noise Amplitude Analysis
The noise amplitude distribution in images in common environments is commonly described by a single Gaussian model (SGM) [19], using a one-dimensional single Gaussian function to fit the amplitude in the extracted noise data. Figure 3 corresponds to an example curve of SGM and the fit curve to the noise amplitude using f (x) = k 1 √ 2πσ e −(x−u) 2 /2σ 2 for fitting curves to noise amplitudes at different accumulated doses, where µ determines the location and σ determines the amplitude [20], and the resulting fitted covariates are shown in Table 1.
The distribution of noise quantities in amplitude at different accumulated doses is given in Figure 3. At an accumulated dose below 300 Gy, the image noise amplitude is concentrated between 40 and 90, fluctuating around the mean value. The fit result is good as seen from the R-square and RMSE metrics. The effects of gamma radiation on image sensors can be attributed to radiation-induced transient ionization effects and accumulated dose effects in image sensors [21]. The transient ionization effect leads to an increase in charge at the sensor potential, which produces bright spots in the image. The accumulated dose effect causes a drift in the flat band voltage and threshold voltage, changes the conductivity of the semiconductor, and increases the drain current [22], resulting in temporary or long-term abnormal output of some elements. When the accumulated doses reach 300 Gy, the noise amplitude begins to be biased towards higher areas. As the accumulated dose continues to increase, the influx of the accumulated dose effect becomes prominent and the image sensor begins to experience abnormalities in the operation of some image elements, with the effect of intrinsic mode noise gradually increasing. The overall distribution curve of the noise amplitude has an asymmetrical character, skewing towards the higher amplitude regions. The SGM can no longer describe the amplitude distribution of the noise. described by a single Gaussian model (SGM) [19], using a one-dimensional single Gaussian function to fit the amplitude in the extracted noise data. Figure 3 corresponds to an example curve of SGM and the fit curve to the noise amplitude using for fitting curves to noise amplitudes at different accumulated doses, where µ determines the location and σ determines the amplitude [20], and the resulting fitted covariates are shown in Table 1.  The distribution of noise quantities in amplitude at different accumulated doses is given in Figure 3. At an accumulated dose below 300 Gy, the image noise amplitude is concentrated between 40 and 90, fluctuating around the mean value. The fit result is good as seen from the R-square and RMSE metrics. The effects of gamma radiation on image  A Gaussian mixture model (GMM) can be obtained by the linear superposition of several single Gaussian models with data conforming to a mixture Gaussian distribution [23]. An example curve of a two-component one-dimensional mixed Gaussian model is given in Figure 4. SGM1 and SGM2 are one-dimensional single Gaussian distribution curves with a mean of 5 and a variance of 1.5 and a mean of 15 and a variance of 3, respectively, and the outgoing one-dimensional mixed Gaussian distribution model GMM with a linear superposition of SGM1 and SGM2 with weight coefficients of 2 and 3 are used at higher accumulated doses using a two-component one-dimensional mixed Gaussian model. The noise amplitude is fitted. The fitting function is shown in Equation (2) and k 1 and k 2 denote the weight of each component. Figure 5 corresponds to the fitting curve of the noise amplitude at high accumulated doses using the two-component one-dimensional hybrid Gaussian function, and the resulting fitted parameters are shown in Table 2.
of the noise amplitude at high accumulated doses using the two-component one-dimensional hybrid Gaussian function, and the resulting fitted parameters are shown in Table  2.    According to Figure 5 and Table 2, the fitting of the image noise amplitude at high accumulated doses using a two-component mixture Gaussian distribution is significantly better than that of a one-dimensional single Gaussian distribution. The experimental data are all within the critical range of the fit. This demonstrates that the two-component mixture Gaussian model can fit the image noise amplitude at high accumulated doses.

Noise Quantity Analysis
From separate data analysis of the range of image noise at different accumulated doses and the distribution of the number of noises in consecutive image frames at the same accumulated doses. It can be concluded that the number of noisy images increases non-linearly with the increase of the accumulated doses. Figure 6 shows the trends and fitted curves for the mean value of noise quantities at different accumulated doses. As shown in Figure 6b-f, under the same accumulated doses, the number of radiation image noise shows a strong regularity. The number of noise fluctuates around the mean value. The curve shows the characteristics of the spike large slope shake, with a strong symmetry. The fitting parameters are shown in Table 3. According to the fitting effects in Figure 6b-f, as well as the R-square and RMSE in Table 3, it can be concluded that the onedimensional single Gaussian model can achieve better noise fitting under the same accu-  According to Figure 5 and Table 2, the fitting of the image noise amplitude at high accumulated doses using a two-component mixture Gaussian distribution is significantly better than that of a one-dimensional single Gaussian distribution. The experimental data are all within the critical range of the fit. This demonstrates that the two-component mixture Gaussian model can fit the image noise amplitude at high accumulated doses.

Noise Quantity Analysis
From separate data analysis of the range of image noise at different accumulated doses and the distribution of the number of noises in consecutive image frames at the same accumulated doses. It can be concluded that the number of noisy images increases non-linearly with the increase of the accumulated doses. Figure 6 shows the trends and fitted curves for the mean value of noise quantities at different accumulated doses. As shown in Figure 6b noise shows a strong regularity. The number of noise fluctuates around the mean value. The curve shows the characteristics of the spike large slope shake, with a strong symmetry. The fitting parameters are shown in Table 3. According to the fitting effects in Figure 6b-f, as well as the R-square and RMSE in Table 3, it can be concluded that the one-dimensional single Gaussian model can achieve better noise fitting under the same accumulated doses.

Prediction of Noise
The prediction of gamma radiation image noise is based on the quantity, amplitude, and shape characteristics of the noise. By statistical analysis of the noise and image processing, gamma radiation image noise has the characteristic of appearing at random locations. For the same accumulated doses, the individual noise connected areas are of approximate size and irregular shape, and the amplitude intensity follows a one-dimensional two-component Gaussian mixture distribution. The number of image frames possessing noise quantity is consistent with the one-dimensional single Gaussian distribution. The amplitude and quantity of noise are predicted based on the statistical analysis results. The noise shape is predicted by the random walk algorithm. The application of the random walk algorithm to images is based on graph theory [24], in which the structure of the graph, in which any two nodes may be related, consists of a set K of nodes and a set E representing the relationship of adjacent nodes, denoted as G = (V, E). The image is considered as a pure discrete matrix, which can be represented as a graph with image dimensions w × h nodes and (w − 1) × (h − 1) edges, and each edge is set with a certain number of weights, indicating the probability of the node traveling to that edge, where the formula for finding the walk weights by the Gaussian function is as follows: p i and p j are the magnitudes of pixel x and neighbor x + 1, respectively, a is a custom parameter, and a weight of 0 means that the random walk will not proceed along this edge walk. The random walk on the image is essentially a Dirichlet problem to find whether the boundary is 0 or 1.
In the prediction process, each block noise can be regarded as composed of several different numbers of noise units and has a noise seed. The noise seed is the starting point of the block noise formation process, to carry out the noise generation under different accumulated doses. The position of the noise seeds is random x, y, and the number of noise seeds is N: The formula represents the number of noises Nnmn selected with probability N p, Gy represents the accumulated dose: The parameters in the above equation are determined according to Table 3. The amplitude of noise seeds is F: The formula represents the amplitude of noise Famp selected with probability Fp, Gy represents the accumulated dose: The parameters in the above equation are determined according to Tables 1 and 2. The noise seeds in the range of image size m × n, through the random walk towards the noise seed neighborhood diffusion. Due to the random nature of the noise shape, the noise seeds are spread across the image using random boundary weights and finally produce the same size as the image as the to be processed image containing radiation noise. Figure 7 shows the random walking process of isolated noise seeds.  The pseudo code for the noise prediction is shown below (see Algorithm 1):

Results
To verify the prediction effect of this paper on the image noise of the gamma radiation environment, we have conducted both subjective and objective evaluations of the effectiveness of noise prediction.
The noise prediction of irradiated room images and natural images at different accumulated doses using this method is given in Figures 8 and 9. With the predicted images at different evaluation doses, it can be concluded that the predicted noise patches have better results. Subjective evaluation methods rely heavily on the subjective awareness of the evaluator, and the similarities and differences between the images cannot be quantified well. Objective methods of image quality evaluation are based on mathematical models that analyze the degree of difference and similarity based on reference images [26]. The objective evaluation method for evaluating the quality of predicted noise in this paper is to evaluate the probability of obtaining the actual radiated noise image from the actual radiated noise set, the predicted radiated noise set, and the Gaussian noise set by calculating the similarity. The specific steps are as follows: 1. Five hundred randomly selected as samples from the actual radiation noise set, 1000 selected as matching target dataset I 500 X , 1000 randomly selected as matching target dataset II 1000 O from the predicted data, and 1000 randomly selected as matching target dataset III G from the Gaussian generated noise data; With the predicted images at different evaluation doses, it can be concluded that the predicted noise patches have better results. Subjective evaluation methods rely heavily on the subjective awareness of the evaluator, and the similarities and differences between the images cannot be quantified well. Objective methods of image quality evaluation are based on mathematical models that analyze the degree of difference and similarity based on reference images [26]. The objective evaluation method for evaluating the quality of predicted noise in this paper is to evaluate the probability of obtaining the actual radiated noise image from the actual radiated noise set, the predicted radiated noise set, and the Gaussian noise set by calculating the similarity. The specific steps are as follows: 1 Five hundred randomly selected as samples from the actual radiation noise set, 1000 selected as matching target dataset I X 500 , 1000 randomly selected as matching target dataset II O 1000 from the predicted data, and 1000 randomly selected as matching target dataset III G 1000 from the Gaussian generated noise data; 2 Select one image from X 500 in turn and match the similarity in O 1000 , P 1000 , and G 1000 . If the image with the highest similarity to the sample is from the target dataset O 1000 then it is denoted as m = −1, if the image with the highest similarity to the sample is from the target dataset P 1000 then it is denoted as m = 1, if the image with the highest similarity to the sample is from the target dataset G 1000 then it is denoted as m = −0.2; 3 Repeat step two until all of X 500 has been traversed; Conduct different accumulated doses experiments on X 500 , O 1000 , P 1000 , and G 1000 .
The specific results are shown in Table 4  As can be seen from the table, under the accumulated dose of 300 Gy and below, some of the actual radiation noise similarity is close to Gaussian noise. When the accumulated dose becomes large, the noise is rarely or never discerned as Gaussian noise. Meanwhile, the predicted radiation noise in this paper is closer to the actual noise matching results. Under 1000 Gy, 262 samples were matched to the actual radiation noise dataset I, 238 samples with the predicted radiated noise were matched to the actual radiated noise dataset I, and 238 samples were matched to the predicted radiated noise sample set II. Both subjective and objective evaluation methods prove the effectiveness of the algorithm for gammaradiation noise image prediction.

Discussion
With the development of unmanned machine systems in recent years, increased operations in harsh environments are being replaced by robots. The camera plays a very important role as the eyes of the robot. The noise in the image affects the normal operation of the robot. The predicted noise of an image is of importance as it can be used. For example, (1) the predicted image noise can be used as a training set for deep learning models for image denoising, and (2) the predicted image noise can be used to evaluate the effectiveness of denoising algorithms.
To further demonstrate the spillover effect of this paper's research, we used a deep residual network denoising model from the literature [8]. The network structure is shown in Figure 10.
After the predicted noisy images are fed into the network as a dataset for training, the real noisy images are used in the tests. The PSNR and SSIM were able to reach 35.472 and 0.971 respectively. The denoised visual results are shown in Figure 11. important role as the eyes of the robot. The noise in the image affects the normal operati of the robot. The predicted noise of an image is of importance as it can be used. For exa ple, (1) the predicted image noise can be used as a training set for deep learning mod for image denoising, and (2) the predicted image noise can be used to evaluate the eff tiveness of denoising algorithms.
To further demonstrate the spillover effect of this paper's research, we used a de residual network denoising model from the literature [8]. The network structure is show in Figure 10. ...

Noise image
Residual images Pure Image Figure 10. Structure of a deep residual network.
After the predicted noisy images are fed into the network as a dataset for traini the real noisy images are used in the tests. The PSNR and SSIM were able to reach 35.4 and 0.971 respectively. The denoised visual results are shown in Figure 11. The images generated using the prediction method in this paper were put into a deep residual network as the training set, which was able to achieve good denoising results. This result demonstrates some of the spillover implications of this paper's research.
The experiments in this article provide some enlightenment for our future work. We start from the formation causes and nature of image noise in gamma radiation environments, to study the noise in gamma radiation images and provide new ideas for image denoise and robot operation in gamma radiation environments. Our method proposed in this paper predicts and evaluates the image noise at different accumulated doses in the gamma radiation environment. Although the method has been implemented in a single environment and controlled situation, the work is significant because it provides the results of radiation noise prediction in the environment of high accumulated doses. In the future, the unconventional image noise generated in other malignant environments should also be studied.

Conclusions
In order to complete the prediction of image noise in the harsh environment of a gamma radiation environment, this paper improves the threshold selection method of the three inter-frame difference method and introduces the Canny operator to detect the noise of the image to obtain the amplitude, location, and quantity information of the noise. Then we use probability statistics to process the amplitude and quantity information of the noise, build a statistical model of the noise, and combine the model with a random walk to generate the noise. Finally, we add the generated noise to the image and calculate the probability by similarity matching to objectively evaluate the noise prediction effect. In the discussion session, we used the predicted noisy image as a sample input to a deep residual network for training, and the network was able to achieve better denoising results. Some spillover effects of the research have been demonstrated. The results show that the predicted gamma radiation image noise in this paper can replace the real gamma radiation image noise in some scenarios, solving the characteristics that image noise in the gamma radiation environment is highly random and difficult to determine. It provides conditions for objective evaluation of the performance verification of the speckle noise denoising algorithm in the gamma radiation environment, which is conducive to the elimination of image noise in this environment and promotes the development of image processing in this harsh environment of gamma radiation. The images generated using the prediction method in this paper were put into a deep residual network as the training set, which was able to achieve good denoising results. This result demonstrates some of the spillover implications of this paper's research.
The experiments in this article provide some enlightenment for our future work. We start from the formation causes and nature of image noise in gamma radiation environments, to study the noise in gamma radiation images and provide new ideas for image denoise and robot operation in gamma radiation environments. Our method proposed in this paper predicts and evaluates the image noise at different accumulated doses in the gamma radiation environment. Although the method has been implemented in a single environment and controlled situation, the work is significant because it provides the results of radiation noise prediction in the environment of high accumulated doses. In the future, the unconventional image noise generated in other malignant environments should also be studied.

Conclusions
In order to complete the prediction of image noise in the harsh environment of a gamma radiation environment, this paper improves the threshold selection method of the three inter-frame difference method and introduces the Canny operator to detect the noise of the image to obtain the amplitude, location, and quantity information of the noise. Then we use probability statistics to process the amplitude and quantity information of the noise, build a statistical model of the noise, and combine the model with a random walk to generate the noise. Finally, we add the generated noise to the image and calculate the probability by similarity matching to objectively evaluate the noise prediction effect. In the discussion session, we used the predicted noisy image as a sample input to a deep residual network for training, and the network was able to achieve better denoising results. Some spillover effects of the research have been demonstrated. The results show that the predicted gamma radiation image noise in this paper can replace the real gamma radiation image noise in some scenarios, solving the characteristics that image noise in the gamma radiation environment is highly random and difficult to determine. It provides conditions for objective evaluation of the performance verification of the speckle noise denoising algorithm in the gamma radiation environment, which is conducive to the elimination of image noise in this environment and promotes the development of image processing in this harsh environment of gamma radiation.