Iterative inversion de-aliasing method based on mixed norm self-supervised learning

Abstract

The invention discloses an iterative inversion de-aliasing method based on mixed norm self-supervised learning, and belongs to the technical field of multi-seismic-source collection aliasing signal separation. The invention aims to solve the problem of improving the stability of a model when facing the problems of non-Gaussian noise, abnormal values and data sparsity. The method comprises the following steps: constructing a denoising convolutional neural network; the method comprises the following steps: generating primary aliasing data from original seismic data through a pseudo-separation process, generating secondary aliasing data through an aliasing operator in combination with the pseudo-separation process, and calculating to obtain synthetic noise; constructing an input and a label of a de-noising convolutional neural network by combining primary aliasing data with synthetic noise; constructing a de-noising convolutional neural network loss function to obtain a trained de-noising convolutional neural network; using the trained de-noising convolutional neural network to input original acquisition data, and outputting a de-noising result; and carrying out inversion on a denoising result by using a projection gradient descent algorithm to obtain an inversion result to replace the original seismic data, and repeating the steps until an evaluation standard is met. The coating is good in stability.

Description

Technical Field

[0001] The present invention belongs to the technical field of aliasing signal separation in multi-source acquisition, and in particular relates to an iterative inversion de-aliasing method based on hybrid norm self-supervised learning. Background Art

[0002] As global demand for oil and natural gas resources continues to grow, the role of geophysical exploration in energy exploration is becoming increasingly prominent. As one of the core technologies in geophysical exploration, seismic exploration can provide important information about underground geological structure and resource distribution by recording and analyzing the propagation, reflection, and refraction of artificially excited seismic waves in underground media, providing key support for the discovery and evaluation of oil and gas reservoirs. However, seismic data acquisition accounts for a high proportion of the cost of the entire oil and gas exploration process, with field acquisition costs typically exceeding 80% of the total budget. With the increasing complexity of exploration targets, the ever-increasing resolution requirements, and the cost pressures brought about by the continued low international oil prices, major oil companies urgently need to improve acquisition efficiency and reduce economic costs while ensuring imaging quality.

[0003] Simultaneous Source Acquisition (SSA) has emerged as a result. This technology allows multiple seismic sources to be excited in a non-overlapping or random manner within a short period of time, breaking the time and space limitations of traditional single-source acquisition methods. By mixing excitation and reception, more seismic trace data can be acquired in the same time, significantly improving acquisition efficiency and data coverage density. However, unlike traditional single-source acquisition data, the individual source signals in blended data overlap in time and space, resulting in severe aliasing, which directly affects subsequent data processing, especially posing challenges in migration imaging and inversion analysis. Therefore, effectively separating the source signals in blended data has become a key step in realizing the industrial application of this technology.

[0004] Early mixed-sample denoising methods were mostly based on the assumption that interference exhibits incoherent characteristics within certain domains, employing traditional signal processing techniques to suppress aliased noise. Furthermore, low-rank constraints, as an alternative to sparse models, have also been widely used in mixed-sample data separation in recent years. These methods do not directly rely on the transform domain, but instead exploit the redundancy and coherence within the data matrix, assuming that unaliased data exhibit a low-rank structure. Finally, with the rapid development of deep learning technology in fields such as computer vision and speech recognition, seismic signal processing has gradually entered a data-driven phase. In recent years, convolutional neural networks (CNNs), U-Net architectures, and attention mechanisms have been widely introduced to the task of separating seismic mixed-sample data, forming a deep learning aliasing system centered on end-to-end training.

[0005] However, in practical applications, clean seismic data is extremely scarce and expensive to obtain. Although existing methods have attempted to use traditional processing results as pseudo-labels to replace real labels, the traditional methods themselves suffer from insufficient accuracy, poor fidelity, or high computational costs, which greatly limits the performance and transferability of deep models. Therefore, researchers have begun to gradually turn to the more flexible and practical unsupervised learning paradigm. Summary of the Invention

[0006] The problem to be solved by the present invention is to improve the stability of the model when facing non-Gaussian noise, outliers and data sparsity problems, and propose an iterative inversion de-aliasing method based on hybrid norm self-supervised learning.

[0007] To achieve the above object, the present invention is implemented through the following technical solutions:

[0008] An iterative inversion anti-aliasing method based on mixed norm self-supervised learning includes the following steps:

[0009] S1. Construct a denoising convolutional neural network.

[0010] S2. Acquire raw seismic data, generate primary aliased data through a pseudo-separation process, then generate secondary aliased data through an aliasing operator combined with the pseudo-separation process on the primary aliased data, and then calculate synthetic noise.

[0011] S3. Construct the input and label of the denoising convolutional neural network using the primary aliased data combined with the synthetic noise obtained in step S2;

[0012] S4. Construct a denoising convolutional neural network loss function and train the denoising convolutional neural network using the input and labels of all common receiver gathers obtained in step S3 to obtain a trained denoising convolutional neural network.

[0013] S5. Use the trained denoising convolutional neural network to input the original collected data and output the denoised results.

[0014] S6. Invert the denoising result using a projected gradient descent algorithm to obtain an inversion result;

[0015] S7. Replace the original seismic data with the inversion result obtained in step S6, and repeat steps S2-S7 until the evaluation criteria are met.

[0016] Furthermore, the denoising convolutional neural network constructed in step S1 is a DnCNN network, which includes 10 layers, namely the first layer, 8 intermediate layers and the last layer. The convolution kernel size of each layer is 3×3, the number of features is set to 64, and the number of channels is set to 1; the denoising convolutional neural network uses residual learning to optimize the noise part.

[0017] Furthermore, the specific implementation method of step S2 includes the following steps:

[0018] S2.1. Acquisition of raw seismic data , the original seismic data is generated into aliased data through the pseudo separation process , the expression is:

[0019]

[0020] in, is a pseudo-fraction operator;

[0021] S2.2. Generate secondary aliased data by combining the aliasing operator with the pseudo-separation process , the expression is:

[0022]

[0023] in, is the aliasing operator;

[0024] S2.3. Based on the primary and secondary aliasing data, the synthetic noise is calculated by considering the synthetic noise intensity parameter. The expression is:

[0025]

[0026] in, is the synthetic noise intensity parameter, .

[0027] Furthermore, the specific implementation method of step S3 is to construct two sets of input data that serve as input and label for each other;

[0028]

[0029]

[0030] in, For the first set of input data, For the second set of input data, Input label coefficients for self-supervision.

[0031] Furthermore, the specific implementation method of step S4 includes the following steps:

[0032] S4.1. Constructing the denoising convolutional neural network loss function, we change it from supervised N2C to N2N, and then introduce residual learning and symmetric loss function to transform from N2N to Robust N2N to obtain the denoising convolutional neural network loss function. , the expression is:

[0033]

[0034]

[0035] in, is the mixed norm weight coefficient, for The corresponding output represents The denoising result is for The corresponding output represents The denoising result of

[0036] S4.2. Use the input and labels of all the common detector gathers obtained in step S3 to train a denoising convolutional neural network, with an initial learning rate of 0.001.

[0037] Furthermore, the specific implementation method of step S6 is to invert the output denoising result using the projected gradient algorithm to obtain the output inversion result , the expression is:

[0038] Z

[0039] in, for The corresponding output denoising result, is the coefficient that controls the inversion step size;

[0040] Set the initial inversion step size to:

[0041]

[0042] in, is the initial inversion step size, For operator The maximum eigenvalue of .

[0043] Furthermore, the evaluation criteria set in step S7 include:

[0044] Criterion 1: Learning rate of denoising convolutional neural network in machine learning;

[0045] Criterion 2: Inversion The absolute value of

[0046] Standard 3: External time and computing equipment requirements;

[0047] The evaluation criteria are meeting criteria 1 and / or criteria 2 and / or criteria 3.

[0048] Beneficial effects of the present invention:

[0049] The present invention discloses an iterative inversion de-aliasing method based on self-supervised learning of a mixed norm, which combines a projected gradient descent algorithm to iteratively attenuate aliasing interference, so that the network operates in a zero-sample unsupervised manner during the separation process. The present invention re-aliases the original aliased data according to the original time delay to construct two sets of data containing quadratic aliasing noise, which serve as network input and label respectively. The symmetric loss function and residual learning scheme based on the mixed norm are adopted to effectively enhance the network's ability to extract coherent signal components. The output of the network is then iteratively inverted using a projected gradient descent algorithm, and the result of the iterative inversion is used as a new input to generate a new synthetic noise optimization denoising network and output result. The present invention is tested on synthetic data, actual data of onshore controllable seismic sources, and actual marine data. The experimental results show that the SSID method of the present invention can achieve relatively accurate data separation in both simple and complex aliasing noise conditions, exhibits good generalization ability, and has high practical application value and promotion potential. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of the mixed sample data separation method (SSID) combining deep learning and inversion methods described in the present invention;

[0051] Figure 2 A schematic diagram of the neural network structure used in the present invention;

[0052] Figure 3 Figure 2 is a diagram of separation of simple aliased synthetic data of common receiver gathers, where (a) is seismic data without aliasing noise, (b) is seismic data with simple aliasing noise, (c) is the result of Robust N2N separation of (b), (d) is the result of SSID separation of (b), (e) is the difference between (a) and (c), and (f) is the difference between (a) and (d);

[0053] Figure 4 Figure 2 is a diagram of separation of simple aliased synthetic data of common shot gathers, where (a) is seismic data without aliasing noise, (b) is seismic data with simple aliasing noise, (c) is the result of Robust N2N separation of (b), (d) is the result of SSID separation of (b), (e) is the difference between (a) and (c), and (f) is the difference between (a) and (d);

[0054] Figure 5Figure 2 is the ocean data separation diagram of the common receiver gather, where (a) is the seismic data without aliasing noise, (b) is the seismic data with simple aliasing noise, (c) is the result of Robust N2N separation of (b), (d) is the result of SSID separation of (b), (e) is the difference between (a) and (c), and (f) is the difference between (a) and (d);

[0055] Figure 6 Figure 2 is the separation diagram of ocean data of common shot gather, where (a) is the seismic data without aliasing noise, (b) is the seismic data with simple aliasing noise, (c) is the result after Robust N2N separation of (b), (d) is the result after SSID separation of (b), (e) is the difference between (a) and (c), and (f) is the difference between (a) and (d); DETAILED DESCRIPTION

[0056] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present invention and are not intended to limit the present invention. That is, the specific embodiments described herein are only some embodiments of the present invention, not all embodiments. Generally, the components of the specific embodiments of the present invention described and illustrated in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0057] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely representative of selected specific embodiments of the present invention. All other specific embodiments obtained by those skilled in the art based on the specific embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0058] In order to further understand the content, features and effects of the present invention, the following specific embodiments are given as examples, and the attached Figure 1 -Attached Figure 6 The detailed instructions are as follows:

[0059] Example 1:

[0060] An iterative inversion anti-aliasing method based on mixed norm self-supervised learning includes the following steps:

[0061] S1. Construct a denoising convolutional neural network.

[0062] Furthermore, the denoising convolutional neural network constructed in step S1 is a DnCNN network, which includes 10 layers, namely the first layer, 8 middle layers and the last layer. The convolution kernel size of each layer is 3×3, the number of features is set to 64, and the number of channels is set to 1. The denoising convolutional neural network uses residual learning to optimize the noise part.

[0063] The first layer is convolution + ReLU; the middle layer is convolution + BN (batch normalization) + ReLU, and the last layer is convolution.

[0064] Furthermore, this structure has shown superior performance in a variety of image and signal denoising tasks and can effectively avoid the occurrence of overfitting. Figure 2 The direct output is noise. This is because the training model in this embodiment uses residual learning, which optimizes the noise component rather than the original image data. Residual learning can effectively improve the network's convergence speed and generalization ability in denoising tasks.

[0065] S2. Acquire raw seismic data, generate primary aliased data through a pseudo-separation process, then generate secondary aliased data through an aliasing operator combined with the pseudo-separation process on the primary aliased data, and then calculate synthetic noise.

[0066] Furthermore, the specific implementation method of step S2 includes the following steps:

[0067] S2.1. Acquisition of raw seismic data , the original seismic data is generated into aliased data through the pseudo separation process , the expression is:

[0068]

[0069] in, is a pseudo-fraction operator;

[0070] S2.2. Generate secondary aliased data by combining the aliasing operator with the pseudo-separation process , the expression is:

[0071]

[0072] in, is the aliasing operator;

[0073] S2.3. Based on the primary and secondary aliasing data, the synthetic noise is calculated by considering the synthetic noise intensity parameter. The expression is:

[0074]

[0075] in, is the synthetic noise intensity parameter, If the original time-delayed synthetic noise is used, it will contain all the actual noise and part of the real signal. Therefore, the de-aliasing method based on denoising will inevitably cause signal leakage. Therefore, it is proposed to introduce the synthetic noise intensity parameter;

[0076] Furthermore, in conventional seismic acquisition, seismic observation data can be expressed as ,in Indicates time, receiving point and source respectively. When using mixed source acquisition, the receiver is designed to continuously record the signals of multiple nearly simultaneous excitation sources. For example, for a specific receiving point The recorded signal becomes a time superposition combination of multiple source responses, and the mathematical expression is:

[0077]

[0078] in, It is The random assignment of the excitation time delays for each source, It is the receiving point The total number of earthquake sources participating in the mixed channel.

[0079] The above formula can be simplified into matrix form:

[0080]

[0081] where B is the aliasing operator that includes all excitation delay time offsets, D is the unmixed response matrix, and b is the mixed measurement result.

[0082] Furthermore, pseudo-dealiasing is equivalent to reversing the time migration and segmenting the hybrid record into segments corresponding to the time length of a conventional seismic record. The resulting data still retains the interference of overlapping sources. This remnant (often called aliasing noise) is not eliminated during the pseudo-dealiasing process.

[0083] S3. Construct the input and label of the denoising convolutional neural network using the primary aliased data combined with the synthetic noise obtained in step S2;

[0084] Furthermore, the specific implementation method of step S3 is to construct two sets of input data that serve as input and label for each other;

[0085]

[0086]

[0087] in, For the first set of input data, For the second set of input data, Input label coefficients for self-supervision.

[0088] Further, take as its optimal value.

[0089] S4. Construct a denoising convolutional neural network loss function and train the denoising convolutional neural network using the input and labels of all common receiver gathers obtained in step S3 to obtain a trained denoising convolutional neural network.

[0090] Furthermore, the specific implementation method of step S4 includes the following steps:

[0091] S4.1. Constructing the denoising convolutional neural network loss function, we change it from supervised N2C to N2N, and then introduce residual learning and symmetric loss function to transform from N2N to Robust N2N to obtain the denoising convolutional neural network loss function. , the expression is:

[0092]

[0093]

[0094] in, is the mixed norm weight coefficient, for The corresponding output represents The denoising result is for The corresponding output represents The denoising result of

[0095] Further, Take 1 / 3.

[0096] S4.2. Use the input and labels of all the common detector gathers obtained in step S3 to train a denoising convolutional neural network, with an initial learning rate of 0.001.

[0097] Furthermore, in the task of noise suppression in seismic data, while the pure L2-norm loss (i.e., mean squared error) effectively measures the overall error, it is sensitive to irregular noise (such as outliers or high-amplitude interference), often leading to overfitting of the model around these outliers and reducing the robustness of the denoising effect. In contrast, the L1-norm (i.e., absolute error) is more robust in dealing with such abnormal interference and better preserves the signal's structural information. However, using the L1-norm alone can affect the model's overall fit due to slow error convergence.

[0098] Therefore, the loss function of this embodiment is first changed from supervised N2C to N2N, that is, from:

[0099] Transform to:

[0100]

[0101] Where y represents noisy data and x represents clean data. and represents noisy data containing mutually independent noise.

[0102] Then, residual learning and symmetric loss function were introduced to transform N2N to Robust N2N, namely:

[0103]

[0104] Finally, in order to achieve a good balance between robustness and fitting performance, this paper introduces a weighted mixed norm loss function. Although the L1 norm achieves aggressive denoising in the early iterations, the mixed norm loss always achieves the highest final signal-to-noise ratio among the three. In addition, the mixed norm shows stronger adaptability when dealing with different levels of mixed noise, achieving a balance between denoising strength and signal coherence preservation. Future work can explore changing parameters during the iteration process. , adaptively balancing the contributions of different norms. This method also utilizes all common-receiver points to train the model, improving its overall efficiency. The robust denoising model constructed through self-supervised iterative inversion using SSID achieves robust denoising results compared to models trained on a single common-receiver gather. Training the model using all common-receiver points sharing the same time delay information maintains strong robustness, achieving denoising results comparable to those originally trained on a single common-receiver gather, while significantly improving computational efficiency.

[0105] S5. Use the trained denoising convolutional neural network to input the original collected data and output the denoised results.

[0106] S6. Invert the denoising result using a projected gradient descent algorithm to obtain an inversion result;

[0107] Furthermore, the specific implementation method of step S6 is to invert the output denoising result using the projected gradient algorithm to obtain the output inversion result , the expression is:

[0108] Z

[0109] in, for The corresponding output denoising result, is the coefficient that controls the inversion step size;

[0110] Set the initial inversion step size to:

[0111]

[0112] in, is the initial inversion step size, For operator The maximum eigenvalue of .

[0113] Further, Take 1.

[0114] Furthermore, within the PGD framework, if the projection operator is convex, the algorithm is guaranteed to converge to the global optimal solution. Although in practical applications, the projection operator is often non-convex, research has shown that PGD remains a practical and effective optimization strategy in such cases. The step size 𝑡 decays exponentially with iterations to improve stability and convergence speed. Furthermore, the initial step size is crucial: an inappropriate setting can cause the algorithm to fall into a local minimum with poor performance; however, a properly chosen step size facilitates better convergence.

[0115] S7. Replace the original seismic data with the inversion result obtained in step S6, and repeat steps S2-S7 until the evaluation criteria are met.

[0116] Furthermore, the evaluation criteria set in step S7 include:

[0117] Criterion 1: Learning rate of denoising convolutional neural network in machine learning;

[0118] Criterion 2: Inversion The absolute value of

[0119] Standard 3: External time and computing equipment requirements;

[0120] The evaluation criteria are meeting criteria 1 and / or criteria 2 and / or criteria 3.

[0121] Furthermore, since the SSID is By generating synthetic noise and training the network, the network parameters will also be affected by the inversion operation, which in turn affects the next step of the network output. Therefore, the inversion operation is actually a global inversion of the entire process, which can achieve good iterative optimization effects.

[0122] The test was performed using the method of this embodiment as follows:

[0123] Test 1: Use the Robust N2N method and the SSID method to operate on simple synthetic data with weak aliasing, and obtain de-aliased seismic data. The signal-to-noise ratio of the de-aliased seismic data is shown in Table 1:

[0124] Table 1

[0125]

[0126] From Table 1 , we can observe that the SSID method has a higher signal-to-noise ratio than the Robust N2N method, that is, the quality of the seismic data after de-aliasing is better;

[0127] refer to Figure 3 As shown in Figure 4, Robust N2N can restore the original signal to a certain extent, but there are still residual noise and signal leakage. This is because Robust N2N uses a time delay different from the original aliased data, so there is an offset between the synthetic noise and the actual noise. Noise residual is inevitable during denoising. Figure 3 As shown in Figures 4 (d) and (f), the SSID exhibits only slight signal leakage. This is because the same time delay as the original aliased data is used, so there is no offset between the synthesized noise and the actual noise. Inversion also provides signal compensation and noise suppression. The results show that while Robust N2N can restore the original signal to a certain extent, its denoising capability and detail recovery accuracy are significantly inferior to those of the SSID.

[0128] Test 2: The Robust N2N method and the SSID method were used to operate on actual ocean data to obtain de-aliased seismic data. The signal-to-noise ratio of the de-aliased seismic data is shown in Table 2:

[0129] Table 2

[0130]

[0131] From Table 2 , we can observe that the SSID method has a higher signal-to-noise ratio than the Robust N2N method, that is, the quality of the seismic data after de-aliasing is better;

[0132] refer to Figure 5 Although the RN2N method achieves some degree of aliasing noise suppression (S / N = 10.1 dB), slight signal leakage can still be observed in its residual image (e). In contrast, the SSID method achieves a cleaner anti-aliasing result, with a significantly improved S / N ratio of 21.7 dB and almost no visible signal leakage.

[0133] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0134] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and components may be substituted with equivalents without departing from the scope of the present application. In particular, as long as there are no structural conflicts, the various features of the embodiments disclosed herein may be combined with each other in any manner, and the omission of an exhaustive description of these combinations in this specification is solely for the sake of space and resource conservation. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions within the scope of the claims.

Claims

1. An iterative inversion anti-aliasing method based on mixed norm self-supervised learning, characterized in that: The steps include: S1. Construct a denoising convolutional neural network. S2. Acquire raw seismic data, generate primary aliased data through a pseudo-separation process, then generate secondary aliased data through an aliasing operator combined with the pseudo-separation process on the primary aliased data, and then calculate synthetic noise. S3. Construct the input and label of the denoising convolutional neural network using the primary aliased data combined with the synthetic noise obtained in step S2; S4. Construct a denoising convolutional neural network loss function and train the denoising convolutional neural network using the input and labels of all common receiver gathers obtained in step S3 to obtain a trained denoising convolutional neural network. S5. Use the trained denoising convolutional neural network to input the original collected data and output the denoised results. S6. Invert the denoising result using a projected gradient descent algorithm to obtain an inversion result; S7. Replace the original seismic data with the inversion result obtained in step S6, and repeat steps S2-S7 until the evaluation criteria are met.

2. The iterative inversion anti-aliasing method based on mixed norm self-supervised learning according to claim 1, characterized in that: The denoising convolutional neural network constructed in step S1 is a DnCNN network, which contains 10 layers, namely the first layer, 8 intermediate layers and the last layer. The convolution kernel size of each layer is 3×3, the number of features is set to 64, and the number of channels is set to 1; the denoising convolutional neural network uses residual learning to optimize the noise part.

3. The iterative inversion anti-aliasing method based on mixed norm self-supervised learning according to claim 1 or 2, characterized in that: The specific implementation method of step S2 includes the following steps: S2.

1. Acquisition of raw seismic data , the original seismic data is generated into aliased data through the pseudo separation process , the expression is: ； in, is a pseudo-fraction operator; S2.

2. Generate secondary aliased data by combining the aliasing operator with the pseudo-separation process , the expression is: ； in, is the aliasing operator; S2.

3. Based on the primary and secondary aliasing data, the synthetic noise is calculated by considering the synthetic noise intensity parameter. The expression is: ； in, is the synthetic noise intensity parameter, .

4. The iterative inversion anti-aliasing method based on mixed norm self-supervised learning according to claim 3, characterized in that: The specific implementation method of step S3 is to construct two sets of input data that serve as input and label for each other; ； ； in, For the first set of input data, For the second set of input data, Input label coefficients for self-supervision.

5. The iterative inversion anti-aliasing method based on mixed norm self-supervised learning according to claim 4, characterized in that: The specific implementation method of step S4 includes the following steps: S4.

1. Constructing the denoising convolutional neural network loss function, we change it from supervised N2C to N2N, and then introduce residual learning and symmetric loss function to transform from N2N to Robust N2N to obtain the denoising convolutional neural network loss function. , the expression is: ； in, is the mixed norm weight coefficient, for The corresponding output represents The denoising result is for The corresponding output represents The denoising result of S4.

2. Use the input and labels of all the common detector gathers obtained in step S3 to train a denoising convolutional neural network, with an initial learning rate of 0.

001.

6. The iterative inversion anti-aliasing method based on mixed norm self-supervised learning according to claim 5, characterized in that: The specific implementation method of step S6 is to invert the output denoising result using the projected gradient algorithm to obtain the output inversion result , the expression is: Z ； in, for The corresponding output denoising result, is the coefficient that controls the inversion step size; Set the initial inversion step size to: ； in, is the initial inversion step size, For operator The maximum eigenvalue of .

7. The iterative inversion anti-aliasing method based on mixed norm self-supervised learning according to claim 6, characterized in that: The evaluation criteria set in step S7 include: Criterion 1: Learning rate of denoising convolutional neural network in machine learning; Criterion 2: Inversion The absolute value of Standard 3: External time and computing equipment requirements; The evaluation criteria are meeting criteria 1 and / or criteria 2 and / or criteria 3.

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