Preprocessing method for digital X-Ray weld images

Pipelines represent the main mode of transportation for oil and gas, and failure caused by weld defects is the primary cause of accidents, presenting significant risks to personal and environmental safety. Therefore, regularly inspecting pipeline welds is essential for reducing accidents, ensuring personal safety, protecting the environment, and achieving sustainable development. Although manual photographic X-ray inspection is widely utilized for the detection of weld defects in various industries, this process is challenging since X-ray images are noisy and unclear, with uneven grey values. This study proposed a noise reduction framework by introducing a Wiener filter into the wavelet domain to reduce noise in X-ray images while minimizing information loss. Furthermore, a comprehensive evaluation factor that combined contrast and the noise reduction level was proposed to reduce the dependence of image processing performance on wavelet thresholds. Additionally, this study improved the Laplace method by adaptively adjusting the normal and tangential diffusion coefficients to enhance the weld X-ray image contrast without increasing the noise. Through qualitative comparison and quantitative analysis, it has been determined that the suggested methods exhibit better properties than alternative industrial pipeline weld X-ray image processing algorithms. This superiority is observed in objective values as well as subjective visualizations.


Introduction
Since oil is transported by underground pipelines connected by welds, the weld defects caused by improper welding and various other factors often cause pipeline accidents.Therefore, regularly inspecting oil and gas pipeline welds is essential to ensure safety.X-ray inspection based on radiography is commonly used for non-destructive testing during pipeline weld defect detection.Weld defects are directly detected and evaluated on the X-ray film.However, due to the unique nature of the film, the digitized weld image may be noisy and unclear, with uneven gray value distribution, adversely affecting weld defect feature extraction.Therefore, efficient pipeline weld image processing methods are essential to reduce accidents, ensure personal and environmental safety, and promote sustainable development.
The main methods used for welding X-ray image processing are noise abatement and intensification of the radiographic images.X-ray image noise is mainly classified into electronic, photoelectronic, and particle noise [1], which is categorized as Gaussian white noise.The traditional methods to reduce these IOP Publishing doi:10.1088/1742-6596/2770/1/012016 2 three types of noise mainly include Wiener filtering, wavelet transform, mean filtering, and median filtering [2][3][4].Wiener filtering, also known as least squares filtering, is sensitive to Poisson noise, is unsuitable for pretzel noise, and blurs edges and details.Wavelet transform involves nonlinear filtering via wavelet decomposition and reconstruction, which damages the edges and details of the image.Median and mean filtering involves calculating the pixel mean and median in the filter window.Mean filtering blurs the edges and details, while median filtering does not blur the edges but damages the image details.
Reducing X-ray image noise using wavelet transform is mainly accomplished via the wavelet decomposition of the original noisy image, solving the band noise coefficients, estimating the wavelet coefficients by calculating the threshold of each coefficient in each layer, and recovering the image via wavelet inverse transform [5].In addition, some scholars translated Poisson noise into Gaussian noise through the Anscomble transform, followed by bilateral filtering for noise reduction to improve the noise reduction effects [6].Some studies solved the NLM Gaussian kernel using the gradient descent method, yielding an improved technique known as non-local mean filtering [7].Although the noise reduction ability was enhanced by improving traditional filtering methods, adaptive filtering and detail preservation challenges remain.
Studies have proposed an adaptive filtering method to reduce the influence of the traditional filter window and threshold on the noise reduction results.Adaptive neighborhood filtering is the most prominent X-ray image adaptive filtering technique and involves reasonably estimating noise variance.A linear relationship is established between the noise variance of the X-ray message and the gray value at the pixel level, with the noise variance being computed from the local gray values [8].Researchers decomposed the local patches to reduce the noise in X-ray images [9].Adaptive weighted median filtering involves the automatic pixel-weighted updating of the window threshold [4] and, combined with wavelet transform, can eliminate pretzel and Gaussian noise.
The detail loss problem during X-ray image noise reduction is solved via detail compensation during filtering.This includes the improved bilateral filtering method, which introduces a local grayscale compensation function and constrains the image similarity by the similarity between the pixel's gray scale value and the center point to avoid the detail loss caused by excessive noise reduction.The compensation function determines whether a pixel needs to be retained based primarily on the difference between the pixel and the center of the filter window [10].In addition, the image boundary is estimated using the Canny contour detector to compensate for the detail loss due to the filtering.The cost function is used to determine the final pixel value of the noise-reduced image to facilitate simultaneous filtering and detail preservation [11].The diffusion coefficient is calculated by determining the gradient information of the image, presenting varying diffusion coefficient weights for different parts of the Xray image to effectively avoid detail loss [12].
Weld X-ray image enhancement methods are typically categorized into two groups: those based on histogram equalization and grayscale transformation techniques.Histogram equalization, as outlined in reference [13], involves adjusting the gray levels of the image to achieve a more uniform distribution, aiming to cover as many gray levels as possible.Despite being widely used extensively in actual projects due to its simplicity and ease of application, histogram equalization often leads to artifacts and color distortion.Some studies have explored dividing histograms of images into subhistograms in order to address issues like unnatural exposure [14][15][16][17][18][19][20][21].Adjusting the image histogram at the pixel level can help alleviate artifacts [22][23][24].Subsequently, dividing the image into subregions and applying histogram equalization can address missing local gray levels [25][26].To combat detail loss, the scholars introduced an adaptive histogram equalization method [27].At the same time, they developed a method of self-adaptive histogram equalization for contrast [28].Despite its ability to enhance image contrast, histogram equalization may still result in color distortion, impacting the overall image quality.
Gray scale variation-based methods process each pixel point in an image via a mapping function to improve its visual appearance.Gamma correction [29], one of the best-known grayscale transformation techniques, maps luminance levels to offset the nonlinear brightness of presentation equipment.Yet, the IOP Publishing doi:10.1088/1742-6596/2770/1/0120163 effect of gamma correction suffers from incorrect exposure and loss of details when attempting to improve X-ray images with low gray values.Although research has addressed these issues [30][31], uneven exposure remains a primary challenge associated with grayscale techniques.
Achieving adaptive noise reduction without damaging the image details in weld X-rays is challenging.We proposed an adaptive noise reduction method based on the wavelet domain and Wiener filtering to address this problem.Combining wavelet transform and Wiener filtering preserves more high-frequency components to minimize the detail loss due to excessive noise reduction.Furthermore, a comprehensive evaluation factor is proposed to assess the noise decrease in the radiographic image, reduce the influence of the wavelet transform threshold, and realize adaptive noise reduction.For weld X-ray image enhancement, enhancements with artifacts, distortion, and other phenomena affecting feature extraction are the problems to be solved.Therefore, this paper proposes an adaptive anisotropic image enhancement method based on local variance.This technique involves one-level Taylor expansion of the traditional Laplace algorithm and adaptive diffusion coefficient adjustment in the normal and tangential directions to address artifacts, distortions, and over-enhanced phenomena caused by traditional image enhancement using the Laplace algorithm.Qualitative and quantitative experiments show that the proposed noise reduction and enhancement method outperformed other weld X-ray image processing methods.

The adaptive weld x-ray image noise reduction method based on wavelet domain and wiener filtering
During image acquisition, the digitized negative weld images are prone to noise due to negative shooting, low digitizing scanner light source brightness, and poor brightness uniformity, presenting challenges during the subsequent evaluation of the weld defect type and level.Therefore, developing algorithms to effectively remove noise without losing weld information is imperative.

Wavelet Transforms.
Wavelet transform is an analysis method based on Fourier and Gabor transform.It presents the advantages of the Fourier transform while avoiding some of its shortcomings.Since the noise wavelet coefficients in wavelet transform [32][33] are lower than those of non-noise, it can be utilized to select a suitable empirical wavelet threshold.The signals larger than the wavelet threshold are inverted to obtain the theoretical noise reduction image.Since the wavelet waveform can make various local changes according to the image processing analysis requirements, it presents a certain degree of adaptivity.Wavelets display a low-frequency resistance for signals with high frequencies and give low frequencies a high degree of resolution.Therefore, the wavelet transform method is suitable for image processing, quantum mechanics, and other scientific fields.
Since wavelet transform displays good time-frequency resolution and flexible basic function selection, it can better retain the spikes and mutations in a useful signal during noise reduction.Therefore, wave transform was applied to process the digitized negative pipeline weld images.The commonly used wavelet noise reduction algorithms include translation invariant wavelet noise reduction [33], modulo maximal noise reduction [34][35][36], and wavelet thresholding noise reduction [37].This paper mainly examines wavelet thresholding noise reduction.
After performing the Wavelet Decomposition of the harmonic novelty signs, the energy of the detail component signals concentrates mainly on the high-frequency coefficients.Meanwhile, the approximation component signals are scattered in the low-frequency coefficients.The signal and noise can be separated using the wavelet transform characteristics to set the appropriate empirical wavelet threshold, retain wavelet coefficients higher than the threshold, and remove those lower.
The wavelet threshold noise reduction process consisted of three steps: (1) Discrete wavelet decomposition.The basic wavelet function and the number of decomposition layers were determined, after which the noise-containing signal was subjected to diffuse wavelet transform to obtain the corresponding high and low-frequency wavelet coefficients.(2) Wavelet threshold quantization.The wavelet coefficients were processed to obtain estimated high-frequency coefficients, while low-frequency coefficients remained unchanged.(3) Wavelet coefficient reconstruction.The low-frequency and estimated high-frequency coefficients were used for wavelet inversion to obtain the noise-reduced signal.Figure 1 shows the entire reduction process.For the noise-containing signal wavelet decomposition, the non-noise signal and the noise signal show different performances in wavelet coefficients.The capability of non-noise signals is concentrated in the larger coefficients.However, the energy of the noise signal is focused on the smaller coefficients.
The one-dimensional non-smooth and noise-containing signal is expressed as: (1) where f( ) is the original signal, ( ) is the Gaussian white noise, and x( ) is the noise-containing signal.Discrete wavelet transform of x( ) is expressed as: where , ( ) is the basic discrete wavelet function.
A threshold value is selected μ in view of demographic wavelet coefficient properties of the nonnoise and noisy signals.Wavelet coefficients exceeding this threshold result from the useful signal, while wavelet coefficients below this threshold are considered the product of noise.The threshold μ and its function are used to process wavelet coefficients∫ x( ) , ( ) .Thresholding the wavelet factors at every level yields the processed coefficients and threshold functions to coefficients and inverted to obtain the denoised signal x ( ).

Wiener filtering.
Wiener filtering is mainly used to filter an image based on the accuracy of the image noise variance estimation, i.e., the mean square error between the original image ( , ) ( , ) is required to be minimized after estimating the local mean and variance values of the pixels.W and H denote the width and height of the negative weld image centered on the ( , ).The mean and variance of the pixel gray value are calculated as: where μ is the mean value of the pixel point requiring processing, and σ is the variance value of the desired processed pixel point.Then, the mean square error is: The Wiener filter equation is: Figure 2. The noise reduction process in weld X-ray images.A lower threshold was selected after the wavelet transform of the weld X-ray image, while wavelet coefficients exceeding the threshold were retained, and wavelet inverse transform was performed to obtain the negative weld image after the first wavelet noise reduction.A comprehensive evaluation factor was used to assess the image.The iterative noise reduction process was terminated when the image met the noise reduction requirements.Otherwise, it was necessary to perform Wiener filtering and a second wavelet transform process until the noise reduction requirements were met.
After wavelet noise reduction, images are subjected to comprehensive evaluation to assess the following indexes: (1) Grayscale standard deviation (STD) Gray scale STD indicates the degree of dispersion between the grayscale and mean values of an image.A larger grayscale STD indicates a higher image quality and contrast.The grayscale STD is calculated using the following formula: where W and H denote the width and height of the negative weld image, and u is the mean value of the negative pixels.(2) Contrast The contrast ratio (CR) represents the gradation level of the weld negative from black to white.More levels allow more image information to be expressed, making it easier to reveal subtle defects and ensuring the efficacy of the negative preprocessing results.The contrast is calculated via the fourneighborhood method, where the weld negative is copied and expanded from four directions, from × to ( +2)×( +2) to to .The calculation formula is Equation (9): IOP Publishing doi:10.1088/1742-6596/2770/1/012016 where ( , ) denotes the weld negative and f represents the grayscale difference between the adjacent pixels.
(3) Spatial frequency (SF) The SF mirrors the integral fusion effect on the welded negative in the air domain.A higher SF value indicates a better noise reduction effect.The calculation formula is Equation ( 11 Combining the above three evaluation factors for images, this paper proposes a comprehensive evaluation factor Q to verify the noise reduction in negative weld images, which is calculated as Equation ( 14): where , , and are the weights of the three evaluation factors after synthesis, presenting weight coefficients of 0.5, 0.2, and 0.3, respectively.

Laplace image enhancement.
For Laplace image enhancement, Dennis Gabor proposed improving the high-frequency component of the signal by reversing the temporal orientation of the thermal transport pattern [38].The Gabor temporal evolutionary pattern is specified as Equation ( 15): (, ,) ( , , ) ,0 (,, 0 ) (,) The Laplace enhancement algorithm, represented by the equation, involves the Laplace operator Δ, which may be broken down according to the direction of the gradient n and the direction of the orthogonal tangent s.This decomposition is possible because the operator exhibits isotropic characteristics, as shown in Equation ( 16).(,, 0 ) (,) The Laplace operator can enhance the image isotropically, that is, amplify the noise while enhancing image details.The noise pollution increases as the image is enhanced, and the image boundary is more IOP Publishing doi:10.1088/1742-6596/2770/1/0120167 likely to overshoot.We proposed a set of enhancement algorithms in view of the Laplace that enhanced the edge details of the negative weld image and effectively suppressed noise.

The Adaptive Anisotropy Enhancement Method Based on Localized
Variance.This paper subjected the traditional Laplace algorithm to a first-level Taylor expansion and adaptively adjusted the diffusion coefficients in the normal and tangential directions, denoted as α and β, respectively.Then, an adaptive anisotropy enhancement algorithm was proposed based on local variance, as indicated in Equation ( 18 where The results of the solution are as in Equation ( 20): The results of and , , , and can be calculated using the central difference scheme as in Equation ( 21): Since the grayscale variance effectively distinguished image details from the background noise, this paper used local variance to construct the adaptive diffusion coefficient and the image at ( , ).The local variance in the 3×3 range is expressed as Equation ( 22): where ̅ ( , ) is the mean gray value in the point ( , ) 3×3 range.Grayscale processing was performed on the local variance to select the subsequent calculation parameter: where is the maximum local variance of the image, and is the minimum local variance.Assuming that T is the variance threshold, the diffusion coefficient with respect to the local variance is constructed using the trigonometric feature α( ):  255) Here, α( ) value is positive if the partial covariance ranges from 0 to T/2 and negative at local variance exceeding T/2.This paper used an adaptive variance threshold T, defined as in Equation ( 25): Figure 3 shows the variation curve of variance threshold T with iteration numbers n, where T0=20.The variance threshold T decreased as n increased.From the above derivation, when variance T is smaller, the range where α( ) is positive is smaller, which means, the region where this enhancement algorithm is a positive diffusion model is the smaller.The image edge detail and noise signals are positively diffused in the tangent direction.The diffusion coefficient β must be a positive constant to facilitate noise removal.On the normal orientation, when the partial squareness is greater than T/2, and the α( ) is negative, the enhancement algorithm will perform the reverse diffusion, which enhances the image's detailed features.The detailed feature enhancement of the image is maximized when the local variance at the threshold T reaches a minimum value of -1.In summary, as the iterations of the enhancement algorithm increase, the smaller the variance threshold T. The negative value interval α( ) increases, effectively enhancing the negative weld image.

The noise reduction experiment
This section compares and analyzes the noise reduction performance of the Wiener filter noise reduction algorithm based on wavelet thresholding, Wiener filtering, and wavelet transform via MATLAB 2018a_win6 simulation.Figure 4 illustrates the test comparison graph.The weld X-ray images were cropped to remove the sensitive data, such as the weld joint sections.From a visual perspective, the Wiener filtering methodology using wavelet thresholding suggested was more effective in reducing noise than the traditional wavelet transform and Wiener filtering algorithms.
This paper determined the empirical interval of the comprehensive evaluation factor Q as [0.03,20] using the noise reduction values of 64001 collected negative weld images.A higher interval value indicates better noise reduction algorithm performance.Table 1 shows the specific comparison.
Table 1.A comparison between the three treatment methods.  1, the image quality of the weld seam negative processed using the noise reduction algorithm proposed in this paper was high, clearly showing the weld seam defects.The wavelet transform noise reduction algorithm was more successful in highlighting the contrast than the Wiener filtering algorithm, with a higher spatial frequency and comprehensive evaluation factor Q, while the grayscale STD was lower.Overall, the noise reduction algorithm proposed in this paper is most suitable for reducing noise in negative weld seam images, followed by the wavelet transform noise reduction algorithm.

Weld X-ray image enhancement experiments
3.2.1 Parameter sensitivity.The impact of the coefficient β in direction on the image enhancement of weld negatives was analyzed.Figure 5 shows the image enhancement algorithm for weld negatives at β=0, β=0.5, and β=1, with an initial variance threshold value of T0=8, and n=4 iterations (since Figure 5 contains sensitive data such as the weld joint number, this paper targeted weld negatives of this kind IOP Publishing doi:10.1088/1742-6596/2770/1/01201610 with masked sensitive data).Different β values at the same time caused enhancement variation.A value of β=0 enhanced both the negative weld image details and the noise.When β=1, although the noise has been effectively reduced, the image details are also subject to smoothing to a certain degree.A value of β=0.5 enhanced the image details while minimally increasing the noise.Therefore, the diffusion coefficient β in the tangential direction was set to 0.5 in the enhancement algorithm proposed in this paper. .The effect of n on the weld negative image enhancement was analyzed.Figure 6 shows the weld negative image enhancement results at n=2, n=5, and n=8, with an initial variance threshold value of T0=10 (since Figure 6 contains sensitive data such as the weld joint number, this paper targeted weld negatives of this kind with masked sensitive data).As can be seen from Figure 6, fewer iterations n reduced the negative weld image details, which was gradually enhanced by a higher number of iterations n.However, the image edges appeared prone to overshooting, which was addressed by setting the iteration number of this paper to n=5. .The importance of adaptive variance T in this enhancement methodology was analyzed.Figure 7 shows the enhanced negative weld seam image plots with T as a fixed value T0 and T as an adaptive value = • with an initial variance threshold value of T0=8 and n=5 iterations (since Figure 7 contains sensitive data such as the weld joint number, this paper targeted weld negatives of this kind with masked sensitive data).At a fixed variance threshold, the algorithm enhanced the edges of the negative weld seam image but could not effectively protect the details, while more image details were enhanced at an adaptive variance threshold.Therefore, an adaptive variance threshold T was used in this section for the enhancement algorithm.Figure 8 compares the negative weld seam images after enhancement by the two algorithms (Figure 8 was cropped to remove the sensitive data, such as the weld joint sections).The enhancement algorithm proposed.Although the Laplace enhancement algorithm was more successful at enhancing negative weld images, it also increased the noise, affecting the weld information.The proposed methodology increased the weld seam detail information while distinctly demarcating the weld seam and background.Therefore, weld defects were more prominent (focus on the region), while some of the weld seam detail information was less affected by noise.
The two enhancement algorithms were compared and analyzed using three parameters commonly used to assess the Laplace algorithm to objectively evaluate the quality of the results after negative weld image processing.
(1) Information entropy (IE) IE [40] measures the degree of system orderliness.A lower IE indicates a more organized system, while a higher IE denotes a more chaotic system.Therefore, the IE of an image after enhancement can indicate noise.
where ( , ) denotes the probability that the point (x, y) occurs in a 3×3 range.
(2) Peak signal-to-noise ratio (PSNR) The PSNR [40], which represents the proportion of maximal probable signal power to the noise power affecting accuracy for its representation, is often used to measure the adequacy of an image processing procedure.As shown in Table 2, the IE of the image exceeded that of the Laplace enhancement algorithm after image enhancement.Therefore, both the image details and noise were increased significantly.The PSNR of the image was lower than that used in this paper, while the RMSE was larger, indicating that the proposed enhancement technique was much better than the Laplace enhancement technique and more suitable for enhancing negative weld images.

Conclusion
In this paper, a technique for noise reduction of pipeline welding X-ray images using wavelet domain and Wiener filtering is proposed.Combining wavelet transform and Wiener filtering reduces weld Xray image noise while preserving the weld image details to a large extent.Furthermore, a comprehensive evaluation factor is proposed to measure noise reduction, decreasing dependence on the wavelet threshold.In addition, an adaptive enhancement method is proposed to improve the contrast in pipeline weld X-ray images.This technique suppresses noise increase in weld X-ray images by setting the forward diffusion coefficient and enhances the image details using the inverse diffusion coefficient.This enhances the image details while avoiding the artifacts and distortions caused by a significant noise increase.Qualitative and quantitative experiments show that the method increases clarity and contrast, improves weld defect feature extraction, and is highly significant for the safe operation and sustainable development of pipelines in practical settings.Comparison experiments show that the method in this paper for enhancing weld X-ray images and reducing noise outperformed other image processing methods.
Although the method in this paper displays excellent noise reduction and enhancement performance, the techniques in this paper are independent of each other.Future research will investigate integrated weld X-ray image processing methods that reduce noise in conjunction with enhancement to decrease method complexity.

Figure 3 .
Figure 3.The variation curve of the variance threshold T.From the above derivation, when variance T is smaller, the range where α( ) is positive is smaller, which means, the region where this enhancement algorithm is a positive diffusion model is the smaller.The image edge detail and noise signals are positively diffused in the tangent direction.The diffusion coefficient β must be a positive constant to facilitate noise removal.On the normal orientation, when the partial squareness is greater than T/2, and the α( ) is negative, the enhancement algorithm will perform the reverse diffusion, which enhances the image's detailed features.The detailed feature enhancement of the image is maximized when the local variance at the threshold T reaches a minimum value of -1.In summary, as the iterations of the enhancement algorithm increase, the smaller the variance threshold T. The negative value interval α( ) increases, effectively enhancing the negative weld image.

Figure 4 .
Figure 4. (a) Original; (b) Image after noise reduction; (c) Image after wavelet denoising; (d) Image after Wiener filtering; (e) The image after denoising via Wiener filtering based on the wavelet threshold.The sections marked in red in Figure 4(e) represent the weld defect locations that need to be focused on.From a visual perspective, the Wiener filtering methodology using wavelet thresholding suggested was more effective in reducing noise than the traditional wavelet transform and Wiener filtering algorithms.This paper determined the empirical interval of the comprehensive evaluation factor Q as [0.03,20] using the noise reduction values of 64001 collected negative weld images.A higher interval value indicates better noise reduction algorithm performance.Table1shows the specific comparison.Table1.A comparison between the three treatment methods.

Figure 5 .
Figure 5. Weld X-ray image.(a) Original drawing; (b) β=0; (c) β=0.5;(d) β=1.The effect of n on the weld negative image enhancement was analyzed.Figure6shows the weld negative image enhancement results at n=2, n=5, and n=8, with an initial variance threshold value of T0=10 (since Figure6contains sensitive data such as the weld joint number, this paper targeted weld negatives of this kind with masked sensitive data).As can be seen from Figure6, fewer iterations n reduced the negative weld image details, which was gradually enhanced by a higher number of iterations n.However, the image edges appeared prone to overshooting, which was addressed by setting the iteration number of this paper to n=5.

Figure 6 .
Figure 6.Weld X-ray image.(a) Original drawing; (b) n=2; (c) n=5; (d) n=8.The importance of adaptive variance T in this enhancement methodology was analyzed.Figure7shows the enhanced negative weld seam image plots with T as a fixed value T0 and T as an adaptive value = • with an initial variance threshold value of T0=8 and n=5 iterations (since Figure7contains sensitive data such as the weld joint number, this paper targeted weld negatives of this kind with masked sensitive data).At a fixed variance threshold, the algorithm enhanced the edges of the negative weld seam image but could not effectively protect the details, while more image details were enhanced at an adaptive variance threshold.Therefore, an adaptive variance threshold T was used in this section for the enhancement algorithm.

Figure 7 .
Weld X-ray image.(a) Original drawing; (b) T=T0; (c) T=T0 *e -n .3.2.2Enhanced performance analysis.The traditional Laplace methodology and the proposed methodology were used to process and compare negative weld seam images.The formula parameters included an adaptive variance threshold value of = • , n=5 iterations, and a diffusion coefficient in the tangential direction of β=0.5.

Figure 8 .
Figure 8.(a) Original image of the negative weld image; (b) The Laplace enhancement algorithm; (c)The enhancement algorithm proposed.Although the Laplace enhancement algorithm was more successful at enhancing negative weld images, it also increased the noise, affecting the weld information.The proposed methodology increased the weld seam detail information while distinctly demarcating the weld seam and background.Therefore, weld defects were more prominent (focus on the region), while some of the weld seam detail information was less affected by noise.The two enhancement algorithms were compared and analyzed using three parameters commonly used to assess the Laplace algorithm to objectively evaluate the quality of the results after negative weld image processing.(1)Information entropy (IE) IE[40]  measures the degree of system orderliness.A lower IE indicates a more organized system, while a higher IE denotes a more chaotic system.Therefore, the IE of an image after enhancement can indicate noise.
The Wavelet noise reduction process.Wavelet threshold functions comprise hard and soft threshold functions.The hard threshold functions in the wavelet domain are subject to sudden changes, causing the image to produce unnecessary local jitter after noise reduction.The soft threshold function for wavelet transform yields a smoother wavelet domain and image after noise reduction.
Wiener filter noise reduction based on wavelet thresholding methods.We proposed an improved adaptive wavelet transform algorithm for wavelet transform threshold selection.This method combined wavelet transform and Wiener filtering to reduce image noise after many iterations.Figure2shows the noise reduction process of a Wiener-filtered weld X-ray image based on wavelet thresholding.
Root mean square error (RMSE)The RMSE quantifies the disparity between observation and real value.Table2lists objective assessment metric pairs of results for negative weld images processed via different enhancement algorithms.Table2.A comparison between the evaluation parameters of the various algorithms for negative weld images.