Inertial confinement fusion x-ray image denoising method based on improved DDIM

Abstract

The application discloses an inertial confinement fusion X-ray image denoising method based on improved DDIM, and comprises the following steps: generating a batch of noise-free X-ray images through parameterized geometric modeling, ray tracing and disturbance enhancement; constructing a physically perceived improved DDIM forward diffusion process and a matched reverse sampling denoising process; building a multi-scale U-Net as a noise prediction network; taking the noise-free X-ray images as training samples, generating noise images at each time step through the improved forward diffusion process; inputting the noise images at each time step into the trained noise prediction network to obtain the predicted spatially correlated noise at each time step; and performing reverse sampling denoising on the X-ray image to be processed through the reverse sampling denoising process, and outputting a denoised clean image. The application takes into account the denoising performance and detail fidelity, and meets the image diagnosis requirements of the full evolution stage of ICF experiments.

Description

Technical Field

[0001] This invention belongs to the field of experimental diagnosis and X-ray image processing technology of inertial confinement fusion (ICF), specifically involving a noise reduction method for X-ray images of inertial confinement fusion based on improved DDIM. Background Technology

[0002] In inertial confinement fusion experiments, backlit X-ray imaging is a core diagnostic tool for observing the implosion dynamics of target pellets and retrieving surface density distribution. By projecting X-rays through the target pellet, key information such as the shell profile, density gradient, and evolution of interface instabilities can be obtained. The imaging quality directly determines the accuracy of physical parameter inversion and experimental law analysis.

[0003] With the widespread adoption of digital detectors such as CCD and CMOS, the temporal and spatial resolution of imaging has significantly improved. However, this has also introduced multiple layers of composite noise: first, shot noise generated by statistical fluctuations of X-ray photons, the intensity of which is positively correlated with the local signal amplitude and exhibits spatial correlation; second, periodic speckle noise introduced by scintillators and optical links; and third, detector electronic noise. The superposition of these noises typically results in an image signal-to-noise ratio of only 12–18 dB, severely masking weak contrast structures. Especially during the Rayleigh-Taylor RT instability development stage in the late implosion phase, the interface perturbation amplitude is small and the density gradient is weak, making it easy for noise to distort the true perturbation morphology, leading to significant deviations in the measurement of key parameters such as the instability growth factor and boundary position.

[0004] Existing X-ray image denoising techniques are mainly divided into three categories, each with its own limitations:

[0005] 1. Traditional signal processing methods, such as median filtering, Wiener filtering, and BM3D collaborative filtering, rely on manually designed filtering rules. They are poorly adaptable to complex noise and easily cause edge blurring and loss of details while suppressing noise, which cannot meet the needs of high-precision physical diagnosis.

[0006] 2. Discriminative methods based on convolutional neural networks: such as U-Net and DnCNN, establish a mapping from noisy images to clean images through supervised learning, achieving better noise reduction results than traditional methods. However, these methods rely on training with pairs of clean and noisy images, while ICF experiments are expensive, effective data is scarce, and it is impossible to obtain noise-free labels corresponding to real images, which limits the training sufficiency and generalization ability of the model.

[0007] 3. Standard Denoising Diffusion Implicit Model (DDIM): This model learns the image distribution through progressively adding noise forward and progressively denoising backward. It only requires clean images for training and does not require paired labels. However, its default forward process assumes that the noise is independent and identically distributed Gaussian white noise, which does not match the physical formation mechanism of ICF X-ray shot noise, which is "positively correlated with signal intensity and spatially correlated." Direct application of this model will result in residual structured noise and insufficient accuracy in restoring RT instabilities in low-contrast structures.

[0008] Furthermore, ICF experiments are characterized by high costs and significant variations in operating conditions, making it extremely difficult to obtain large datasets of real, noise-free images. Existing models often rely on simulated Gaussian noise to construct training data, which differs considerably from the physical characteristics of real experimental noise, further limiting the effectiveness of these models in practical applications. Therefore, there is an urgent need for an X-ray image denoising method that can accurately simulate experimental noise characteristics, efficiently suppress mixed noise, and preserve key structural information to address the shortcomings of existing technologies. Summary of the Invention

[0009] To address the problems existing in existing technologies, this invention proposes a noise reduction method for X-ray images from inertial confinement fusion (ICF) based on an improved DDIM (Digital Deposition Modeling). Through parametric geometric modeling and ray tracing, high-fidelity, noise-free X-ray images covering hollow spherical shells and RT instabilities are synthesized in batches as a training set. The forward noise addition formula of DDIM is improved to address the physical characteristics of ICF shot noise, constructing a physically-aware diffusion process. A self-consistent deterministic inverse sampling recursive formula is derived. Model training is completed using only clean synthesized images, ultimately achieving high-precision noise reduction for real ICF experimental images. This invention aims to solve the following technical problems:

[0010] The problem of scarce training data and insufficient realism: The number of ICF experimental images is limited and there are no corresponding clean labels, making it difficult to support the effective training of deep learning denoising models; existing synthetic data methods have simple shapes and lack real imaging features, failing to restore real characteristics such as spherical shell geometry, uneven illumination, and interface perturbation, resulting in insufficient model generalization performance.

[0011] The standard DDIM noise modeling mismatch problem: The Gaussian white noise assumption of the standard DDIM does not conform to the signal correlation and spatial correlation of X-ray shot noise, resulting in incomplete removal of shot noise, a lot of structural residue, and low accuracy of weak structure recovery such as RT instability.

[0012] The self-consistency problem of the improved reverse process: After the forward noise addition formula is modified, it is necessary to derive a mathematically self-consistent deterministic reverse denoising recursive relationship to ensure the theoretical consistency and result stability of the diffusion model sampling process.

[0013] The challenge of balancing noise suppression and detail preservation: Existing methods are prone to over-smoothing or local oscillations, making it difficult to effectively remove multilayer noise while accurately preserving key physical structures such as spherical shell boundaries and RT perturbation peaks, thus affecting the accuracy of subsequent quantitative analysis.

[0014] To achieve the above-mentioned technical objectives, the present invention provides the following technical solution:

[0015] A noise reduction method for inertial confinement fusion X-ray images based on improved DDIM, specifically including:

[0016] Constructing a noise-free X-ray image dataset: Through parametric geometric modeling, ray tracing, and perturbation enhancement, noise-free X-ray images covering hollow spherical shells and RT instabilities are generated in batches;

[0017] An improved forward diffusion process for physical perception in DDIM is constructed: Based on the physical characteristics of X-ray shot noise in inertial confinement fusion, the forward noise addition formula is reconstructed. The current noisy image is designed to be determined by the previous noisy image, the initial noise-free clean image, the noise intensity coefficient, and spatially correlated noise. The noise intensity coefficient accumulates with each diffusion time step, and the spatially correlated noise is obtained by applying a two-dimensional Gaussian blur kernel convolution to standard Gaussian white noise.

[0018] A reverse sampling denoising process is constructed to improve the forward diffusion process of DDIM: The noisy image of the current step is input into the noise prediction network to obtain the spatial correlation noise of the current step; the clean image estimate of the current step is obtained based on the spatial correlation noise of the current time step and the forward denoising formula; deterministic sampling is performed and interpolation coefficients are calculated based on the cumulative noise intensity coefficients of adjacent steps; the clean image estimate of the current step and the noisy image of the current step are weighted and interpolated based on the interpolation coefficients to obtain the noisy image of the previous step; the reverse time step is iterated to time step 1 to obtain the denoised clean image;

[0019] A multi-scale U-Net is constructed as a noise prediction network to predict spatially correlated noise at each time step of the inverse sampling denoising process.

[0020] An improved DDIM model is constructed, using the noise-free X-ray image as training samples. Noisy images at each time step are generated through the improved DDIM forward diffusion process. The noisy images at each time step are input into a multi-scale U-Net to obtain the predicted spatial correlation noise at each time step. The loss function is then calculated by combining the actual spatial correlation noise to train the multi-scale U-Net. The trained multi-scale U-Net is then embedded into the inverse sampling denoising process to perform inverse sampling denoising on the ICF experimental X-ray image to be processed, outputting a denoised clean image.

[0021] Furthermore, the step of generating batches of noise-free X-ray images covering hollow spherical shells and RT instabilities through parametric geometric modeling, ray tracing, and perturbation enhancement specifically includes:

[0022] Parametric modeling of the target structure: A geometric model of the target including a hollow spherical shell and a RT instability structure is constructed. The hollow spherical shell is characterized by two concentric spherical surfaces, and the shell thickness can be continuously adjusted to cover the shell size at different implosion compression stages. The RT instability structure generates multimodal interface perturbations through circumferential division and sinusoidal function topography modulation. At the same time, position offset control is set to support the overall center offset of the hollow spherical shell and the RT instability structure, simulating the target positioning deviation in the experiment.

[0023] Backlight illumination field modeling: Define the three-dimensional coordinates of the light source, the base intensity, and the major and minor axis dimensions of the elliptical light spot to generate an elliptical illumination area; introduce the illumination center offset parameter to make the light spot center deviate from the image center in a controllable manner to simulate experimental setup and adjustment errors; use the arctangent function to construct a radial intensity attenuation curve so that the illumination intensity transitions smoothly from the center to the edge, while superimposing the global base brightness to match the dark background characteristics of the detector.

[0024] For each pixel on the detector recording surface, a tracking ray is emitted into the backlight illumination field. The total transmission path length of the tracking ray through the hollow spherical shell and RT instability structure is calculated by the ray tracing method. The gray value of each pixel is calculated based on the Beer-Lambert transmission attenuation law to obtain the initial projection image.

[0025] The initial projected image is subjected to geometric post-processing and imaging defect simulation, including stretching and scaling, region cropping and occlusion simulation, and the spherical shell interface is enhanced by smoothing perturbation through low-frequency deformation field.

[0026] Samples were generated in batches using parameter traversal and random perturbation. Based on the size of the spherical shell and the intensity of the perturbation, the samples were divided into three subsets: the quasi-static subset in the early stage of implosion, the linear growth subset in the middle stage of implosion, and the nonlinear development subset in the late stage of implosion.

[0027] All samples were normalized to a 16-bit grayscale format, and pixel values ​​were mapped to the same dynamic range as the real detector, resulting in noise-free X-ray images covering the hollow spherical shell and RT instability structure.

[0028] Furthermore, the RT instability structure generates multimodal interface perturbations through circumferential partitioning and sinusoidal function topography modulation, specifically as follows:

[0029] The number of RT instability structural modes is defined, and the circumference of the hollow spherical shell is divided into a corresponding number of polygonal partitions, each partition corresponding to an independent RT instability structural protrusion unit; the interface morphology within each partition is represented by a sine function, expressed by the formula:

[0030] ;

[0031] in, Let be the normalized horizontal coordinates of the interface shape of this partition. This represents the radial protrusion height of the interface topography of this partition. The height of the raised foundation; determined by the RT instability width coefficient W and the sharpness coefficient. The perturbation width and tip strength are controlled separately; and a thickness control coefficient is introduced to adjust the transmission intensity weights of the RT instability structure and the hollow spherical shell respectively, to simulate the perturbation morphology at different growth stages.

[0032] Furthermore, for each pixel on the detector recording surface, a tracking ray is emitted into the backlight illumination field. The total transmission path length of the tracking ray through the hollow spherical shell and the RT instability structure is calculated using the ray tracing method as follows:

[0033] For each tracking ray, the ray parametric equation is substituted into the equations of the inner and outer spherical surfaces of the hollow spherical shell to obtain a quadratic equation. The discriminant is used to determine the intersection of the tracking ray with the inner and outer spherical surfaces. If the tracking ray passes through both the inner and outer spherical surfaces simultaneously, the four intersection points are sorted according to the propagation direction, and the effective path length of the tracking ray in the hollow spherical shell medium is calculated. If the tracking ray only brushes against the outer spherical shell, the effective path length is 0.

[0034] For the tracking ray passing through the RT instability structure, the transmission path length of the RT instability structure region is calculated separately. After weighting the transmission path length by introducing the RT instability thickness control coefficient, the total transmission path length is obtained by superimposing it with the effective path length of the tracking ray in the hollow spherical shell medium.

[0035] Furthermore, regarding the physical characteristics of X-ray shot noise in inertial confinement fusion, the forward noise addition formula is reconstructed, and the design of the current noisy image being determined by the previous noisy image, the initial noise-free clean image, the noise intensity coefficient, and spatially correlated noise is as follows:

[0036] Calculate the product of the noise intensity coefficient of the current step, the square root of the initial noise-free clean image, and the spatially correlated noise; design the current step noisy image as the sum of the previous step noisy image and the product, i.e., the improved forward noise addition formula is expressed as:

[0037] ;

[0038] in, Indicates the current time step; For the noisy image of the current step, This is the noisy image from the previous step. The initial noise-free and clean image; This represents the noise intensity coefficient for the current step. For space-related noise, For Gaussian white noise that follows a standard normal distribution, For a two-dimensional Gaussian blur kernel with standard deviation σ, Represents a two-dimensional spatial convolution operation;

[0039] Based on the recursive relationship, the improved forward noise addition formula can be expressed in a form related to the cumulative noise intensity coefficient, as follows:

[0040] ;

[0041] in, This is the cumulative noise intensity coefficient obtained from time step 1 to the current step t.

[0042] Furthermore, the step of obtaining the clean image estimate for the current time step based on the spatial correlation noise of the current time step and the forward noise addition formula specifically involves:

[0043] Noisy image in the current step Input the noise prediction network to obtain the spatially correlated noise of the current step. ;

[0044] Will Substituting the improved forward noise formula ,get:

[0045] ,remember Then we have:

[0046] ;

[0047] Calculation with The discriminant of a quadratic equation with one variable as the independent variable ,get:

[0048] ;

[0049] Solving for the results In each current step of the inverse sampling denoising process, the initial noise-free clean image is replaced with the clean image estimate of the current step to obtain the clean image estimate of the current step. .

[0050] Further, the step of performing deterministic sampling and calculating interpolation coefficients based on the cumulative noise intensity coefficients of adjacent steps, and then performing weighted interpolation between the current step clean image estimate and the current step noisy image based on the interpolation coefficients to obtain the previous step noisy image specifically involves:

[0051] Conditional distribution in the inverse sampling noise reduction process Follows Gaussian distribution get:

[0052] ;

[0053] in, This is the noisy image from the previous step. , Conditional distributions The mean and variance of the Gaussian distribution it follows; , For coefficients;

[0054] Perform deterministic sampling, take ,get

[0055] ;

[0056] Combining the improved forward noise formula By using recursive relationships and the principle of coefficient consistency, we set... , ,in From time step 1 to time step The accumulated noise intensity coefficient is obtained;

[0057] In each current step of the reverse sampling denoising process, the initial noise-free clean image is replaced with the clean image estimate of the current step, resulting in the noisy image of the previous step:

[0058] ;

[0059] in, Indicates the interpolation coefficients for the current step. This is a clean image estimate for the current step.

[0060] Furthermore, the specific structure of the multi-scale U-Net includes:

[0061] Time step embedding module: Sine / cosine position coding is used to map discrete time steps into high-dimensional feature vectors. After transformation by two fully connected layers, the vectors are injected into the residual model of each layer of the downsampling encoder, enabling the network to perceive the current noise intensity and the denoising stage.

[0062] Downsampling encoder: It contains multiple feature extraction layers. Each feature extraction layer consists of two residual modules and a downsampling layer. It gradually reduces the feature map size and increases the number of channels to extract multi-scale image features. A spatial attention module is added to the medium and low resolution layers to enhance the ability to capture long-range dependencies.

[0063] Bottleneck layer: Contains two residual modules and a self-attention module, which fuse multi-scale features and capture global contextual information;

[0064] Upsampling decoder: Contains multiple upsampling layers symmetrical to the downsampling encoder. Each layer fuses the image features of the corresponding scale output by the downsampling encoder through skip connections, gradually restoring the image resolution and detail information.

[0065] Output layer: The output of the last upsampling layer is normalized and nonlinearly activated, and then a 3×3 convolution layer is used to output a prediction result with the same size as the input. The prediction result is spatially correlated noise.

[0066] Furthermore, the loss function is the mean square error (MSE) of the predicted spatial correlation noise and the actual spatial correlation noise.

[0067] Based on the above technical solution, the present invention has at least the following beneficial effects:

[0068] 1. High-fidelity dataset solves the data scarcity problem: Through a multi-level generation process of geometric modeling, ray tracing, and perturbation enhancement, noise-free images covering the entire evolution stage of static morphology and RT instability are synthesized in batches, and the morphology and illumination features are highly consistent with real experiments; only clean images are needed to complete model training, without relying on scarce experimental data and manually labeled pairs, which greatly reduces the cost of data acquisition.

[0069] 2. Strong physical consistency in noise modeling and more thorough noise reduction: The improved forward noise addition formula reflects both the positive correlation between shot noise and signal strength and spatial correlation. Compared with the white noise assumption of standard DDIM, it is more consistent with the noise formation mechanism of ICF X-ray imaging, resulting in more thorough removal of shot noise and less structured residue.

[0070] 3. The reverse process is mathematically consistent and the results are stable and reliable: Based on the improved noise addition formula, the corresponding deterministic reverse recursive formula is derived, which ensures the theoretical consistency between the forward and reverse processes of the diffusion model. The sampling process has no additional randomness, and the output results are stable and reproducible.

[0071] 4. Excellent preservation of fine structure and high diagnostic accuracy: The multi-scale U-Net combined with the attention mechanism and the progressive diffusion denoising mechanism can accurately preserve key physical details such as RT instability perturbation peaks, spherical shell boundaries, and density gradients while reducing noise, avoiding the edge blurring and over-smoothing problems of traditional methods, and significantly improving the accuracy of experimental diagnosis.

[0072] 5. Multi-layer noise synergistic suppression and strong generalization ability: Although the model only designs the noise addition process for shot noise, it can also effectively suppress periodic speckle noise by learning the overall distribution of the image. Through randomized enhancement of noise intensity and diversified training samples, the model has strong adaptability to experimental images with different noise levels and different morphologies, and can adapt to the ICF image noise reduction requirements under different experimental conditions. Attached Figure Description

[0073] Figure 1 This is an overall flowchart of the inertial confinement fusion X-ray image noise reduction method based on the improved DDIM proposed in this invention;

[0074] Figure 2 These are typical synthetic image examples of the three subsets in the method proposed in this invention;

[0075] Figure 3 This is a schematic diagram illustrating the implementation principle of the improved DDIM forward diffusion process in the method proposed in this invention.

[0076] Figure 4 This is a diagram showing the overall structure of the multi-scale U-Net in the method proposed in this invention.

[0077] Figure 5 This is a schematic diagram of the parametric modeling of the hollow spherical shell in the embodiment;

[0078] Figure 6 This is a schematic diagram of the parameterized modeling of the Rayleigh-Taylor instability structure in the embodiment;

[0079] Figure 7 The noise reduction visual effect is shown for different implosion stages in the embodiment.

[0080] Figure 8 This is a comparison of the pixel value profile curves along the horizontal axis of the images before and after noise reduction in the embodiment.

[0081] Explanation of reference numerals in the attached figures: Figure 5 In the diagram, S represents the light source. Indicates the outer radius. Indicates the inner radius. The thickness of the shell is indicated; P1, P2, P3, and P4 represent the four points where the light rays intersect the hollow spherical shell. Figure 6 In this context, R represents the radius of the spherical shell. To raise the height of the foundation, The width coefficient of Rayleigh-Taylor instability. is the Rayleigh-Taylor instability sharpness coefficient. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0083] Although the steps in this invention are arranged by reference numerals, this is not intended to limit the order of the steps. Unless the order of the steps is explicitly stated or the execution of a step requires other steps as a basis, the relative order of the steps can be adjusted. It is understood that the term "and / or" as used herein refers to and covers any and all possible combinations of one or more of the associated listed items.

[0084] The implementation environment in this embodiment is as follows:

[0085] Hardware environment: Processor: Intel i5-12400 processor; Graphics card: Dual NVIDIA GeForce RTX 3090 graphics cards (24GB VRAM per card); Operating system: 64-bit Linux operating system.

[0086] Software environment: Deep learning framework: PyTorch 2.5.1; Programming language: Python 3.11; Image processing libraries: NumPy, OpenCV, Pillow, scikit-image.

[0087] like Figure 1 As shown, this application proposes a noise reduction method for inertial confinement fusion X-ray images based on improved DDIM, which specifically includes:

[0088] S1. Construct a noise-free X-ray image dataset: Generate noise-free X-ray images covering hollow spherical shells and RT (Rayleigh-Taylor instability) instability structures in batches through parametric geometric modeling, ray tracing and perturbation enhancement;

[0089] This application utilizes a five-stage generation process—geometric modeling, illumination calculation, projection imaging, post-processing, and perturbation enhancement—to generate clean training samples that conform to the characteristics of ICF backlight imaging in batches, thus addressing the problem of scarce experimental data. All training samples are 576×800 pixels in single-channel 16-bit grayscale format, containing only clean signals, eliminating the need for pre-created noisy labels, and can be directly used for subsequent diffusion model training.

[0090] In a preferred embodiment, step S1 specifically includes:

[0091] Parametric modeling of target structure: Constructing a geometric model of the target including a hollow spherical shell and RT instability structure;

[0092] Parametric modeling of a hollow spherical shell includes defining the three-dimensional coordinates and inner radius of the hollow spherical shell. Outer radius With respect to the material absorption coefficient μ, shell thickness The hollow spherical shell characterizes the shell structure of the target pellet through two concentric spherical surfaces, such as... Figure 5 As shown, the center of the sphere is aligned with the optical axis of the detector, and the shell thickness can be continuously adjusted to cover the shell size for different implosion compression stages.

[0093] RT instability structures generate multimodal interface perturbations through circumferential partitioning and sinusoidal function topography modulation, specifically, as follows: Figure 6 As shown:

[0094] The number of RT instability structural modes, N, is set, and the circumference of the hollow spherical shell is divided into a corresponding number of polygonal partitions. In this embodiment, N=4. Each partition corresponds to an independent RT instability structural protrusion unit. The interface morphology within each partition is represented by a sine function, expressed by the following formula:

[0095] ;

[0096] in, Let be the normalized horizontal coordinates of the interface shape of this partition. This represents the radial protrusion height of the interface topography of this partition. The height of the raised foundation; determined by the RT instability width coefficient. ( (not actually in the formula) and sharpness coefficient The perturbation width and tip strength are controlled separately; and a thickness control coefficient is introduced to adjust the transmission intensity weights of the RT instability structure and the hollow spherical shell respectively, to simulate the morphology of the RT instability structure at different growth stages.

[0097] In addition, one partition can be selected as the reference partition, the coordinates of the two boundary endpoints of the partition can be calculated, a local coordinate system can be established, and other partitions can be characterized by their own interface morphology based on the sinusoidal function interface morphology equation of the reference partition through coordinate system transformation, thereby uniformly describing the interface morphology of the RT instability structure.

[0098] Simultaneously, position offset control is set to support the overall center offset of the hollow spherical shell and the RT unstable structure, simulating the target positioning deviation in the experiment.

[0099] Backlight illumination field modeling: Define the three-dimensional coordinates of the light source, the base intensity, and the major and minor axis dimensions of the elliptical light spot to generate an elliptical illumination area; introduce the illumination center offset parameter to make the light spot center deviate from the image center in a controllable manner to simulate experimental setup and adjustment errors; use the arctangent function to construct a radial intensity attenuation curve so that the illumination intensity transitions smoothly from the center to the edge, while superimposing the global base brightness to match the dark background characteristics of the detector.

[0100] For each pixel on the detector recording surface, a tracking ray is emitted into the backlight illumination field. The total transmission path length of the tracking ray through the hollow spherical shell and the RT instability structure is calculated by the ray tracing method.

[0101] In a preferred embodiment, in this example, for each pixel on the detector recording surface, a tracking ray is emitted into the backlight illumination field. The total transmission path length of the tracking ray through the hollow spherical shell and the RT instability structure is calculated using the ray tracing method as follows:

[0102] For each tracking ray, the ray parametric equation is substituted into the equations of the inner and outer spherical surfaces of the hollow spherical shell to obtain a quadratic equation. The discriminant is used to determine the intersection of the tracking ray with the inner and outer spherical surfaces. If the tracking ray passes through both the inner and outer spherical surfaces simultaneously, the four intersection points are sorted according to the propagation direction, and the effective path length of the tracking ray in the hollow spherical shell medium is calculated. If the tracking ray only brushes against the outer spherical shell, the effective path length is 0.

[0103] For a tracking ray passing through the RT instability structure, the transmission path length of the RT instability structure region is calculated separately. An RT instability thickness control coefficient (used to match the material density characteristics of the RT instability region) is introduced to weight the transmission path length. The transmission path length within a single RT instability structure protrusion unit is then calculated. for:

[0104] ;

[0105] in, RT instability thickness control coefficient This represents the radial distance from the sampling point within the partition to the center of the hollow spherical shell. The radius of the hollow spherical shell is given; this is then added to the effective path length of the tracking ray within the hollow spherical shell medium to obtain the total transmission path length. .

[0106] Then, based on the Beer-Lambert transmission attenuation law, the grayscale value of each pixel is calculated, and the grayscale value of each pixel is... ;in Given the incident backlight intensity at the pixel location, the initial projected image is obtained.

[0107] Geometric post-processing and imaging defect simulation are performed on the initial projected image to further approximate the morphology of the real experimental image, including:

[0108] Stretching and scaling: Applying an isotropic stretch to an image at a random scale to simulate magnification deviation in an imaging system;

[0109] Region cropping: Randomly select a sub-region within the original image for cropping, and adjust the position and proportion of the target in the final image;

[0110] Occlusion simulation: Generates slanted black occlusion bands at the image edges to simulate detector edge response failure and field of view occlusion, supporting random black border generation in four directions: top, bottom, left, and right.

[0111] To enhance sample generalization, this application further enhances the smooth perturbation of the spherical shell interface through a low-frequency deformation field. Specifically, a two-dimensional random displacement field with the same size as the image is generated, and the displacement field is smoothed by Gaussian low-pass filtering to control the spatial scale and continuity of the deformation. The overall interface is smoothed and distorted by image remapping, so that the regular periodic perturbation produces irregular offsets, simulating the asymmetric evolution and secondary structure of the interface in the nonlinear stage, thereby improving the morphological diversity and physical realism.

[0112] Samples are generated in batches using parameter traversal and random perturbation. In this embodiment, the parameter traversal involves traversing the spherical shell radius, thickness, RT instability structure width coefficient, and RT instability sharpness coefficient within a given range. The random perturbation involves randomly selecting the illumination intensity, light spot size, light spot position, occlusion height, shell strength control coefficient, and RT instability structure strength control coefficient within a given range.

[0113] The generated samples were divided into three subsets based on the size of the spherical shell and the intensity of the RT instability: the early quasi-static subset of implosion, the mid-implosion linear growth subset, and the late-implosion nonlinear development subset.

[0114] The early-stage quasi-static subset of implosion corresponds to the initial stage of implosion compression. The target shell morphology is close to that of an ideal smooth spherical shell, with weak interface perturbation RT instability and high overall symmetry. This type of sample is used to establish the model's understanding of the baseline morphology of a clean spherical shell, supporting the noise reduction needs of basic diagnostic scenarios such as hollow spherical shell radius measurement and symmetry assessment.

[0115] The linearly growing subset during the implosion phase corresponds to the linear development stage of Rayleigh-Taylor instability. The interface exhibits a regular multimodal periodic RT instability structure with moderate instability amplitudes and continuous, predictable morphology. This type of sample constitutes the main body of the dataset and is used to train the model's noise suppression and detail preservation capabilities for conventional RT instability structures, meeting the noise reduction requirements of most experimental conditions.

[0116] The late-stage nonlinear development subset of implosion corresponds to the nonlinear evolution stage of instability. The interface forms a convex structure, exhibiting high sharpness and large amplitude of RT instability, accompanied by irregular interface deformation, significantly increasing morphological complexity. This type of sample is used to enhance the model's feature learning of complex, strong RT instability structures, avoiding excessive smoothing and structural distortion at the edges of late-stage strong RT instability structures, and ensuring the diagnostic accuracy of quantitative calculation of instability growth factors.

[0117] For each sample class, variables such as shell radius, thickness, RT instability amplitude, absorption coefficient, illumination intensity, spot position, and occlusion morphology are randomized within the parameter range to ensure dataset diversity. Finally, all samples are normalized to 16-bit grayscale format, with pixel values ​​mapped to the same dynamic range as the real detector, and uniformly saved in TIFF format. The three subsets correspond to the morphological features of different evolution stages of target implosion, with typical synthetic image samples as shown below. Figure 2 As shown, from left to right, are noise-free X-ray images of the early quasi-static stage, the middle linear growth stage, and the late nonlinear development stage of implosion.

[0118] S2. Constructing an improved DDIM forward diffusion process based on physical perception: Addressing the physical characteristics of X-ray shot noise in inertial confinement fusion, the forward noise addition formula is reconstructed to make the diffusion process conform to the formation rules of real noise; the current noisy image is designed to be determined by the previous noisy image, the initial noise-free clean image, the noise intensity coefficient, and spatially correlated noise; the noise intensity coefficient accumulates with each diffusion time step, and the spatially correlated noise is obtained by applying a two-dimensional Gaussian blur kernel convolution to standard Gaussian white noise;

[0119] As a preferred embodiment, in this embodiment, such as Figure 3 As shown, step S2 specifically involves:

[0120] Standard DDIM forward noise addition is based on the assumption of additive white Gaussian noise, and the formula is expressed as:

[0121] ;

[0122] in, The cumulative product coefficient, Standard Gaussian white noise, For the initial noise-free and clean image, This is the noisy image from the current step. It is evident that the Gaussian white noise assumption of the standard DDIM does not conform to the signal and spatial correlation of X-ray shot noise, resulting in incomplete shot noise removal, significant structural residue, and low accuracy in recovering weak structures such as RT instability.

[0123] The improved DDIM forward diffusion process proposed in this application is as follows:

[0124] Calculate the product of the noise intensity coefficient of the current step, the square root of the initial noise-free clean image, and the spatially correlated noise; design the current step noisy image as the sum of the previous step noisy image and the product, i.e., the improved forward noise addition formula is expressed as:

[0125] ;

[0126] in, Indicates the current time step; For the noisy image of the current step, This is the noisy image from the previous step. The initial noise-free and clean image; This represents the noise intensity coefficient for the current step. To simulate the spatial smoothing characteristics of noise introduced by the scintillator and detector, we performed a spatially correlated noise simulation. For Gaussian white noise that follows a standard normal distribution, The standard deviation is Two-dimensional Gaussian blur kernel, Represents a two-dimensional spatial convolution operation;

[0127] Based on the recursive relationship, the improved forward noise addition formula can be expressed in a form related to the cumulative noise intensity coefficient, as follows:

[0128] ;

[0129] in, This is the cumulative noise intensity coefficient obtained from time step 1 to the current step t. Depend on The noise is generated cumulatively, with a total diffusion time step of T, and the noise intensity gradually increases from 0 to a set maximum value. (In this embodiment, it is set to 0.5). During training, the standard deviation σ of the Gaussian blur kernel is randomly sampled within the range of [0.3, 3.5], and... By applying random scaling within ±10%, the robustness of the model to different noise intensities is improved through data augmentation.

[0130] Therefore, the improved forward noise addition formula proposed in this application reflects both the positive correlation between shot noise and signal strength and spatial correlation. Compared with the white noise assumption of standard DDIM, it is more consistent with the noise formation mechanism of ICF X-ray imaging, and the shot noise removal is more thorough with less structured residue.

[0131] S3. Based on the improved forward noise addition formula, a reverse sampling noise reduction process matching the improved DDIM forward diffusion process is constructed to ensure mathematical consistency between the forward and reverse processes, achieving gradual recovery from a noisy image to a clean image: The noisy image of the current step is input into the noise prediction network to obtain the spatial correlation noise of the current step; the clean image estimate of the current step is obtained based on the spatial correlation noise of the current time step and the forward noise addition formula; deterministic sampling is performed and interpolation coefficients are calculated based on the cumulative noise intensity coefficients of adjacent steps; the clean image estimate of the current step and the noisy image of the current step are weighted and interpolated based on the interpolation coefficients to obtain the noisy image of the previous step; the reverse time step is iterated to time step 1 to obtain the denoised clean image;

[0132] As a preferred embodiment, the specific derivation process of the reverse sampling noise reduction process in this embodiment is as follows:

[0133] Noisy image in the current step Input the noise prediction network to obtain the spatially correlated noise of the current step. ;

[0134] Will Substituting the improved forward noise formula ,get:

[0135] ,remember Then we have:

[0136] ;

[0137] Calculation with The discriminant of a quadratic equation with one variable as the independent variable ,get:

[0138] In actual reverse sampling noise reduction, a very small constant is usually added. Make To avoid numerical instability;

[0139] Solving for the results In each current step of the inverse sampling denoising process, the initial noise-free clean image is replaced with the clean image estimate of the current step to obtain the clean image estimate of the current step. .

[0140] Next, based on the conditional distribution in the inverse sampling denoising process Follows Gaussian distribution get:

[0141] ;

[0142] in, This is the noisy image from the previous step. , Conditional distributions The mean and variance of the Gaussian distribution it follows; , For coefficients;

[0143] Since the objective of this application is image denoising, deterministic sampling is performed, taking... ,get

[0144] ;

[0145] Combining the improved forward noise formula By replacing t with t-1 using the recurrence relation, we obtain... ;

[0146] Then, by the principle of coefficient consistency, we can obtain , Therefore, set , ,in From time step 1 to time step The accumulated noise intensity coefficient is obtained from this; thus, the accumulated noise intensity coefficient is obtained. ;

[0147] Interpolation coefficients are calculated based on the noise intensity coefficients of adjacent time steps. Then, in each current step of the reverse sampling denoising process, the initial noise-free clean image is replaced with the clean image estimate of the current step, resulting in the noisy image of the previous step:

[0148] ;

[0149] Since it is not a Markov process, and It can be replaced with and ,in Let this be the desired number of time steps. Repeat the above process in the direction of decreasing time steps. Assuming the noise prediction network is well-trained, when the time step reaches 1, the output can be considered the initial noise-free and clean image. This reverse process is a deterministic sampling method, which does not require the addition of random noise, and the sampling speed is fast and the results are stable.

[0150] S4. Construct a multi-scale U-Net as a noise prediction network to predict spatially correlated noise at each time step of the inverse sampling denoising process;

[0151] As a preferred embodiment, in this embodiment, such as Figure 4 As shown, the specific structure of the multi-scale U-Net includes:

[0152] Time step embedding module: Sine / cosine position coding is used to map discrete time steps into high-dimensional feature vectors. After transformation by two fully connected layers, the vectors are injected into the residual model of each layer of the downsampling encoder, enabling the network to perceive the current noise intensity and the denoising stage.

[0153] Downsampling encoder: It contains multiple feature extraction layers. Each feature extraction layer consists of two residual modules and a downsampling layer. It gradually reduces the feature map size and increases the number of channels to extract multi-scale image features. A spatial attention module is added to the medium and low resolution layers to enhance the ability to capture long-range dependencies.

[0154] Bottleneck layer: Contains two residual modules and a self-attention module, which fuse multi-scale features and capture global contextual information;

[0155] Upsampling decoder: Contains multiple upsampling layers symmetrical to the downsampling encoder. Each layer fuses the image features of the corresponding scale output by the downsampling encoder through skip connections, gradually restoring the image resolution and detail information.

[0156] Output layer: The output of the last upsampling layer is normalized and nonlinearly activated, and then a 3×3 convolution layer is used to output a prediction result with the same size as the input. The prediction result is spatially correlated noise.

[0157] The residual module serves as the foundational feature processing unit for the downsampling encoder, upsampling decoder, and bottleneck layer. It employs a pre-activated residual architecture with temporal conditional injection, maintaining the feature map spatial size throughout the process and simultaneously performing local image feature extraction and diffusion time information fusion. The module consists of a main feature branch, a temporal conditional injection branch, and a short-circuit residual branch. The main feature branch uses a concatenated structure of two sets of "group normalization - Swish nonlinear activation - 3×3 convolution," with the group normalization group number set to 32. A Dropout layer is connected between the two sets of convolutions to suppress overfitting, with a Dropout rate of 0.1. The first set of convolutions handles channel dimension alignment and the first round of feature extraction, while the second set deepens feature representation within the same channel dimension. The temporal conditional injection branch maps the global temporal step embedding vector to the corresponding channel dimension via a fully connected layer and then element-wise superimposes it onto the intermediate features of the main branch through a broadcast mechanism, ensuring that each feature layer is aware of the noise intensity of the current diffusion stage. The short-circuit residual branch uses a direct connection when the number of input and output channels is the same, and a 1×1 connection when the number of channels is different. After convolution completes channel alignment and is connected, the outputs of the main branch and the short-circuit branch are added element by element to construct a gradient direct path, which alleviates the gradient vanishing problem in deep networks and ensures training stability.

[0158] Spatial Self-Attention Module: This is a long-range feature enhancement unit deployed at the 16×16 resolution encoding / decoding layer and network bottleneck layer. It is used to model the global spatial relationships between pixels in the entire image, overcoming the limitation of convolution operations that can only capture local neighborhood information. The module adopts a pre-normalization architecture, which does not change the spatial size and number of channels of the feature map throughout the process. The input features are first processed by 32 sets of normalization, and then three independent 1×1 convolutions are used to generate query, key, and value attention features respectively. After flattening the two-dimensional feature map into a pixel sequence, the similarity between pixels is obtained by scaling dot product operation, and the attention weights are obtained by normalization using the Softmax function. Then, the value features are weighted and summed to complete the fusion of global context information. The fused features are restored to the two-dimensional feature map format, and after the output projection is completed by 1×1 convolution, they are added element-wise with the original input features to build residual connections, which preserve the original local features while incorporating global dependency information.

[0159] In this embodiment, a multi-scale U-Net network with 4 levels of downsampling encoders and 4 levels of upsampling decoders is constructed. The basic number of channels is 64, and the channel multiplication factor is [1,2,4,8]. Each level contains 2 residual modules, and a spatial attention module is added at the 16×16 resolution level. The dropout rate is set to 0.1, and the number of group normalization groups is 32.

[0160] S5. Build an improved DDIM model, using the noise-free X-ray image as training sample, and generate noisy images at each time step through the improved DDIM forward diffusion process; input the noisy images at each time step into a multi-scale U-Net to obtain the predicted spatial correlation noise at each time step, and then calculate the loss function by combining it with the real spatial correlation noise to train the multi-scale U-Net.

[0161] In this embodiment, as a preferred implementation, the loss function is the predicted spatial correlation noise. Real-space related noise Mean Squared Error (MSE), Loss Function Represented as , This refers to the batch sample size. For sample index;

[0162] Training parameters are set as follows: batch size of 4, Adam optimizer, and initial learning rate of 2×10⁻⁶. -4 The gradient clipping threshold is 1.0; the total number of training epochs is 100; EMA weight smoothing is enabled with a decay coefficient of 0.999;

[0163] In each training round, the time step and blur standard deviation of each clean image are randomly sampled, and noisy images are generated according to the improved forward diffusion formula. The MSE loss is calculated and the parameters are updated by backpropagation. The optimal model weights are saved until the training is completed.

[0164] The trained multi-scale U-Net is embedded into the inverse sampling denoising process to obtain the trained improved DDIM model. Inverse sampling denoising is then performed on the ICF experimental X-ray image to be processed, and a denoised clean image is output.

[0165] In this embodiment, a test set of 16 backlight X-ray images from the hollow spherical shell stage and the RT instability development stage in the real ICF experiment was selected. Based on the improved DDIM model proposed in this invention and trained by the present invention, 30-step deterministic sampling was used for noise reduction.

[0166] Noise reduction visual effects at different implosion stages, such as Figure 7 From top to bottom, they correspond to the early quasi-static stage of implosion, the middle linear growth stage of implosion, and the late nonlinear development stage of implosion.

[0167] As can be seen from the figure, in the early quasi-static stage of implosion, the original noisy image has significant granular shot noise, and the outline of the spherical shell boundary is blurred due to noise interference. After noise reduction by this method, the noise is completely suppressed, the spherical shell boundary is clear and continuous, and the grayscale transition is smooth and natural.

[0168] During the linear growth phase of the implosion, the periodic RT instability structure in the original image is masked by noise, and its weak contrast features are difficult to distinguish. After denoising using this method, the multimodal periodic RT instability structure is clearly revealed, and the amplitude and periodic features of the RT instability structure are completely preserved without structural distortion.

[0169] For the late nonlinear development stage of implosion, the original image has a lower signal-to-noise ratio and the morphology of the RT instability structure is blurred under strong noise. After denoising by the method of this invention, the peaks and depressions of the RT instability structure can be clearly identified, and the morphological features of the nonlinear evolution are completely preserved without edge blurring or artifacts.

[0170] For example Figure 8 As shown, the graphs present a comparison of the pixel value profile curves along the vertical axis of the image before and after denoising in three stages. The red curve represents the pixel value profile curve along the vertical axis (i.e., along the row direction) of the original noisy image, and the blue curve represents the pixel value profile curve along the vertical axis of the image after denoising (the horizontal axis represents the row number, and the total pixel value is the corresponding pixel value).

[0171] As can be seen from the figure, the pixel value profile curve of the horizontal axis of the original noisy image fluctuates violently. The smoothness of the pixel value profile curve of the horizontal axis of the image after noise reduction is significantly improved, and the boundary position and transition slope are highly consistent with the distribution of the real signal, without boundary blurring caused by excessive smoothing.

[0172] In summary, the method proposed in this invention achieves excellent mixed noise suppression in all three implosion stages, while accurately preserving the key physical structures of each stage, balancing noise reduction performance and detail fidelity, and meeting the image diagnostic requirements of the entire evolution stage of ICF experiments.

[0173] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0174] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0175] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A noise reduction method for X-ray images of inertial confinement fusion based on improved DDIM, characterized in that, Specifically, the following steps are included: Constructing a noise-free X-ray image dataset: Through parametric geometric modeling, ray tracing, and perturbation enhancement, noise-free X-ray images covering hollow spherical shells and RT instabilities are generated in batches; An improved forward diffusion process for physical perception in DDIM is constructed: Based on the physical characteristics of X-ray shot noise in inertial confinement fusion, the forward noise addition formula is reconstructed. The current noisy image is designed to be determined by the previous noisy image, the initial noise-free clean image, the noise intensity coefficient, and spatially correlated noise. The noise intensity coefficient accumulates with each diffusion time step, and the spatially correlated noise is obtained by applying a two-dimensional Gaussian blur kernel convolution to standard Gaussian white noise. Construct a reverse sampling denoising process to improve the DDIM forward diffusion process: input the noisy image of the current step into the noise prediction network to obtain the spatial correlation noise of the current step; Based on the spatial correlation noise of the current time step and the forward noise addition formula, the clean image estimate of the current step is obtained; deterministic sampling is performed and interpolation coefficients are calculated according to the cumulative noise intensity coefficients of adjacent steps; the clean image estimate of the current step and the noisy image of the current step are weighted and interpolated based on the interpolation coefficients to obtain the noisy image of the previous step; the reverse time step is iterated to time step 1 to obtain the denoised clean image; A multi-scale U-Net is constructed as a noise prediction network to predict spatially correlated noise at each time step of the inverse sampling denoising process. An improved DDIM model is constructed, using the noise-free X-ray image as training samples. Noisy images at each time step are generated through the improved DDIM forward diffusion process. The noisy images at each time step are input into a multi-scale U-Net to obtain the predicted spatial correlation noise at each time step. The loss function is then calculated by combining the actual spatial correlation noise to train the multi-scale U-Net. The trained multi-scale U-Net is then embedded into the inverse sampling denoising process to perform inverse sampling denoising on the ICF experimental X-ray image to be processed, outputting a denoised clean image.

2. The method for denoising inertial confinement fusion X-ray images based on improved DDIM according to claim 1, characterized in that, The process of generating noise-free X-ray images covering hollow spherical shells and RT instabilities in batches through parametric geometric modeling, ray tracing, and perturbation enhancement specifically includes: Parametric modeling of the target structure: A geometric model of the target including a hollow spherical shell and a RT instability structure is constructed. The hollow spherical shell is characterized by two concentric spherical surfaces, and the shell thickness can be continuously adjusted to cover the shell size at different implosion compression stages. The RT instability structure generates multimodal interface perturbations through circumferential division and sinusoidal function topography modulation. At the same time, position offset control is set to support the overall center offset of the hollow spherical shell and the RT instability structure, simulating the target positioning deviation in the experiment. Backlight illumination field modeling: Define the three-dimensional coordinates of the light source, the base intensity, and the major and minor axis dimensions of the elliptical light spot to generate an elliptical illumination area; introduce the illumination center offset parameter to make the light spot center deviate from the image center in a controllable manner to simulate experimental setup and adjustment errors; use the arctangent function to construct a radial intensity attenuation curve so that the illumination intensity transitions smoothly from the center to the edge, while superimposing the global base brightness to match the dark background characteristics of the detector. For each pixel on the detector recording surface, a tracking ray is emitted from the backlight illumination field to that pixel. The total transmission path length of the tracking ray through the hollow spherical shell and RT instability structure is calculated by the ray tracing method. The gray value of each pixel is calculated based on the Beer-Lambert transmission attenuation law to obtain the initial projection image. The initial projected image is subjected to geometric post-processing and imaging defect simulation, including stretching and scaling, region cropping and occlusion simulation, and the spherical shell interface is enhanced by smoothing perturbation through low-frequency deformation field. Samples were generated in batches using parameter traversal and random perturbation. Based on the size of the spherical shell and the intensity of instability, the samples were divided into three subsets: the quasi-static subset in the early stage of implosion, the linear growth subset in the middle stage of implosion, and the nonlinear development subset in the late stage of implosion. All samples were normalized to a 16-bit grayscale format, and pixel values ​​were mapped to the same dynamic range as the real detector, resulting in noise-free X-ray images covering the hollow spherical shell and RT instability structure.

3. The method for denoising inertial confinement fusion X-ray images based on improved DDIM according to claim 2, characterized in that, The RT instability structure generates multimodal interface perturbations through circumferential partitioning and sinusoidal function topography modulation. Specifically: The number of RT instability structural modes is defined, and the circumference of the hollow spherical shell is divided into a corresponding number of polygonal partitions, each partition corresponding to an independent instability protrusion unit; the interface morphology within each partition is represented by a sine function, expressed by the formula: ； in, Let be the normalized horizontal coordinates of the interface shape of this partition. This represents the radial protrusion height of the interface topography of this partition. The height of the raised foundation; determined by the RT instability width coefficient W and the sharpness coefficient. The width and tip strength of the RT instability were controlled separately; and a thickness control coefficient was introduced to adjust the transmission intensity weights of the RT instability structure and the hollow spherical shell, respectively, to simulate the RT instability morphology at different growth stages.

4. The method for denoising inertial confinement fusion X-ray images based on improved DDIM according to claim 2, characterized in that, For each pixel on the detector recording surface, a tracking ray is emitted into the backlight illumination field. The total transmission path length of the tracking ray through the hollow spherical shell and the RT instability structure is calculated using the ray tracing method as follows: For each tracking ray, the ray parametric equation is substituted into the equations of the inner and outer spherical surfaces of the hollow spherical shell to obtain a quadratic equation. The discriminant is used to determine the intersection of the tracking ray with the inner and outer spherical surfaces. If the tracking ray passes through both the inner and outer spherical surfaces simultaneously, the four intersection points are sorted according to the propagation direction, and the effective path length of the tracking ray in the hollow spherical shell medium is calculated. If the tracking ray only brushes against the outer spherical shell, the effective path length is 0. For the tracking ray passing through the RT instability structure, the transmission path length of the RT instability structure region is calculated separately. After weighting the transmission path length by introducing the RT instability thickness control coefficient, the total transmission path length is obtained by superimposing it with the effective path length of the tracking ray in the hollow spherical shell medium.

5. The method for denoising inertial confinement fusion X-ray images based on improved DDIM according to claim 1, characterized in that, The physical characteristics of X-ray shot noise in inertial confinement fusion are addressed by reconstructing the forward noise addition formula. Specifically, the current noisy image is determined by the previous noisy image, the initial noise-free clean image, the noise intensity coefficient, and spatially correlated noise. Calculate the product of the noise intensity coefficient of the current step, the square root of the initial noise-free clean image, and the spatially correlated noise; design the current step noisy image as the sum of the previous step noisy image and the product, i.e., the improved forward noise addition formula is expressed as: ； in, Indicates the current time step; For the noisy image of the current step, This is the noisy image from the previous step. The initial noise-free and clean image; This represents the noise intensity coefficient for the current step. For space-related noise, For Gaussian white noise that follows a standard normal distribution, For a two-dimensional Gaussian blur kernel with standard deviation σ, Represents a two-dimensional spatial convolution operation; Based on the recursive relationship, the improved forward noise addition formula can be expressed in a form related to the cumulative noise intensity coefficient, as follows: ； in, This is the cumulative noise intensity coefficient obtained from time step 1 to the current step t.

6. The method for denoising inertial confinement fusion X-ray images based on improved DDIM according to claim 5, characterized in that, The process of obtaining the clean image estimate for the current time step based on the spatial correlation noise of the current time step and the forward noise addition formula is as follows: Noisy image in the current step Input the noise prediction network to obtain the spatially correlated noise of the current step. ; Will Substituting the improved forward noise formula ,get: ,remember Then we have: ； Calculation with The discriminant of a quadratic equation with one variable as the independent variable ,get: ； Solving for the results In each current step of the inverse sampling denoising process, the initial noise-free clean image is replaced with the clean image estimate of the current step to obtain the clean image estimate of the current step. .

7. The method for denoising inertial confinement fusion X-ray images based on improved DDIM according to claim 5, characterized in that, The process of performing deterministic sampling and calculating interpolation coefficients based on the cumulative noise intensity coefficients of adjacent steps, and then performing weighted interpolation between the clean image estimate of the current step and the noisy image of the current step based on the interpolation coefficients to obtain the noisy image of the previous step, specifically involves: Conditional distribution in the inverse sampling noise reduction process Follows Gaussian distribution get: ； in, This is the noisy image from the previous step. , Conditional distributions The mean and variance of the Gaussian distribution it follows; , For coefficients; Perform deterministic sampling, take ,get ； Combining the improved forward noise formula By using recursive relationships and the principle of coefficient consistency, we set... , ,in From time step 1 to time step The accumulated noise intensity coefficient is obtained; In each current step of the reverse sampling denoising process, the initial noise-free clean image is replaced with the clean image estimate of the current step, resulting in the noisy image of the previous step: ； in, Indicates the interpolation coefficients for the current step. This is a clean image estimate for the current step.

8. The method for denoising inertial confinement fusion X-ray images based on improved DDIM according to claim 1, characterized in that, The specific structure of the multi-scale U-Net includes: Time step embedding module: Sine / cosine position coding is used to map discrete time steps into high-dimensional feature vectors. After transformation by two fully connected layers, the vectors are injected into the residual model of each layer of the downsampling encoder, enabling the network to perceive the current noise intensity and the denoising stage. Downsampling encoder: It contains multiple feature extraction layers. Each feature extraction layer consists of two residual modules and a downsampling layer. It gradually reduces the feature map size and increases the number of channels to extract multi-scale image features. A spatial attention module is added to the medium and low resolution layers to enhance the ability to capture long-range dependencies. Bottleneck layer: Contains two residual modules and a self-attention module, which fuse multi-scale features and capture global contextual information; Upsampling decoder: Contains multiple upsampling layers symmetrical to the downsampling encoder. Each layer fuses the image features of the corresponding scale output by the downsampling encoder through skip connections, gradually restoring the image resolution and detail information. Output layer: The output of the last upsampling layer is normalized and nonlinearly activated, and then a 3×3 convolution layer is used to output a prediction result with the same size as the input. The prediction result is spatially correlated noise.

9. The method for denoising inertial confinement fusion X-ray images based on improved DDIM according to claim 1, characterized in that, The loss function is the mean square error (MSE) between the predicted spatial correlation noise and the actual spatial correlation noise.

Images