An MFR-Net unwrapping method for strong noise wrapped phase

Abstract

A method for unwrapping MFR-Net phases in the face of strong noise includes the following steps: S1, acquiring samples of the real phase dataset; S2, adding noise to the real phase to obtain samples of the noisy wrapped phase dataset; S3, establishing and partitioning the dataset; S4, inputting the training and validation sets into the MFR-Net multi-module filtering layer to obtain a stitched image; S5, inputting the stitched image obtained in S4 into the back-end network of the MFR-Net for training; S6, inputting the test set into the MFR-Net trained in S5 to obtain the phase unwrapping result output by the network; S7, post-processing the phase unwrapping result obtained in S6 to obtain the final phase unwrapping result. This method can obtain accurate unwrapped phases under strong noise caused by factors such as strong laser coherence, scattering from rough optical component surfaces, electronic interference, and thermal noise. It is of great significance for reconstructing the real phase and improving the accuracy of digital holographic measurements in cases containing speckle and additive mixed noise.

Description

Technical Field

[0001] This invention belongs to the field of optical detection and image processing technology, and specifically relates to an MFR-Net unwrapping method for phase wrapped by strong noise. Background Technology

[0002] Digital holography combines traditional holography, computer technology, and photoelectric detection technology, and has been widely applied in three-dimensional measurement fields such as particle field measurement and microstructure device morphology detection. In the digital holographic reconstruction of the light field, the obtained encapsulated phase is distributed in the interval (-π, π], requiring further unwrapping to recover the true phase information of the object. However, in actual measurements, interference factors such as the strong coherence of lasers, defects on the surface of optical components, or environmental disturbances often introduce speckle noise and Gaussian noise into the encapsulated phase, leading to the inability to obtain correct phase information or even unwrapping failure, seriously affecting the accuracy of the measurement results.

[0003] Traditional phase unwrapping algorithms include branch-cutting methods, quality map-guided methods, and discrete cosine least squares methods. These methods unwrap the phase by avoiding noise points or substituting noise points with calculations from surrounding points. However, these algorithms fail to handle strong speckle noise and additive noise caused by factors such as strong laser coherence and scattering from rough optical surfaces. In recent years, with the rapid development of deep learning, research has been conducted on related neural network algorithms for phase unwrapping, such as DLPU, VUR-Net, and DeepLabV3+. However, these conventional networks can only achieve good unwrapping results when the noise level is low, and they still exhibit significant unwrapping errors in cases of strong noise, failing to accurately reproduce the true phase information.

[0004] Therefore, when faced with the phase unwrapping problem under strong noise conditions, neither traditional algorithms nor existing neural network algorithms can obtain the correct unwrapped phase, which affects the measurement accuracy of subsequent digital holography. Summary of the Invention

[0005] To overcome the shortcomings of the existing technology, the present invention aims to provide an MFR-Net unwrapping method for phase wrapping in strong noise. First, the input image is fed into a multi-module filtering layer, undergoing edge-preserving filtering and mean filtering respectively. The average of the two filtering results is calculated. By stitching the original image, the two filtered images, and the mean image, the stitched image is used as the input to the later-stage network of MFR-Net, providing more filtered feature information. This network reduces training difficulty, facilitates parameter learning, and improves the generalization ability of phase unwrapping under strong noise. Second, dilated convolution and coordinate attention mechanisms are added to the ResUNet network backbone. By expanding the feature receptive field and capturing the correlation information of pixels in the horizontal and vertical directions, the network's ability to extract spatial features and handle noise under strong noise is enhanced. Finally, the unwrapped phase output from MFR-Net is post-processed. Through smoothing operations and mean filtering, the unwrapping effect in regions where the phase jumps from -π to π is further improved, further enhancing the accuracy of the phase recovery result. This effectively solves the problem of inaccurate phase information acquisition under strong noise and improves the phase unwrapping capability.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: an MFR-Net unwrapping method for phase wrapped by strong noise, comprising the following steps: including the algorithm construction process (steps S1 to S5) and the algorithm usage process (steps S6 to S7), which can be further broken down into the following steps:

[0007] Step S1: Generate the original three-dimensional phase using the random matrix amplification method, which serves as a sample of the real phase dataset.

[0008] Step S2: Add noise of different levels to the real phase to obtain a noisy phase, and perform a wrapping operation on the phase to obtain a noisy wrapped phase dataset sample.

[0009] Step S3: The noisy wrapped phase and the true phase are used as a pair of input and output to generate a dataset, which is divided into training set, validation set and test set in a ratio of 18:1:1.

[0010] Step S4: Input the training set and validation set obtained in step S3 into the multi-module filtering layer of the MFR-Net network to obtain the results of edge-preserving filtering and mean filtering respectively. Then, calculate the average of the two filtering results to obtain a double-filtered image. Finally, stitch the original image, the edge-preserving filtered image, the mean-filtered image, and the double-filtered image together to obtain a stitched image.

[0011] Step S5: Input the stitched image obtained in step S4 into the back-end network of MFR-Net for training, and obtain the trained MFR-Net network.

[0012] Step S6: Input the test set into the MFR-Net network trained in step S5 to obtain the unwrapping result output by the network.

[0013] Step S7: Perform smoothing and mean filtering on the unwrapping results obtained in step S6 to obtain the final unwrapping results of the test set.

[0014] Preferably, step S1 specifically includes:

[0015] Step S101: Generate multiple random matrices with a size between 5×5 pixels and 10×10 pixels and a random height distributed in the range of [0 rad, 40 rad].

[0016] Step S102: The random matrix generated in step S101 is enlarged to 256×256 pixels using bilinear interpolation to form the phase of the noiseless object light wave field, thus constituting a real phase dataset sample φ.

[0017] Preferably, step S2 specifically includes:

[0018] Step S201: Add speckle noise of different levels and fixed Gaussian noise to the real phase dataset sample φ obtained in step S102 to obtain a noisy phase. The specific implementation process is as follows:

[0019] The noise in the holographic wrapper phase consists of two parts: speckle and additive noise. The speckle can be represented by multiplicative noise, and the object wave containing speckle noise can be represented as:

[0020] U′=Aexp[jφ][1+σn R exp(jn I (1)

[0021] In equation (1), A represents the amplitude of the noise-free object light wave, which is set to 1 here; φ represents the phase of the noise-free object light wave, i.e., the true phase obtained in step S102; σ represents the standard deviation of speckle noise, which determines the magnitude of the speckle noise level; n R and n I Let represent random Gaussian noise with a mean of 0 and a standard deviation of 1, and j represent the imaginary unit. Then, the object light wave containing speckle and additive noise can be expressed as:

[0022]

[0023] In equation (2), the additive noise N GThe Gaussian noise with a mean of 0 and a standard deviation of 0.2 is used to divide the real phase dataset samples obtained in step S102 into 11 groups. Different levels of noise with σ of 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9 and 2.0 are added to each group to obtain the corresponding object light waves containing noise.

[0024] Step S202: Perform phase extraction on the noisy object light wave to obtain a noisy package phase dataset sample. The specific implementation process is as follows:

[0025]

[0026] In equation (3), Im represents the imaginary part operation and Re represents the real part operation.

[0027] Preferably, step S3 specifically includes:

[0028] The real phase dataset sample φ obtained in step S102 and the noisy wrapped phase dataset sample corresponding to step S202 are compared. As a dataset, it is divided into training set, validation set and test set in a ratio of 18:1:1.

[0029] Preferably, step S4 specifically includes:

[0030] Step S401: The noise-wrapped phase in the training set and validation set is recorded as input and input into the multi-module filtering layer of the MFR-Net network. The part of input that has a -π jump to π is defined as the boundary region, and the rest is defined as the flat region. Flat region identification is performed on input.

[0031] Step S402: Use a 3×3 traversal box to calculate the variance of each point in the input, and use the variance of the flat area obtained in step S401 to determine the noise level, thereby obtaining the noise level of the input wrapping phase input.

[0032] Step S403: For the flat region identified by input in step S401, if the variance value is greater than the noise level of input, the area near the point is considered to be a steep gradient range similar to a boundary, and adaptive bilateral filtering is applied to the point to preserve its gradient information; if the variance value is less than the noise level, the area near the point is considered to be a flat gradient range, and mean filtering is applied to the point to eliminate the influence of noise; for the identified non-flat region, adaptive bilateral filtering is used to denoise based on the variance value corresponding to each point. The filtered image obtained after the above operations is called the edge-preserving filter image, denoised as input_bm;

[0033] Step S404: For the input wrapping phase input, global mean filtering is applied, and the resulting filtered image is called the mean filtered image, denoted as input_m;

[0034] Step S405: Calculate the average of input_bm obtained in step S403 and input_m obtained in step S404. The resulting filtered image is called the double-filtered image and is denoted as input_bmam.

[0035] Step S406: Perform a concatenation operation cat on the input graph input, the edge-preserving filtered graph input_bm, the mean-filtered graph input_m, and the double-filtered graph input_bmam, and convert it into tensor form, denoted as input_cat.

[0036] Preferably, step S5 specifically includes:

[0037] Step S501: Input the input_cat obtained in step S406 into the downsampling part of the back-end network of MFR-Net. The downsampling part includes four steps. Each step goes through a feature extraction module composed of multiple dilated convolutions. The extracted feature map is divided into two parts. One part is sent directly to the upsampling part of the network through a shortcut. The other part is entered into the next step for deeper feature extraction through max pooling.

[0038] Step S502: After the downsampling part is completed, the upsampling part is entered. The upsampling part also has four steps. The input of each step is obtained by the feature map output by the previous module and the feature map cat output by the shortcut. Each step includes three parts: coordinate attention mechanism, feature fitting module and transposed convolution module.

[0039] Step S503: After upsampling, the result is passed through a 1×1 convolution layer to output the phase unwrapping result predicted by the network.

[0040] Step S504: Compare the phase unwrapping result predicted in step S503 with the true value, and calculate the loss feedback correction network parameters.

[0041] Step S505: Repeat the above steps until the predetermined number of rounds is reached to complete the training of the MFR-Net network.

[0042] Preferably, step S6 specifically includes:

[0043] The input phase map in the test set is denoted as input1. It is fed into the MFR-Net network trained in step S5 to obtain the phase unwrapping result of the network output, denoted as output_net1.

[0044] Preferably, step S7 specifically includes:

[0045] Smoothing and global mean filtering are performed on the output_net1 obtained in step S6. The result obtained is the final unwrapped result, denoted as output.

[0046] Compared with the prior art, the beneficial effects of the present invention are:

[0047] In practical digital holographic measurements, factors such as strong laser coherence, light scattering caused by rough surfaces of optical components, and external interference often introduce significant speckle and Gaussian noise into holograms, severely impacting the accuracy of subsequent reconstruction results. While traditional algorithms and conventional networks exhibit good phase unwrapping capabilities under low-noise conditions, they struggle to achieve accurate unwrapping results or even fail under strong noise conditions. Compared to traditional methods and conventional networks, this invention proposes an MFR-Net phase unwrapping network for strong noise conditions. First, the noisy wrapped phase is input into a multi-module filtering layer to obtain three wrapped phase filtering results. These are then concatenated with the original input phase and input into the later stages of the MFR-Net network. This provides more feature information after processing different levels of noise, reducing the training difficulty and improving the network's generalization ability. Second, this method adds multi-path dilated convolution and coordinate attention mechanisms to the ResUNet backbone network. By expanding the feature receptive field and capturing pixel correlation information in both horizontal and vertical directions, it enhances the network's ability to extract spatial features such as inter-pixel gradient information under strong noise, improving the network's noise handling capabilities. Finally, smoothing and mean filtering are used to post-process the phase results obtained by the network, improving the fitting error that occurs when the wrapped phase jumps from -π to π, and further enhancing the accuracy of unwrapping. Based on these advantages, the proposed method can obtain the correct unwrapped phase under strong noise conditions, which is of great significance for reproducing true phase information and improving the accuracy of holographic measurements. Attached Figure Description

[0048] Figure 1 This is a flowchart of an MFR-Net unwrapping method for strong noise-wrapped phase according to an embodiment of the present invention.

[0049] Figure 2 These are wrapper phase images containing different levels of strong noise, as described in an embodiment of the present invention.

[0050] Figure 3a This is an example dataset with a noise standard deviation of 1.0, as described in this embodiment of the invention.

[0051] Figure 3b This is an example dataset with a noise standard deviation of 1.4, as described in this embodiment of the invention.

[0052] Figure 3cThis is an example dataset with a noise standard deviation of 1.7, as described in this embodiment of the invention.

[0053] Figure 3d This is an example dataset with a noise standard deviation of 2.0, as described in this embodiment of the invention.

[0054] Figure 4 Embodiments of the present invention Figure 2 Image recognition of flat regions enclosed by σ = 1.0.

[0055] Figure 5 Embodiments of the present invention Figure 2 The filtered images of the image with σ = 1.0.

[0056] Figure 6 This is a schematic diagram of the MFR-Net network architecture according to an embodiment of the present invention.

[0057] Figure 7 Embodiments of the present invention Figure 3a , Figure 3b , Figure 3c , Figure 3d The corresponding unwrapping phase results. Detailed Implementation

[0058] The invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0059] Reference Figure 1 This invention discloses an MFR-Net unwrapping method for phase wrapped by strong noise, and the specific implementation steps are as follows:

[0060] Step S1 involves generating the original three-dimensional phase using the random matrix amplification method, which serves as a sample for the real phase dataset. Step S1 specifically includes:

[0061] Step S101: Generate multiple random matrices with a size between 5×5 pixels and 10×10 pixels and a random height distributed in the range of [0 rad, 40 rad].

[0062] Step S102: Use bilinear interpolation to enlarge the size of the random matrix generated in step S101 to 256×256 pixels as the noise-free object light wave phase, forming a real phase dataset sample φ.

[0063] Step S2 involves adding noise of different levels to the true phase to obtain a noisy phase, and then wrapping the phase to obtain a noisy wrapped phase dataset sample. Step S2 specifically includes:

[0064] Step S201: Add speckle noise of different levels and fixed Gaussian noise to the real phase dataset sample φ obtained in step S102 to obtain a noisy phase. The specific implementation process is as follows:

[0065] The noise in the holographic wrapper phase consists of two parts: speckle and additive noise. The speckle can be represented by multiplicative noise, and the object wave containing speckle noise can be represented as:

[0066] U′=Aexp[jφ][1+σn R exp(jn I (1)

[0067] In equation (1), A represents the amplitude of the noise-free object light wave, which is set to 1 here; φ represents the phase of the noise-free object light wave, i.e., the true phase obtained in step S102; σ represents the standard deviation of speckle noise, which determines the magnitude of the speckle noise level; n R and n I Let represent random Gaussian noise with a mean of 0 and a standard deviation of 1, and j represent the imaginary unit. Then, the object light wave containing speckle and additive noise can be expressed as:

[0068]

[0069] In equation (2), the additive noise N G The Gaussian noise with a mean of 0 and a standard deviation of 0.2 is used to divide the real phase dataset samples obtained in step S102 into 11 groups. Different levels of noise with σ of 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9 and 2.0 are added to each group to obtain the corresponding object light waves containing noise.

[0070] Step S202: Perform phase extraction on the noisy object light wave to obtain a noisy package phase dataset sample. The specific implementation process is as follows:

[0071]

[0072] In equation (3), Im represents the imaginary part extraction operation, and Re represents the real part extraction operation. By performing an arctangent operation on the ratio of the imaginary to real parts of the noisy object light wave, the noisy encapsulation phase can be obtained. Reference Figure 2 As shown, speckle noise and fixed additive noise with noise levels of σ=1.0, σ=1.4, σ=1.7, and σ=2.0 are added to the same phase. It can be seen that the noise becomes more and more severe as the noise level increases.

[0073] Step S3 involves using the noisy wrapped phase and the true phase as a pair of input and output to generate a dataset, which is then divided into a training set, a validation set, and a test set in a 18:1:1 ratio. Step S3 specifically includes:

[0074] The real phase dataset sample φ obtained in step S102 and the noisy wrapped phase dataset sample corresponding to step S202 are compared. The dataset is divided into training, validation, and test sets in a 18:1:1 ratio. (Some datasets are referenced from...) Figure 3a , Figure 3b , Figure 3c , Figure 3d As shown, input is the noisy wrapped phase, and gt is the corresponding true phase.

[0075] Step S4 involves inputting the training and validation sets obtained in step S3 into the multi-module filtering layer of the MFR-Net network to obtain the results of edge-preserving filtering and mean filtering, respectively. The average of the two filtering results is then calculated to obtain a double-filtered image. The original image, the edge-preserving filtered image, the mean-filtered image, and the double-filtered image are then stitched together to obtain a stitched image. Step S4 specifically includes:

[0076] Step S401, refer to Figure 6 The MFR-Net architecture takes noisy, phase-wrapped inputs from the training and validation sets and feeds them into the multi-module filtering layer of the MFR-Net network. It defines the portion of the input that transitions from -π to π as a boundary region, and the remaining portion as a flat region. Flat region identification is then performed on the input. Figure 4 As shown, the specific method for identifying flat regions is as follows:

[0077] like Figure 4 As shown in (a), the values ​​in the noisy wrapped phase input are... The part within is labeled as -π, and the value is in The part inside is marked as 0, and the value is in The part inside is labeled as π, and the resulting image is called a three-level graph.

[0078] The obtained three-level image is denoised. For pixels with the same eight neighboring pixel values, the pixel values ​​of the surrounding pixels are assigned to that pixel.

[0079] Using a 5x5 window, the denoised three-level image is traversed. If the difference between the number of π and -π pixels in the window is less than 5, the center point of the window is identified as a boundary point. Simultaneously, the eight neighboring pixels of this boundary point are also identified as boundary points. The set of all boundary points constitutes the boundary region. The result is as follows... Figure 4As shown in (b), the black part is the identified flat area, and the white part is the identified boundary area;

[0080] Step S402, will Figure 5 (a) Using the input as an example operation object, a 3×3 window is used to traverse the input, and the variance of the nine data points within the window is calculated as the variance value of the window center point. The average variance values ​​of the flat points identified in step S401 are taken, and the corresponding mean value is the noise level of the input;

[0081] Step S403: In the flat region of the input, points with variance values ​​greater than the input noise level are subjected to bilateral filtering, while those with lower variance values ​​are subjected to mean filtering. In the boundary region of the input, the variance value of each boundary point is compared with the variance values ​​of its eight neighboring pixels. The smallest variance value is taken as the variance value of the center boundary point, and then bilateral filtering is applied to that point. The specific parameters of the bilateral filtering are: the spatial variance parameter is twice the radius of the filtering traversal box, which is 4; the pixel variance parameter is four times the variance of that point. This filtering operation preserves the edge portion surrounding the phase transition point well, so the image obtained after the above filtering operation is called the edge-preserving filtered image, denoted as input_bm, such as... Figure 5 As shown in (b);

[0082] Step S404: Apply mean filtering to the entire input. Mean filtering effectively smooths out fluctuations caused by noise, which is beneficial for noise removal in flat areas of the input. The image obtained after this operation is called the mean-filtered image, denoted as input_m. Figure 5 As shown in (c).

[0083] Step S405: Edge-preserving filtering, due to the lack of smoothing effect in the flat region with large gradients in the input using bilateral filtering, and mean filtering also failing to preserve the boundary portion well, reduces the errors caused by the two filtering methods in different regions. The input_bm and input_m obtained in steps S403 and S404 are averaged. The filtered image after this operation is called the double-filtered image, denoted as input_bmam. Figure 5 As shown in (d).

[0084] Step S406: The input graph input, the edge-preserving filtered graph input_bm, the mean-filtered graph input_m, and the double-filtered graph input_bmam are concatenated using the cat (concate) operation, and their size is converted into a tensor form of 1×4×256×256, denoted as input_cat.

[0085] Step S5: Input the stitched image obtained in step S4 into the back-end network of MFR-Net for training, to obtain the trained MFR-Net network; Step S5 specifically includes:

[0086] Step S501: Input_cat obtained in step S406 is input into the downsampling part of the MFR-Net back-end network. The downsampling part consists of four steps, each including a feature extraction module and a max pooling module, as described in detail below:

[0087] Each step begins with the feature extraction module, referring to... Figure 6 (b) The feature extraction module consists of 5 layers. The first layer directly adds the results from other layers to a 1×1 convolution (Conv) and batch normalization (BN), forming a shortcut. The other four layers extract features using dilated convolution layers (Convd) of different sizes, BN, and Rectified Linear Unit (ReLU). Finally, the resulting feature maps are cated and added to the first layer. This feature extraction module takes a feature map tensor of size B×C×H×W as input and outputs a feature map tensor of size B×C1×H×W. Here, B is the batch size, which is set to 16 in this paper; C and C1 are the number of channels, and the values ​​for all channel numbers are shown in [reference]. Figure 6 (a) Parameters under each Bk module; H and W are image dimensions;

[0088] The feature map obtained by the feature extraction module is divided into two parts: one part is sent directly to the upsampling part of the network through a shortcut, and the other part is sent to the max pooling module.

[0089] Reference Figure 6 (a) The max pooling module transforms an input tensor of size B×C1×H×W into an output tensor of size B×C1×H / 2×W / 2 through max pooling operations. The feature map processed by the max pooling module is the output.

[0090] Step S502: The feature map obtained in step S501 is fed into the upsampling part. The upsampling part of the network also consists of four steps. Each input is obtained by the feature map output by the previous module and the feature map cat output by the shortcut. Each step consists of three parts: coordinate attention mechanism, feature fitting module and transposed convolution module, which are described in detail below:

[0091] First, the input is fed into the coordinate attention mechanism, which extracts the spatial position information of each point, as well as the spatial features between it and the other pixels in the horizontal and vertical directions, and outputs it into the feature fitting module.

[0092] The feature fitting module is the same as the downsampling feature extraction module, performing result fitting on the input feature map tensor through five different operations. The input feature map tensor of size B×C2×H×W is converted into an output feature map tensor of size B×C3×H×W, which is then fed into the transposed convolution module.

[0093] The transposed convolution module is essentially the inverse process of convolution, used to restore the image size. This step takes a feature map tensor of size B×C3×H×W as input and outputs a feature map tensor of size B×C3×2H×2W. The feature map obtained after passing through the transposed convolution module is the output.

[0094] Step S503: The feature map obtained in step S502 is processed by a 1×1 convolution, and the output is used as the phase unwrapping result predicted by the network, denoted as output_net;

[0095] Step S504: Compare the output_net obtained in step S503 with the true phase, calculate the loss using the mean squared error (MSE), and update the network parameters using the Adam optimizer. The mathematical expression for the mean squared error (MSE) is:

[0096]

[0097] In equation (4), x is the output_net obtained in step S503; y is the true phase; m and n are the number of pixels in the horizontal and vertical directions of image x, respectively; i and j represent the rows and columns in the image matrix, respectively.

[0098] Step S505: Repeat the above steps until the predetermined number of rounds is reached to complete the training process of MFR-Net.

[0099] Step S6 involves inputting the test set into the MFR-Net network trained in step S5 to obtain the unwrapping result output by the network. Step S6 specifically includes:

[0100] The test set is used as the test data for this phase unwrapping algorithm. The noisy wrapped phase map in the test set is denoted as input1 and input into MFR-Net for processing. The phase unwrapping result output by the network is denoted as output_net1.

[0101] Step S7 involves smoothing and mean filtering the unwrapped results obtained in step S6 to obtain the final unwrapped results for the test set. Step S7 specifically includes:

[0102] Step S7: Perform smoothing and mean filtering on the output_net1 obtained in step S6 to obtain the final unwrapped result after post-processing, denoted as output. Figure 7 This demonstrates the algorithm's effectiveness. Figure 3a , Figure 3b , Figure 3c , Figure 3d The unwrapping result of the noisy wrapped phase. After the above 7 steps, the MFR-Net unwrapping method for strongly noisy wrapped phase proposed in this invention can be obtained.

Claims

1. A method for unwrapping MFR-Net phases wrapped in strong noise, characterized in that, Includes the following steps: Step S1: Generate the original three-dimensional phase using the random matrix amplification method, which serves as a sample of the real phase dataset. Step S2: Add noise of different levels to the real phase to obtain a noisy phase, and perform a wrapping operation on the phase to obtain a noisy wrapped phase dataset sample. Step S3: The noisy wrapped phase and the true phase are used as a pair of input and output to generate a dataset, which is divided into training set, validation set and test set in a ratio of 18:1:

1. Step S4: Input the training set and validation set obtained in step S3 into the multi-module filtering layer of the MFR-Net network to obtain the results of edge-preserving filtering and mean filtering respectively. Then, calculate the average of the two filtering results to obtain a double-filtered image. Finally, stitch the original image, the edge-preserving filtered image, the mean-filtered image, and the double-filtered image together to obtain a stitched image. Step S5: Input the stitched image obtained in step S4 into the back-end network of MFR-Net for training, and obtain the trained MFR-Net network. Step S6: Input the test set into the MFR-Net network trained in step S5 to obtain the unwrapping result output by the network. Step S7: Perform smoothing and mean filtering on the unwrapping results obtained in step S6 to obtain the final unwrapping results of the test set.

2. The MFR-Net unwrapping method for strong noise-wrapped phases according to claim 1, characterized in that, Step S1 specifically includes: Step S101: Generate multiple random matrices with a size between 5×5 pixels and 10×10 pixels and a random height distributed in the range of [0 rad, 40 rad]. Step S102: The random matrix generated in step S101 is enlarged to 256×256 pixels using bilinear interpolation to form the noise-free object light wave field phase, thus constituting a sample of the real phase dataset. .

3. The MFR-Net unwrapping method for strong noise-wrapped phases according to claim 2, characterized in that, Step S2 specifically includes: Step S201, feed the real phase dataset samples obtained in step S102. Different levels of speckle noise and fixed Gaussian noise are added to obtain a noisy phase. The specific implementation process is as follows: The noise in the holographic wrapper phase consists of two parts: speckle and additive noise. The speckle is represented by multiplicative noise, and the object wave containing speckle noise can be represented as: （1）； In equation (1), This represents the amplitude of a noise-free object's light wave; here, let... ; This represents the phase of the noise-free object light wave, i.e., the true phase obtained in step S102; The standard deviation of the speckle noise represents the magnitude of the speckle noise level. and Let represent random Gaussian noise with a mean of 0 and a standard deviation of 1, and j represent the imaginary unit. Then, the object light wave containing speckle and additive noise can be expressed as: （2）； Additive noise in equation (2) This represents Gaussian noise with a mean of 0 and a standard deviation of 0.

2. The real phase dataset samples obtained in step S102 are divided into 11 groups, and each group is added with... For different noise levels of 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9 and 2.0, corresponding object light waves containing noise were obtained; Step S202: Perform phase extraction on the noisy object light wave to obtain a noisy package phase dataset sample. The specific implementation process is as follows: （3）； In equation (3), Im represents the imaginary part operation and Re represents the real part operation.

4. The MFR-Net unwrapping method for strong noise-wrapped phases according to claim 3, characterized in that, Step S3 specifically includes: The real phase dataset sample obtained in step S102 Noisy packaged phase dataset samples corresponding to step S202 As a dataset, it is divided into training set, validation set and test set in a ratio of 18:1:

1.

5. The MFR-Net unwrapping method for strong noise-wrapped phases according to claim 1, characterized in that, Step S4 specifically includes: Step S401: The noise-wrapped phases in the training and validation sets are recorded as input and fed into the multi-module filtering layer of the MFR-Net network to filter out the noise-wrapped phases in the input. Jump to The part is defined as the boundary region, and the rest is defined as the flat region. Flat region identification is performed on the input. Step S402: Use a 3×3 traversal box to calculate the variance of each point in the input, and use the variance of the flat area obtained in step S401 to determine the noise level, thereby obtaining the noise level of the input wrapping phase input. Step S403: For the flat region identified by input in step S401, if the variance value is greater than the noise level of input, the area near the point is considered to be a steep gradient range similar to a boundary, and adaptive bilateral filtering is applied to the point to preserve its gradient information; if the variance value is less than the noise level, the area near the point is considered to be a flat gradient range, and mean filtering is applied to the point to eliminate the influence of noise; for the identified non-flat region, adaptive bilateral filtering is used to denoise based on the variance value corresponding to each point. The filtered image obtained after the above operations is called the edge-preserving filter image, denoised as input_bm; Step S404: For the input wrapping phase input, global mean filtering is applied, and the resulting filtered image is called the mean filtered image, denoted as input_m; Step S405: Calculate the average of input_bm obtained in step S403 and input_m obtained in step S404. The resulting filtered image is called the double-filtered image and is denoted as input_bmam. Step S406: Perform a concatenation operation cat on the input graph input, the edge-preserving filtered graph input_bm, the mean-filtered graph input_m, and the double-filtered graph input_bmam, and convert it into tensor form, denoted as input_cat.

6. The MFR-Net unwrapping method for strong noise-wrapped phases according to claim 5, characterized in that, Step S5 specifically includes: Step S501: Input the input_cat obtained in step S406 into the downsampling part of the back-end network of MFR-Net. The downsampling part includes four steps. Each step goes through a feature extraction module composed of multiple dilated convolutions. The extracted feature map is divided into two parts. One part is sent directly to the upsampling part of the network through a shortcut. The other part is entered into the next step for deeper feature extraction through max pooling. Step S502: After the downsampling part is completed, the upsampling part is entered. The upsampling part also has four steps. The input of each step is obtained by the feature map output by the previous module and the feature map cat output by the shortcut. Each step includes three parts: coordinate attention mechanism, feature fitting module and transposed convolution module. Step S503: After upsampling, the result is passed through a 1×1 convolution layer to output the phase unwrapping result predicted by the network. Step S504: Compare the phase unwrapping result predicted in step S503 with the true value, and calculate the loss feedback correction network parameters. Step S505: Repeat the above steps until the predetermined number of rounds is reached to complete the training of the MFR-Net network.

7. The MFR-Net unwrapping method for strong noise-wrapped phases according to claim 6, characterized in that, Step S6 specifically includes: The input phase map in the test set is denoted as input1. It is fed into the MFR-Net network trained in step S5 to obtain the phase unwrapping result of the network output, denoted as output_net1.

8. The MFR-Net unwrapping method for strong noise-wrapped phases according to claim 7, characterized in that, Step S7 specifically includes: Smoothing and global mean filtering are performed on the output_net1 obtained in step S6. The result obtained is the final unwrapped result, denoted as output.

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