Fingerprint image restoration method based on conditional diffusion probability model

Abstract

The invention discloses a fingerprint image restoration method based on a conditional diffusion probability model, and relates to the technical field of security and identity authentication, and the method comprises the following steps: firstly constructing a fingerprint data set containing various fingerprint features, and carrying out the amplification of the fingerprint data set; secondly, performing threshold segmentation on the original fingerprint image to obtain a foreground region containing fingerprint information, namely a to-be-repaired fingerprint image; constructing and training an unconditional diffusion probability model to generate fingerprint prior information; and finally, inputting the known area pixel value and the mask information of the fingerprint image to be repaired into the reverse iteration denoising network as condition information to guide the generation of the fingerprint image. According to the method, rich semantic information of the fingerprint image can be better learned, and the method has relatively strong generalization ability for masks in any shape, so that the repaired fingerprint image is reasonable in structure and clear in texture; subjective and objective test evaluation results and quantitative contrast experiments prove the effectiveness of the method.

Description

Technical Field

[0001] The present invention relates to the technical field of security and identity authentication, and in particular to a fingerprint image restoration method based on a deep generation model. Background Art

[0002] Fingerprint image restoration refers to the process of using the known information of the fingerprint image to restore the missing areas in the damaged image in a specific way. Its purpose is to ensure that the repaired fingerprint can maintain the structural integrity and semantic consistency with the original fingerprint image, so that the restored content has a sense of reality. Fingerprint image restoration technology is an important part of the field of biometric recognition, and its background can be traced back to the development of fingerprint recognition technology. As a unique biometric feature, fingerprints are widely used in identity authentication, financial security, criminal investigation and other fields. However, fingerprint images are often affected by factors such as noise, blur and defects during the acquisition process, which significantly reduces the accuracy and reliability of recognition.

[0003] Traditional fingerprint restoration methods mostly rely on traditional image processing techniques, such as filtering, interpolation, and edge enhancement. Although these methods can improve image quality to a certain extent, they are often difficult to effectively restore complex texture information and perform poorly when processing fingerprint samples in complex scenes. And because fingerprint image restoration is an ill-posed inverse problem, especially when the missing area is large and contains complex content, image restoration becomes more difficult. Therefore, how to obtain image restoration results with reasonable structure and clear texture has always been a research hotspot in the field of fingerprint image restoration. With the rise of deep learning, many researchers have begun to explore fingerprint image restoration methods based on deep learning. It learns the characteristic attributes of the fingerprint image by establishing a network model, and reconstructs the area to be repaired based on this.

[0004] Reference 1 (Adiga VS, Sivaswamy J. Fpd-m-net: Fingerprint image denoising and inpainting using m-net based convolutional neural networks [C] / / Inpainting and denoising challenges. 2019: 51-61.) proposed an end-to-end trainable convolutional neural network architecture based on M-Net, and redesigned the structural similarity loss function in M-Net to better extract fingerprints from noisy backgrounds to achieve the purpose of fingerprint denoising and restoration; Reference 2 (Prabhu R, Yu X, Wang Z, et al. U-finger: Multi-scale dilated convolutional network for fingerprint image denoising and inpainting [C] / / Inpainting and Denoising Challenges. 2019: 45-50.) proposed a fingerprint image restoration network based on a multi-scale convolutional network U-Finger, which adopted the idea of ​​dilated convolution to systematically aggregate multi-scale contextual information without losing resolution, and can effectively preserve the texture information of fine fingerprints.

[0005] With the development of deep generative models, in order to improve the accuracy of restoration results, many scholars have tried to use variational autoencoders, generative adversarial networks, autoregressive models, Transformers, and diffusion probability models for image restoration. In order to obtain a variety of reasonable results for image restoration, Reference 3 (Nazeri K. Edge Connect: Generative Image Inpainting with Adversarial Edge Learning [J]. arXiv preprint arXiv: 1901.00212, 2019.) proposed a restoration model that performs image restoration on the feature layer plane and fuses image features through feature equalization. Reference 4 (Liu H, Jiang B, Song Y, et al. Rethinking image inpainting via amutual encoder-decoder with feature equalizations [C] / / European Conference on Computer Vision, 2020, 725-741.) proposed a classic image restoration method that combines edge prior information. This method restores the image in a two-stage manner. First, the edge structure information of the image is obtained, and then fine texture is generated based on the edge structure.

[0006] These technologies have shown strong capabilities in capturing features and generating high-quality images, but their network training process still relies on a large amount of data, which greatly limits the model's ability to generalize to unknown types of masks and performs poorly when dealing with specific types of fingerprint damage, resulting in inaccurate repair results. Summary of the invention

[0007] In order to solve the problems existing in the above-mentioned image restoration methods, a fingerprint restoration method with high-quality restoration effect, strong generalization ability, and adaptability to diversified masks is provided. The present invention proposes a fingerprint image restoration method based on a conditional diffusion probability model. The method uses a pre-trained unconditional diffusion probability model to generate prior information for the fingerprint image, and introduces conditional information by sampling from a given pixel during the reverse iterative denoising process, so as to realize conditional control of the generation process, so that the network can generalize any form of mask during the generation process. In addition, relying on the powerful synthetic prior ability of the pre-trained unconditional diffusion probability model, the fingerprint restoration result structure is more reasonable, the texture is clearer and diverse, and it has strong generalization ability.

[0008] To achieve the above objectives, the technical solution provided by the present invention mainly includes the following contents:

[0009] S1. Collect fingerprint images in different scenarios and perform data augmentation on the fingerprint images to build a fingerprint dataset.

[0010] The fingerprint dataset contains various fingerprint features, such as bows, swirls, and rings. In addition, it contains various types of defects and blurs, such as partial fingerprint loss, stains, scratches, etc.

[0011] Then, the fingerprint data set is amplified, and the amplification methods include random rotation, flipping, brightness transformation, saturation transformation, contrast transformation, histogram equalization and Gaussian noise;

[0012] Finally, the fingerprint dataset is divided into a training set and a test set at a ratio of 9:1; the subsequent network can learn the distribution of fingerprint image data through the training set.

[0013] S2. Use the threshold segmentation method to segment the fingerprint image in complex scenes. The foreground area containing fingerprint information in the image is segmented according to the fingerprint features, and the complex and invalid background area is removed, so as to reduce the processing time of the subsequent links and avoid learning the wrong noise characteristics from the background area in the image restoration stage. The segmentation process is specifically as follows:

[0014] First, assume that the original fingerprint image is y, with a size of h×w, and where y 0(i,j) is the gray value of the original fingerprint image at position (i, j). Count the number of pixels at each gray level of the fingerprint image to be repaired and construct a histogram;

[0015] Secondly, select a threshold τ, and calculate the foreground probability, foreground mean, background probability, and background mean for each possible threshold τ;

[0016] Then, all possible thresholds are traversed, and the inter-class variance of the foreground and background is calculated according to the probabilities and means of the foreground and background, and the optimal threshold τ corresponding to the maximum inter-class variance is selected;

[0017] Finally, the original fingerprint image is binarized according to the found optimal threshold τ:

[0018]

[0019] Where y0(i,j) is the pixel value of the original fingerprint image at position (i,j), and the segmented fingerprint image to be repaired is obtained according to the binarization process

[0020] S3. Construct and train an unconditional diffusion probability model: The unconditional diffusion probability model generates prior information for the fingerprint image, including a forward denoising diffusion process and a reverse iterative denoising process, and learns the probability distribution of the fingerprint image under a given training set; the unconditional diffusion probability model training process is as follows:

[0021] First, assume that the fingerprint image to be repaired is x0, which satisfies the data distribution x0~q(x0); where 0 represents the initial state, i.e., it has not yet started to diffuse;

[0022] Then, random noise is added to the original fingerprint image; the forward noise diffusion process is divided into multiple discrete time steps T. At each time step t (where t∈[1,T]), the data x of the previous time step t-1 is given t-1 Add Gaussian noise to generate a noisy fingerprint image x t , while x t It will also be sent to the next time step t+1 to continue adding noise; after repeated iterations and adding noise T times, as long as T is large enough, according to the properties of the Markov chain, the data x with pure random noise distribution will eventually be obtained. T The diffusion noise process from time step t-1 to time step t can be expressed as:

[0023]

[0024] where x t It is the noise data obtained by continuously applying noise to the repaired fingerprint image x0, which conforms to the Gaussian distribution; is the mean of the noise, β t I is the variance of the noise, and the final noise distribution can be expressed as:

[0025]

[0026] Secondly, in the reverse iterative denoising process, a noise vector is randomly sampled to obtain the fingerprint data x that satisfies the pure random noise distribution. T Perform step-by-step denoising, that is, iteratively restore clear fingerprint data from random noise. Training the unconditional diffusion probability model is to train a Gaussian distribution parameterized by a series of neural networks; the process selects the U-Net network to receive the input noisy fingerprint image. The network consists of a compression path and an expansion path. The compression path compresses the dimension of the noisy fingerprint image passing through the path, and the expansion path expands the compressed noisy fingerprint image back to the original dimension; the sampling residual connection between the downstream layer of the compression path and the upstream layer of the expansion path realizes the flow of feature information of the fingerprint image between different levels; the network can predict noise and output a prediction result of the same size as the input image, realizing multi-level feature extraction of the input fingerprint image;

[0027] The expression of the single-step reverse denoising process from time step t to t-1 is:

[0028]

[0029] Since each step of the reverse iterative denoising process is a parameterized Gaussian distribution, according to the Bayesian formula, the t-1 step Gaussian distribution q(x t-1 |x t ,x0) is expressed as:

[0030]

[0031] Finally, the unconditional diffusion probability model predicts the noise residual, that is, the distance between the noise distribution predicted in the reverse iterative denoising process and the noise distribution applied in the forward noise diffusion process is required to be minimized; the mean square error loss is used to minimize the noise distribution applied in the forward process and the noise distribution predicted in the backward process to achieve the final target optimization.

[0032] S4. Use conditional information to guide the diffusion probability model to achieve fingerprint image restoration, that is, generate fingerprint prior information based on the pre-trained unconditional diffusion probability model, and build a conditional guided diffusion probability model; use the known area pixel information and mask information as conditional information to guide the change of the original reverse iterative denoising process of the unconditional diffusion probability model, so that the model generates semantically reasonable and textured diversified fingerprint images under the constraints of conditional information; the specific contents are as follows:

[0033] First, assume that the fingerprint image to be repaired is z0, the mask is M, the pixels in the area to be repaired are M⊙z0, and the pixels in the known area are (1-M)⊙z0. Gaussian noise is continuously added to the fingerprint image to be repaired z0, gradually destroying its original data information; finally, a noisy image z containing only Gaussian noise is obtained. t .

[0034] Secondly, conditional information is used to guide the generation; the model is generated from the noise image z t The noise data is sampled from the data distribution of , and in the process of learning denoising through neural network, the mask condition information of the area to be repaired and the pixel information of the known area are introduced to guide the denoising generation process, and the denoised image z is obtained. t-1 , multiply it with the inverted mask M' to get the missing part at time t-1; at the same time, the original noise image is multiplied with the mask M to get the pixels of the known area containing noise; finally, the generated missing fingerprint part is merged with the noisy fingerprint image to get the fingerprint image at time t-1; the final fingerprint restoration result is obtained by continuous iterative denoising; since the iterative denoising process is defined as a Markov chain, the restoration process can be expressed as:

[0035]

[0036] in, is sampled from the data distribution of z0 after noise processing, and It is sampled from the data distribution learned by the neural network model in the reverse iterative process.

[0037] Due to the adoption of the above technical solution, the present invention has the following advantages:

[0038] 1. The present invention proposes a fingerprint restoration method based on the conditional diffusion model. Before restoring the fingerprint image, the threshold segmentation method is used to segment the foreground area containing fingerprint information in the image according to the fingerprint features, and the complex and invalid background area is eliminated, thereby reducing the processing time of subsequent links and avoiding learning erroneous noise characteristics from the background area in the image restoration stage.

[0039] 2. The present invention proposes a fingerprint restoration method based on a conditional diffusion probability model. In view of the problems existing in the current fingerprint image restoration technology field, the present invention first uses a pre-trained unconditional diffusion probability model to generate fingerprint prior information, so that the network can learn richer semantic generation capabilities, which helps to obtain a restoration result with a reasonable structure and clear texture;

[0040] 3. The present invention proposes a fingerprint image restoration method guided by conditional information, which inputs the mask and the known area of ​​the fingerprint image as conditional information into the reverse iterative denoising network. It can enable the network to generalize masks of any size, shape, and position during reasoning, thereby improving the generalization ability of the network to restore fingerprint images. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flow chart of the present invention;

[0042] Figure 2 This is a network principle diagram of an unconditional diffusion probability model used to generate fingerprint priors in the present invention;

[0043] Figure 3 This is a schematic diagram of fingerprint restoration based on the conditional guided diffusion probability model of the present invention;

[0044] Figure 4 This is a comparison chart of the fingerprint image restoration effects of the method of the present invention and the methods of references 3 and 4; DETAILED DESCRIPTION

[0045] In order to have a clearer understanding of the technical features, purposes and beneficial effects of the present invention, an embodiment of the present invention is further described in conjunction with the accompanying drawings. The embodiment is only used to further illustrate the present invention and cannot be understood as limiting the scope of protection of the present invention. Some non-essential improvements and adjustments made by technicians in this field based on the content of the present invention also fall within the scope of protection of the present invention.

[0046] A fingerprint repair method based on a conditional diffusion probability model specifically comprises the following steps:

[0047] S1. Collect fingerprint images in different scenarios and perform data augmentation on the fingerprint images to build a fingerprint dataset.

[0048] The dataset covers various fingerprint features, such as arches, swirls, and rings, and contains various types of defects and blurs, such as partial fingerprint loss, stains, scratches, etc.

[0049] Then, the fingerprint data set is amplified, and the amplification methods include random rotation, flipping, brightness transformation, saturation transformation, contrast transformation, histogram equalization and Gaussian noise;

[0050] Finally, the fingerprint dataset is divided into a training set and a test set in a ratio of 9:1; a total of 75,600 fingerprint images constitute the image training dataset, and a total of 8,400 fingerprint images constitute the image test dataset; the subsequent network can learn the distribution of fingerprint image data through the training set.

[0051] S2. Use the threshold segmentation method to segment the fingerprint image in complex scenes. It segments the foreground area containing fingerprint information in the image according to the fingerprint features, and removes the complex and invalid background area, reducing the processing time of subsequent links and avoiding learning wrong noise characteristics from the background area in the image restoration stage;

[0052] The present invention uses the Otsu method to calculate the optimal threshold of the fingerprint image: the Otsu method is an adaptive threshold selection method based on the image histogram, which aims to find the optimal threshold by maximizing the inter-class variance. The specific method is:

[0053] First, assume that the original fingerprint image is y, with a size of h×w, and where y 0(i,j) is the gray value of the original fingerprint image at position (i, j), count the number of pixels at each gray level of the fingerprint image to be repaired, and construct a histogram;

[0054] Secondly, select a threshold value τ to segment the image into foreground (fingerprint) and background. Pixel values ​​above τ are considered as foreground (fingerprint), and those below τ are considered as background. For each possible threshold value τ, calculate the foreground probability, foreground mean, background probability, and background mean;

[0055] Then, all possible thresholds are traversed, and the inter-class variance of the foreground and background is calculated according to the probabilities and means of the foreground and background, and the optimal threshold τ corresponding to the maximum inter-class variance is selected;

[0056] Finally, each pixel is classified according to the optimal threshold τ found to realize the binarization of the original fingerprint image:

[0057]

[0058] Where y0(i,j) is the pixel value of the original fingerprint image at position (i,j). The fingerprint image to be repaired after segmentation is obtained according to the binarization process:

[0059] S3, build and train an unconditional diffusion probability model to generate fingerprint priors;

[0060] The unconditional diffusion probability model is constructed as Figure 2 As shown, it includes the forward noise diffusion process and the reverse iterative denoising process. The specific steps are as follows:

[0061] First, obtain the fingerprint image data set; assume that the fingerprint image to be repaired is x0, which satisfies the data distribution x0~q(x0); where 0 represents the initial state, that is, diffusion has not yet begun;

[0062] Then, random noise is added to the original fingerprint image, which is the forward noise diffusion process. The forward noise diffusion process is divided into multiple discrete time steps T. At each time step t (where t∈[1,T]), the data x of the previous time step t-1 is given t-1 Add Gaussian noise to generate noisy data x t , while data x t It will also be sent to the next time step t+1 to continue adding noise; after repeated iterations and adding noise T times, as long as T is large enough, according to the properties of the Markov chain, the data x with pure random noise distribution will eventually be obtained. T The noise diffusion process from time step t-1 to time step t can be expressed as:

[0063]

[0064] where x t It is the noise data obtained by continuously adding noise to the original data x0, which conforms to the Gaussian distribution; is the mean of the noise, β t I is the variance of the noise, and the final noise distribution can be expressed as:

[0065]

[0066] Secondly, it is the reverse iterative denoising process, which refers to the process of denoising the fingerprint image data, that is, iteratively recovering clear fingerprint image data from random noise, that is, the model training process. The reverse process selects the U-Net denoising network to receive the input noisy fingerprint image and predict the noise and output the prediction result of the same size image as the input. The U-Net denoising network consists of a compression path and an expansion path. The compression path compresses the data dimension passing through the path, and the expansion path expands the data back to the original dimension; among them, the compression path uses a downsampling layer to reduce the size of the fingerprint feature map, which is specifically achieved through the pooling layer, and the expansion path uses an upsampling layer to restore the spatial size of the fingerprint feature map; in addition, the downstream layer of the compression path and the upstream layer of the expansion path use residual connections to allow information and gradients to flow between different levels; the initial input layer data input dimension of the U-Net network is 2-dimensional, the convolution kernel size is 3*3, and each side of the input data will be zero-filled with 1 pixel.

[0067] Since the process is defined as a Markov chain, the expression of the single-step reverse denoising process from time step t to t-1 is as follows:

[0068]

[0069] Since the Markov chain is composed of a series of Gaussian distributions parameterized by neural networks, the ultimate goal of its training is to obtain a Gaussian distribution of fingerprint image data. Since this distribution is difficult to obtain by direct calculation, the denoising diffusion probability model predicts the parameters of the Gaussian distribution through neural network modeling, that is, the mean μ θ (x t ,t) and variance ∑ θ (x t ,t). According to Bayesian derivation, we finally get the Gaussian distribution q(x) at time step t-1. t-1 |x t ,x0) is expressed as:

[0070]

[0071] Finally, the fingerprint image predicted by the model is compared with the initial fingerprint image, and the loss is calculated to update the model parameters. Since the diffusion probability model predicts the noise residual, it requires that the distance between the noise distribution predicted in the backward process and the noise distribution applied in the forward process be minimized. The mean square error loss is used to minimize the noise distribution applied in the forward process and the noise distribution predicted in the backward process to achieve the final target optimization.

[0072] S4, using conditional information to guide the diffusion probability model to achieve fingerprint image restoration; Figure 4As shown, based on the unconditional diffusion probability model pre-trained in step S3, the pixel information and mask information of the known area of ​​the fingerprint image to be repaired are input into the diffusion probability model denoising network as additional conditional information, and the generation process is adjusted to guide the model to generate content consistent with the surrounding fingerprint area, thereby realizing the guided fingerprint repair generation process; the specific contents are as follows:

[0073] First, determine the mask area of ​​the fingerprint image to be repaired (i.e., the area to be repaired); assume that the fingerprint image to be repaired is z0, the mask is M, the pixels of the area to be repaired are M⊙z0, and the pixels of the known area are (1-M)⊙z0. Gaussian noise is continuously added to the fingerprint image to be repaired z0, gradually destroying its original data information; finally, a noise image z containing only Gaussian noise is obtained. t .

[0074] Secondly, conditional information is used to guide the generation; the model is generated from the noise image z t Noise data is sampled from the data distribution of . In the process of learning denoising through neural network, the mask condition information of the area to be repaired and the pixel information of the known area are introduced to guide the denoising generation process. The fingerprint prior generated by the pre-trained unconditional diffusion probability model can generate a single-step denoised fingerprint image to obtain the denoised image z t-1 , multiply it with the inverted mask M' to get the missing part at time t-1; at the same time, the original noise image is multiplied with the mask M to get the pixels of the known area containing noise; finally, the generated missing fingerprint part is merged with the noisy fingerprint image to get the fingerprint image at time t-1; the final fingerprint restoration result is obtained by continuous iterative denoising; since the iterative denoising process is defined as a Markov chain; the restoration process can be expressed as:

[0075]

[0076] in, is sampled from the data distribution of z0 after noise processing, and It is sampled from the data distribution learned by the neural network model in the reverse iterative process.

[0077] In order to verify the effectiveness of the fingerprint image restoration method based on the conditional diffusion probability model proposed in the present invention, the image restoration method based on the edge generator and image generation network proposed in document 3 and the image restoration method based on the mutual encoder-decoder network proposed in document 4 were selected as comparison methods. When conducting the comparison experiment, the method of the present invention and the comparison method used the same training set and test set and kept the experimental environment and configuration consistent. In order to quantitatively test and evaluate the three methods, four different quantitative indicators, namely peak signal-to-noise ratio, structural similarity, mean absolute error, and Fréchet distance, were selected to evaluate the restoration results and evaluate the performance of the fingerprint restoration method. The quantitative evaluation results of the comparison method and the method of the present invention are shown in Table 1. As can be seen from Table 1, the present invention has a significant improvement in peak signal-to-noise ratio and structural similarity compared with the methods in documents 3 and 4; the mean absolute errors are reduced by 0.0063 and 0.0073 respectively; the Fréchet distances are reduced by 0.9858 and 3.0328 respectively. It shows that the present method can better complete fingerprint image restoration and improve the accuracy of fingerprint restoration.

[0078] Table 1 Quantitative evaluation results of different fingerprint restoration methods

[0079] Evaluation Criteria Reference 3 Reference 4 This method Peak signal-to-noise ratio 26.1879 25.1314 27.1683 Structural similarity 0.8188 0.7874 0.9123 Mean absolute error 0.0187 0.0197 0.0124 Fréchet distance 16.3134 18.3604 15.3276

[0080] from Figure 4 It can be seen that the method of the present invention can restore the details and textures in the fingerprint image more accurately than the methods proposed in Documents 3 and 4, and can retain the important information in the fingerprint image to a greater extent; it can also show strong adaptability under complex backgrounds and noise interference. The method of the present invention is widely applicable to a variety of different fingerprint image defect situations.

[0081] The above is a description of the relevant contents of the present invention, and those skilled in the art will be able to implement the present invention based on these descriptions. Based on the above contents of the present invention, all other embodiments obtained by those skilled in the art without creative work should fall within the scope of protection of the present invention.

Claims

1. A fingerprint image restoration method based on a conditional diffusion probability model, characterized in that: The following steps are involved: S1. Construct a fingerprint dataset, which contains images with various fingerprint features, such as bows, vortices, and rings, and contains various complex scenes and various types of defects and blurs, such as partial fingerprint loss, stains, scratches, etc.; and amplify the fingerprint dataset, and then divide the amplified fingerprint dataset into a training set and a test set; S2. Use the threshold segmentation method to segment the fingerprint image in the fingerprint data set. It segments the foreground area containing fingerprint information in the image according to the fingerprint features, and removes the complex and invalid background area to obtain the fingerprint image to be repaired, so as to reduce the processing time of subsequent links and avoid learning wrong noise characteristics from the background area in the image repair stage; S3. Construct and train an unconditional diffusion probability model: the unconditional diffusion probability model generates prior information for the fingerprint image, including a forward denoising diffusion process and a reverse iterative denoising process, and learns the probability distribution of the fingerprint image under a given training set; S4. Use conditional information to guide the diffusion probability model to achieve fingerprint image repair: Based on the unconditional diffusion probability model trained in step S3, use the fingerprint image to be repaired obtained in step S2, and input its known area pixel values ​​and mask information as conditional information into the reverse iterative denoising network based on the unconditional diffusion probability model to guide the fingerprint repair generation process and complete the repair of the damaged fingerprint image.

2. According to claim 1, a fingerprint image restoration method based on a conditional diffusion probability model is characterized in that: The unconditional diffusion probability model described in step S3 generates prior information for the fingerprint image, including two processes of forward denoising diffusion and reverse iterative denoising for the fingerprint image to be repaired, and learns the probability distribution of the fingerprint image under a given training set; the forward denoising diffusion process is: First, add noise to the fingerprint image through the forward noise diffusion process; assume that the fingerprint image data to be repaired is distributed from x0 to q(x0); where 0 represents the initial state, that is, diffusion has not yet begun; divide the forward noise diffusion process into multiple discrete time steps T, and at each time step t (where t∈[1,T]), add noise to the data x of the previous time step t-1 t-1 Add Gaussian noise to generate a noisy fingerprint image x t , while x t It will also be sent to the next time step t+1 to continue adding noise; after repeated noise addition T times, as long as T is large enough, according to the properties of the Markov chain, the data x with pure random noise distribution will eventually be obtained. T , the noise diffusion process from time step t-1 to time step t can be expressed as: where x t It is the noise data obtained by continuously applying noise to the repaired fingerprint image x0, which conforms to the Gaussian distribution; is the mean of the noise, β t I is the variance of the noise, and the final noise distribution can be expressed as: The reverse iterative denoising process is: Randomly sample a noise vector and apply it to the fingerprint data x that satisfies the pure random noise distribution. T Perform step-by-step denoising, i.e., iteratively recover clear fingerprint data from random noise, and train an unconditional diffusion probability model, i.e., train a Gaussian distribution parameterized by a series of neural networks; the process selects a U-Net network to receive the input noisy fingerprint image, and the network consists of a compression path and an expansion path. The compression path compresses the dimension of the noisy fingerprint image passing through the path, and the expansion path expands the compressed noisy fingerprint image back to the original dimension; the downstream layer of the compression path and the upstream layer of the expansion path are sampled with residual connections to realize the flow of feature information of the fingerprint image between different levels; the network can predict noise and output a prediction result of the same size as the input image, thereby realizing multi-level feature extraction of the input fingerprint image; The expression of the single-step reverse denoising process from time step t to t-1 is as follows: Since each step of the reverse iterative denoising process is a parameterized Gaussian distribution, according to the Bayesian formula, the t-1 step Gaussian distribution q(x t-1 |x t ,x0) is expressed as: Finally, the unconditional diffusion probability model predicts the noise residual, that is, the distance between the noise distribution predicted in the reverse iterative denoising process and the noise distribution applied in the forward noise diffusion process is required to be minimized; the mean square error loss is used to minimize the noise distribution applied in the forward process and the noise distribution predicted in the backward process to achieve the final target optimization.

3. According to the fingerprint image restoration method based on the conditional diffusion probability model of claim 1, it is characterized in that: As described in step S4, the pixel values ​​and mask information of the known area of ​​the fingerprint image to be repaired are input into the diffusion probability model denoising network as conditional information, and the original reverse iterative denoising process of the unconditional diffusion probability model is adjusted so that the model generates a fingerprint image with reasonable semantics and clear texture under the constraint of the conditional information; specifically as follows: First, assume that the fingerprint image to be repaired is z0, the mask is M, the pixels in the area to be repaired are M⊙z0, and the pixels in the known area are (1-M)⊙z0. Gaussian noise is continuously added to the real fingerprint image z0, gradually destroying its original data information; finally, a noisy image z containing only Gaussian noise is obtained. t ; Secondly, conditional information is guided to generate; The model is derived from the noisy image z t The noise data is sampled from the data distribution of , and in the process of learning denoising through neural network, the mask condition information of the area to be repaired and the pixel information of the known area are introduced to guide the denoising generation process, and the denoised image z is obtained. t-1 , multiply it with the inverted mask M' to get the missing part at time t-1; at the same time, the original noise image is multiplied with the mask M to get the pixels of the known area containing noise; finally, the generated missing fingerprint part is merged with the noisy fingerprint image to get the fingerprint image at time t-1; the final fingerprint restoration result is obtained by continuous iterative denoising; since the iterative denoising process is defined as a Markov chain, the restoration process can be expressed as: in, is sampled from the data distribution of z0 after noise processing, and It is sampled from the data distribution learned by the neural network model in the reverse iterative process.

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