Hologram watermarking method and system

Abstract

The application belongs to the technical field of digital watermarking, and particularly relates to a hologram watermark processing method and system, aiming to solve the problem of hologram watermark technology which can meet the requirements of complex structure adaptability and robustness at the same time. The method comprises the following steps: converting an original hologram into a standardized holographic feature map; performing convolution on the real part and the imaginary part of the watermark to obtain a watermark feature map; splicing the standardized holographic feature map after a composite convolution layer with the watermark feature map, and then performing jump connection with the standardized holographic feature map; then compressing the channel number to 3, and performing linear projection reduction to obtain a watermark hologram, wherein the first layer of the composite convolution layer is an isovariant complex convolution, the second layer is a complex batch normalization, the third layer is a generalized tangent ReLU, and no bias parameter is introduced in the isovariant complex convolution. The hologram watermark processing method and system provided by the application significantly improve the adaptability, robustness and extraction accuracy of the hologram watermark.

Description

Technical Field

[0001] This invention belongs to the field of digital watermarking technology, specifically relating to a holographic watermarking processing method and system. Background Technology

[0002] With the rapid development of emerging applications such as holographic communication, remote medical diagnosis, and holographic video live streaming, the large-scale sharing and distribution of digital holograms has become commonplace. In this process, holographic data faces severe security threats, including unauthorized theft, malicious tampering, illegal forgery, and unauthorized copying. At the same time, in scenarios such as copyright dispute resolution and data liability determination, the need for reliable traceability of holographic data and confirmation of copyright ownership is becoming increasingly urgent. Building a security protection system adapted to holograms has become an industry consensus.

[0003] In existing technologies, digital rights management mechanisms and traditional encryption technologies are commonly used means of content protection. However, these technologies are mainly designed for conventional real-number domain data, while holograms have a typical complex structure. Their data includes a real part (corresponding to light field intensity-related information) and an imaginary part (corresponding to light field phase-related information). Furthermore, they need to meet complex physical constraints during transmission, storage, and optical display, making it difficult for traditional DRM and encryption technologies to be directly adapted and unable to provide effective security for holographic data.

[0004] Digital watermarking technology, due to its "imperceptible" characteristic, has become the mainstream technical approach for image copyright protection and security. For the protection of holograms, embedding digital watermarks into holograms is currently recognized as an effective technical direction. Existing research results mainly focus on the following two types of technical solutions:

[0005] The first type is the phase embedding-based watermarking method. This method embeds the watermark information only into the phase component of the hologram, while keeping the amplitude component unchanged, thereby minimizing the impact of watermark embedding on the visual quality of the reconstructed hologram. However, phase information is a core element of holographic optical reconstruction and is extremely sensitive to external interference. Any removal or alteration of the watermark will directly lead to phase distribution disorder, resulting in a drastic decrease in the quality of the reconstructed image. At the same time, this method has weak resistance to common interferences such as channel noise and compression distortion during transmission, and its robustness in practical applications is difficult to meet the requirements.

[0006] The second category is watermarking methods based on conventional real-number convolutional neural networks. This method borrows from the mature architecture of natural image watermarking, constructing a core model of "encoder-generalized decoder" and introducing a discriminator for adversarial training to optimize the imperceptibility and embedding stability of the watermark. Although this method improves the robustness of the watermark to some extent, it is still essentially based on a real-number operational architecture, which cannot fully accommodate the complex domain structure of holograms. When dealing with specific attacks targeting the complex domain (such as phase shifting and complex amplitude scaling), it struggles to effectively extract and process the complex coupling information of the holographic data, resulting in limited protection and failing to meet the deep security requirements of holograms.

[0007] In summary, existing holographic watermarking technologies all have significant limitations. How to simultaneously meet the requirements of complex structure adaptability and robustness of holographic watermarking and construct a watermarking protection technology that adapts to the characteristics of holograms has become an urgent technical problem to be solved. Summary of the Invention

[0008] To address the aforementioned technical problems in the prior art, namely how to achieve holographic watermarking technology that simultaneously satisfies the requirements of complex structure adaptability and robustness, this application provides a holographic watermarking processing method and system.

[0009] In a first aspect of this application, a holographic watermarking processing method is provided, comprising:

[0010] The original hologram is converted into a 3×p×q tensor. The real part Hr and the imaginary part Hi of the tensor are convolved using an n×n complex convolution kernel to obtain the real part Hjr and the imaginary part Hji. Here, 3 is the set number of channels, p×q is the resolution of the original hologram, and n is a preset value.

[0011] Normalize the real part Hjr and the imaginary part Hji respectively to obtain the standardized holographic feature map;

[0012] The real part Mr and the imaginary part Mi of the watermark are convolved by three consecutive 3×3 real number convolution layers to obtain the watermark feature map. The watermark is a binary complex watermark with a length of L.

[0013] The standardized holographic feature map is input into s consecutive 3×3 composite convolutional layers to obtain a multiconvolutional holographic feature map. The first layer of the composite convolutional layer is an equivariant multiconvolution, the second layer is a complex-valued batch normalization, and the third layer is a generalized tangent ReLU. No bias parameter is introduced in the equivariant multiconvolution, where s is preset.

[0014] The watermark feature map and the multiconvoluted holographic feature map are spliced ​​together to obtain the spliced ​​feature map;

[0015] The spliced ​​feature map is spliced ​​with the standardized holographic feature map to obtain a skip connection feature map;

[0016] The number of channels in the skip connection feature map is compressed to 3, and the compressed skip connection feature map is linearly projected back to obtain a watermark hologram.

[0017] Optionally, the number of channels in the skip connection feature map can be compressed to 3 using m consecutive 3×3 composite convolutional layers, where m is determined based on the resolution of the original hologram.

[0018] Optionally, the holographic watermarking method further includes extracting the watermark from the watermark hologram using a generalized decoder. The extraction of the watermark from the watermark hologram using a generalized decoder includes:

[0019] The watermark hologram is set as the complex optical field at the source plane, and a two-dimensional Fourier transform is performed on the complex optical field to obtain the corresponding frequency domain optical field.

[0020] Based on the frequency domain light field, the preset visible light wavelength and the target propagation distance, the angular spectral transfer function is calculated. The angular spectral transfer function is used to characterize the phase accumulation characteristics of each spatial frequency component of the watermark hologram under the conditions of the visible light wavelength and the target propagation distance.

[0021] The frequency domain optical field is multiplied by the angular spectral transfer function, and the result of the multiplication is subjected to a two-dimensional inverse Fourier transform to transform the result of the multiplication to the spatial domain, thereby obtaining a watermarked reconstructed hologram.

[0022] Optionally, the step of using a generalized decoder to extract the watermark from the watermark hologram further includes:

[0023] An attack simulation is performed on the watermarked reconstructed hologram, the attack including Cropout, Dropout, rotation, JPEG compression and / or Gaussian blur, to obtain an attack simulation hologram.

[0024] Optionally, the step of using a generalized decoder to extract the watermark from the watermark hologram further includes:

[0025] The attack simulation hologram is extracted with r consecutive 1×1 convolution kernels to extract complex numerical features, and the attack simulation hologram is restored to a 3×p×q complex feature map. The lengths of the real and imaginary parts of the complex feature map are extended to L / 2 respectively to obtain an extended complex feature map, where r is preset.

[0026] The extended complex feature map is subjected to complex average pooling for dimensionality reduction to obtain a real part watermark feature map and an imaginary part watermark feature map, wherein the real part watermark feature map and the imaginary part watermark feature map are L / 2×1×1 respectively;

[0027] The real part watermark feature map and the imaginary part watermark feature map are mapped to real part watermark vector and imaginary part watermark vector respectively using linear mapping, and the length of the real part watermark vector and the imaginary part watermark vector is L / 2.

[0028] The real and imaginary watermark vectors are normalized and phase-adjusted using a division layer (DIV) to obtain the real part Mr' and imaginary part Mi' of the decoded watermark, and the corresponding decoded watermark is obtained. The division layer (DIV) uses the global average complex value as the scale factor.

[0029] Calculate the similarity between the decoded watermark and the watermark. If the similarity is greater than a preset first threshold, the watermark extraction is determined to be accurate.

[0030] Optionally, the holographic watermarking method further includes:

[0031] The decoded watermark is obtained by extracting the watermark from the N watermark holograms using the generalized decoder. The accuracy of watermark extraction is calculated as R=S1 / N based on the similarity, where S1 is the number of similarities greater than or equal to the first threshold. The watermarks corresponding to the N watermark holograms are all randomly generated and have the same length.

[0032] If the accuracy is less than a preset second threshold, the parameters of the generalized decoder are adjusted until the accuracy is greater than or equal to the second threshold.

[0033] In a second aspect of this application, a holographic watermarking system is provided, the system comprising an encoder, the encoder being used for:

[0034] The original hologram is converted into a 3×p×q tensor. The real part Hr and the imaginary part Hi of the tensor are convolved by an n×n complex convolution kernel to obtain the real part Hjr and the imaginary part Hji. Here, 3 is the set number of channels, p×q is the resolution of the original hologram, and n is a preset value.

[0035] Normalize the real part Hjr and the imaginary part Hji respectively to obtain the standardized holographic feature map;

[0036] The real part Mr and the imaginary part Mi of the watermark are convolved by three consecutive 3×3 real number convolution layers to obtain the watermark feature map. The watermark is a binary complex watermark with a length of L.

[0037] The standardized holographic feature map is input into s consecutive 3×3 composite convolutional layers to obtain a multiconvolutional holographic feature map. The first layer of the composite convolutional layer is an equivariant multiconvolution, the second layer is a complex-valued batch normalization, and the third layer is a generalized tangent ReLU. No bias parameter is introduced in the equivariant multiconvolution, where s is preset.

[0038] The watermark feature map and the multiconvoluted holographic feature map are spliced ​​together to obtain the spliced ​​feature map;

[0039] The spliced ​​feature map is spliced ​​with the standardized holographic feature map to obtain a skip connection feature map;

[0040] The number of channels in the skip connection feature map is compressed to 3, and the compressed skip connection feature map is linearly projected back to obtain a watermark hologram.

[0041] Optionally, the encoder uses m consecutive 3×3 composite convolutional layers to compress the number of channels in the skip connection feature map to 3, where m is determined according to the resolution of the original hologram.

[0042] Optionally, the holographic watermarking processing system further includes a generalized decoder, which is used to extract the watermark from the watermark hologram. Specifically, the generalized decoder is used for:

[0043] The watermark hologram is set as the complex optical field at the source plane, and a two-dimensional Fourier transform is performed on the complex optical field to obtain the corresponding frequency domain optical field.

[0044] Based on the frequency domain light field, the preset visible light wavelength and the target propagation distance, the angular spectral transfer function is calculated. The angular spectral transfer function is used to characterize the phase accumulation characteristics of each spatial frequency component of the watermark hologram under the conditions of the visible light wavelength and the target propagation distance.

[0045] The frequency domain optical field is multiplied by the angular spectral transfer function, and the result of the multiplication is subjected to a two-dimensional inverse Fourier transform to transform the result of the multiplication to the spatial domain, thereby obtaining a watermarked reconstructed hologram.

[0046] Optionally, the generalized decoder is further used for:

[0047] An attack simulation is performed on the watermarked reconstructed hologram, the attack including Cropout, Dropout, rotation, JPEG compression and / or Gaussian blur, to obtain an attack simulation hologram.

[0048] Optionally, the generalized decoder is further used for:

[0049] The attack simulation hologram is extracted with r consecutive 1×1 convolution kernels to extract complex numerical features, and the attack simulation hologram is restored to a 3×p×q complex feature map. The lengths of the real and imaginary parts of the complex feature map are extended to L / 2 respectively to obtain an extended complex feature map, where r is preset.

[0050] The extended complex feature map is subjected to complex average pooling for dimensionality reduction to obtain a real part watermark feature map and an imaginary part watermark feature map, wherein the real part watermark feature map and the imaginary part watermark feature map are L / 2×1×1 respectively;

[0051] The real part watermark feature map and the imaginary part watermark feature map are mapped to real part watermark vector and imaginary part watermark vector respectively using linear mapping, and the length of the real part watermark vector and the imaginary part watermark vector is L / 2.

[0052] The real and imaginary watermark vectors are normalized and phase-adjusted using a division layer to obtain the real watermark Mr' and imaginary watermark Mi', and the corresponding decoded watermark is obtained. The DIV layer uses the global average complex value as the scale factor.

[0053] Calculate the similarity between the decoded watermark and the watermark. If the similarity is greater than a preset first threshold, the watermark extraction is determined to be accurate.

[0054] Optionally, the holographic watermarking processing system further includes an optimization unit, which is used for:

[0055] The decoded watermark is obtained by extracting the watermark from the N watermark holograms using the generalized decoder. The accuracy of watermark extraction is calculated as R=S1 / N based on the similarity, where S1 is the number of similarities greater than or equal to the first threshold. The watermarks corresponding to the N watermark holograms are all randomly generated and have the same length.

[0056] If the accuracy is less than a preset second threshold, the parameters of the generalized decoder are adjusted until the accuracy is greater than or equal to the second threshold.

[0057] In a third aspect of this application, an electronic device is provided, comprising:

[0058] At least one processor; and

[0059] A memory communicatively connected to at least one of the processors; wherein,

[0060] The memory stores instructions that can be executed by the processor to implement the holographic watermarking method described above.

[0061] In a fourth aspect of this application, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions for execution by the computer to implement the above-described holographic watermarking processing method.

[0062] In a fifth aspect of this application, a computer program product comprising instructions is provided, which, when executed by a computer device, cause the computer device to perform the holographic watermarking processing method described above.

[0063] The holographic watermarking method and system provided in this application significantly improve the adaptability, robustness, and extraction accuracy of watermarks, taking into account the complex characteristics of holograms. This application employs a complex convolutional network to perform the watermark embedding and extraction process. By deeply mining the inherent correlations of the complex features of holograms, the watermark information can be more stably fused with holographic data, fundamentally improving the poor adaptability of existing real convolutional architectures and significantly enhancing the robustness of watermarked holograms and the accuracy of watermark extraction. By removing the bias term in conventional complex convolutions, the holographic feature map can maintain geometric equivariance even when subjected to complex scaling attacks, providing a stable foundation for subsequent feature restoration and demonstrating significant robustness advantages. Simultaneously, the removal of the bias term reduces network redundancy parameters without sacrificing watermark performance, lowering memory usage and inference time, enabling real-time watermarking processing even on resource-constrained holographic terminals. Furthermore, this application introduces the angular spectrum method as a reconstruction module between the encoder and the generalized decoder, and incorporates it into the training process. This addresses the pain points of conventional real-valued convolutional watermarking methods, such as holographic quality degradation and watermark extraction failure after reconstruction. While ensuring visual quality, it further improves watermark extraction accuracy. Moreover, the overall architecture adopts a modular design, supporting holographic inputs of different resolutions without requiring additional parameter tuning for various attack scenarios. The end-to-end training mode significantly reduces the computational overhead and operational complexity of watermark embedding and extraction, effectively reducing system deployment and maintenance costs. In summary, the holographic watermarking processing method and system provided in this application fill the current gap in complex convolutional watermarking technology targeting the coupling characteristics of holograms. It exhibits extremely high robustness while balancing holographic quality, processing efficiency, and deployment flexibility, and has broad application prospects in the field of holographic security protection. Attached Figure Description

[0064] Figure 1 This is a flowchart illustrating one embodiment of the holographic watermarking method of this application;

[0065] Figure 2 This is a flowchart illustrating another implementation of the holographic watermarking method of this application;

[0066] Figure 3aThis is a flowchart illustrating one embodiment of step S208 in another implementation of the holographic watermarking method of this application.

[0067] Figure 3b This is a flowchart illustrating another implementation of step S208 in another embodiment of the holographic watermarking processing method of this application.

[0068] Figure 3c This is a flowchart illustrating yet another embodiment of step S208 in another implementation of the holographic watermarking method of this application.

[0069] Figure 3d This is a flowchart illustrating yet another embodiment of step S208 in another implementation of the holographic watermarking method of this application.

[0070] Figure 4 This is a structural block diagram of one embodiment of the holographic watermarking processing system of this application;

[0071] Figure 5 This is a structural block diagram of another embodiment of the holographic watermarking processing system of this application;

[0072] Figure 6 This is a structural block diagram of another embodiment of the holographic watermarking processing system of this application. Detailed Implementation

[0073] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description, in conjunction with the accompanying drawings and examples, further clarifies this application. It should be understood that the specific examples described herein are merely illustrative and not intended to limit the scope of this application. Furthermore, the technical features involved in the various embodiments of this application described below can be combined with each other as long as they do not conflict with each other.

[0074] The present application will now be described in detail with reference to the accompanying drawings. A first aspect of this application provides a holographic watermarking method. Figure 1 The diagram illustrates a flowchart of one embodiment of the holographic watermarking method of this application. Figure 1 As shown, the holographic watermarking processing method of the first embodiment of this application includes:

[0075] Step S101: Convert the original hologram into a 3×p×q tensor, and perform complex convolution on the real part Hr and the imaginary part Hi of the tensor using an n×n complex convolution kernel to obtain the real part Hjr and the imaginary part Hji, where p×q is the resolution of the original hologram, 3 is the set number of channels, and n is a preset value.

[0076] Step S102: Normalize the real part Hjr and the imaginary part Hji respectively to obtain the standardized holographic feature map;

[0077] Step S103: Convolve the real part Mr and the imaginary part Mi of the watermark using three consecutive 3×3 real number convolution layers to obtain the watermark feature map. The watermark is a binary complex watermark with a length of L.

[0078] Step S104: Input the standardized holographic feature map into s consecutive 3×3 composite convolutional layers to obtain a complex convolutional holographic feature map. The first layer of the composite convolutional layer is an equivariant complex convolution, the second layer is a complex-valued batch normalization, and the third layer is a generalized tangent ReLU. No bias parameter is introduced in the equivariant complex convolution. The value of s is determined by multiple experiments and the value with the best effect in the experiment is selected. The preferred value of s is 4.

[0079] Step S105: The watermark feature map and the multi-convoluted holographic feature map are spliced ​​together to obtain a spliced ​​feature map;

[0080] Step S106: The stitched feature map is stitched together with the standardized holographic feature map to obtain a skip connection feature map;

[0081] Step S107: Compress the number of channels in the skip connection feature map to 3, and perform linear projection restoration on the compressed skip connection feature map to obtain a watermark hologram.

[0082] Specifically, in step S101, the hologram is preprocessed. Specifically, based on the RGB (R for red, G for green, B for blue) 3-channel image, the number of channels is set to 3, and the original hologram with a resolution of p×q is converted into a 3×p×q tensor to match the convolution operation, while preserving the original resolution characteristics of the hologram. The tensor includes a real part and an imaginary part. For example, if the original hologram resolution is 384×384, it is converted into a 3×384×384 tensor; if the original hologram resolution is 1920×1080, it is converted into a 3×1920×1080 tensor. The tensor is transformed; then, the real and imaginary parts of the transformed tensor are subjected to complex convolution with an n×n complex convolution kernel, respectively. This process extracts features from the original hologram while avoiding disrupting the coupling between the real and imaginary parts of the original hologram, resulting in the complex convolutioned real part Hjr and imaginary part Hji. The size n of the complex convolution kernel is preset and can be selected empirically to achieve better convolution results. For example, n can be 3 for a resolution of 384×384 and 5 for a resolution of 1920×1080. The above complex convolution can be calculated using conventional complex convolution, so it will not be elaborated further.

[0083] Specifically, in step S102, the real part Hjr and the imaginary part Hji are normalized. When there is only one input original hologram, the normalization has little effect on the real part Hjr and the imaginary part Hji. When there are multiple input original holograms, i.e., when watermarking is performed on multiple original holograms, in step S102, normalization parameters are calculated based on the multiple real parts Hjr and imaginary parts Hji corresponding to the multiple original holograms. Then, the real part Hjr and the imaginary part Hji corresponding to each original hologram are normalized to eliminate the difference in magnitude between different original holograms. It should be noted that when there are multiple input original holograms, each original hologram has the same resolution, and the normalization can use a conventional normalization algorithm. After normalization in step S102, a standardized holographic feature map is obtained, which is represented as a 3×p×q tensor.

[0084] Specifically, in step S103, the watermark is set as a binary complex watermark with a length of L. The real part Mr and the imaginary part Mi of the watermark each have a length of L / 2. Both the real part Mr and the imaginary part Mi are randomly generated binary vectors (taking values ​​of 0 or 1), which are combined to form the binary complex watermark to ensure the independence and security of the watermark information. The length of the watermark can be set according to the resolution of the original hologram. Higher resolutions require longer watermarks to adapt to high-resolution scenarios. For example, if the original hologram resolution is 384×384, the watermark can be 60 bits, with the real part Mr and the imaginary part Mi each having 30 bits. If the original hologram resolution is 1920×1080, the watermark can be 100 bits, with the real part Mr and the imaginary part Mi each having 50 bits. It should be noted that when there are multiple input original holograms, the watermarks of all original holograms are randomly generated and have the same number of bits (same length).

[0085] Specifically, in step S103, the real part Mr and imaginary part Mi of the watermark are convolved using three consecutive 3×3 real convolutional layers to expand the vector dimensions of the real part Mr and the imaginary part Mi, thus obtaining the watermark feature map. This can be calculated using conventional real convolutional layers, so it will not be elaborated further. For example, the watermark feature map obtained after convolving the binary complex watermark with three consecutive 3×3 real convolutional layers can be represented as a tensor of size L / 2×p×q. For instance, if the watermark length is 60, the watermark feature map can be represented as a tensor of size 30×p×q. By performing real convolutions on the real and imaginary parts respectively, a watermark feature map aligned with the resolution of the original hologram can be obtained.

[0086] Specifically, in step S104, s consecutive custom-designed composite convolutional layers are used to perform convolution calculations on the standardized holographic feature map to obtain a multiconvolutional holographic feature map. The custom-designed composite convolutional layers are 3×3 layer structures, comprising three layers: the first layer is an equivariant complex convolution to ensure that the extracted features have initial adaptability to potential complex scaling attacks, and the equivariant complex convolution has no bias term, i.e., it does not introduce bias parameters, thus preserving the equivariance to cope with C-scaling attacks; the equivariant complex convolution is the core of feature extraction in the composite convolutional layer; the second layer is complex batch normalization, i.e., batch normalization of complex values, to stabilize the numerical distribution of features; the third layer is generalized tangent ReLU (GtReLU) to avoid the separation of the real and imaginary parts of complex values ​​by traditional activation functions, preserving key coupling information. The value of s is determined through multiple experiments, and is preferably 4. For example, a complex holographic feature map can be represented as a tensor of 64×p×q.

[0087] Specifically, in step S105, the watermark feature map and the multiconvolutional holographic feature map are spliced ​​along the channel dimension to obtain a spliced ​​feature map. For example, the watermark feature map is 30×p×q, the multiconvolutional holographic feature map is 64×p×q, and after splicing, the spliced ​​feature map is 94×p×q.

[0088] Specifically, in step S106, a skip connection is introduced, and then the stitched feature map and the standardized holographic feature map are stitched together along the channel dimension to obtain a skip connection feature map. For example, the stitched feature map is 94×p×q, the standardized holographic feature map is 3×p×q, and after stitching, the skip connection feature map is 97×384×384. This connection maps the features of the standardized holographic feature map to the stitched feature map, reducing the damage to the original details of the hologram caused by watermark embedding and ensuring visual quality.

[0089] Specifically, in step S107, m consecutive 3×3 composite convolutional layers (i.e., the first layer is an isovariant complex convolution, the second layer is a complex batch normalization, and the third layer is a generalized tangent ReLU composite convolutional layer) can be used to compress the number of channels of the skip connection feature map to a set number of channels, i.e., 3, so that the channel dimension is restored to the same level as the original hologram. Figure 1The compressed skip connection feature map is then linearly projected back to obtain the watermark hologram, thus completing the watermark embedding of the hologram. Here, m is determined based on the resolution of the original hologram, and m can be a commonly used value when compressing images of different resolutions. Since the number of channels is determined by the RGB three primary color channels, linear projection can be used for restoration to the three primary color channels to obtain the watermark hologram. The linear projection can use a conventional linear projection algorithm for restoration.

[0090] It should be noted that the watermark embedding is performed on the original hologram of each input. Except for step S102, which obtains the watermark feature map, the remaining steps are performed on the original hologram of each input.

[0091] Figure 2 A flowchart illustrating another embodiment of the holographic watermarking method of this application is shown, as follows: Figure 2 As shown, the holographic watermarking processing method of the second embodiment of this application includes:

[0092] Step S201: Set the number of channels to 3, convert the original hologram into a 3×p×q tensor, and use an n×n complex convolution kernel to perform complex convolution on the real part Hr and the imaginary part Hi of the tensor respectively to obtain the real part Hjr and the imaginary part Hji, where p×q is the resolution of the original hologram and n is a preset value;

[0093] Step S202: Normalize the real part Hjr and the imaginary part Hji respectively to obtain the standardized holographic feature map;

[0094] Step S203: Convolve the real part Mr and the imaginary part Mi of the watermark using three consecutive 3×3 real number convolutional layers to obtain the watermark feature map. The watermark is a binary complex watermark with a length of L.

[0095] Step S204: Input the standardized holographic feature map into four consecutive 3×3 composite convolutional layers to obtain a complex convolutional holographic feature map. The first layer of the composite convolutional layer is an equivariant complex convolution, the second layer is a complex-valued batch normalization, and the third layer is a generalized tangent ReLU. No bias parameter is introduced in the equivariant complex convolution.

[0096] Step S205: The watermark feature map and the multiconvoluted holographic feature map are spliced ​​together to obtain a spliced ​​feature map;

[0097] Step S206: The stitched feature map is stitched together with the standardized holographic feature map to obtain a skip connection feature map;

[0098] Step S207: Compress the number of channels in the skip connection feature map to 3, and perform linear projection restoration on the compressed skip connection feature map to obtain a watermark hologram.

[0099] Step S208: Use a generalized decoder to extract the watermark from the watermark hologram.

[0100] Specifically, steps S201-S207 can refer to steps S101-S107, steps S201-S207 can be executed by the encoder, and step 208 can be executed by the generalized decoder.

[0101] Specifically, Figure 3a This diagram illustrates a flowchart of one embodiment of step S208 in another implementation of the holographic watermarking method of this application. Specifically, as shown... Figure 3a As shown, in one possible implementation, step S208 may include:

[0102] Step S2081a: Set the watermark hologram as the complex optical field at the source plane, and perform a two-dimensional Fourier transform on the complex optical field to obtain the corresponding frequency domain optical field;

[0103] Step S2082a: Based on the frequency domain light field, the preset visible light wavelength and the target propagation distance, the angular spectral transfer function is calculated. The angular spectral transfer function is used to characterize the phase accumulation characteristics of each spatial frequency component of the watermark hologram under the conditions of the visible light wavelength and the target propagation distance.

[0104] Step S2083a: Multiply the frequency domain optical field with the angular spectral transfer function, perform a two-dimensional inverse Fourier transform on the result of the multiplication, and transform the result of the multiplication to the spatial domain to obtain a watermarked reconstructed hologram.

[0105] In this implementation, step S208 reconstructs the watermark hologram. Specifically, in step S2081, the watermark hologram is set as the complex optical field at the source plane (z=0) to restore the starting point of the real optical scene; then, the complex optical field is transformed into the frequency domain using a two-dimensional Fourier transform, from the spatial domain to the frequency domain, to obtain the corresponding frequency domain optical field. Specifically, in step S2082, based on the frequency domain optical field, and the preset visible light wavelength and target propagation distance, the angular spectral transfer function is calculated. The visible light wavelength can be set to 532nm, and the target propagation distance can be set according to the resolution of the original hologram. A lower resolution results in a shorter target propagation distance. For example, if the original hologram resolution is 384×384, the target propagation distance can be 10cm; if the original hologram resolution is 1920×1080, the target propagation distance can be 15cm to adapt to high-resolution display scenarios. The specific target propagation distance can be set according to the hologram resolution and actual calculation needs. Specifically, in step S2083, the frequency domain optical field and the angular spectral transfer function are multiplied to simulate the propagation process of the complex optical field from the source plane to the target propagation distance plane in free space. Then, a two-dimensional inverse Fourier transform is performed on the result of the multiplication to convert the result to the spatial domain, obtaining the reconstructed complex optical field corresponding to the target propagation distance, and thus obtaining the watermarked reconstructed hologram, i.e., the watermarked hologram corresponding to the reconstructed complex optical field. This achieves the simulation of watermarked holographic reconstruction of a real optical display scene for subsequent attack simulation. It should be noted that the complex optical field setting, two-dimensional Fourier transform, angular spectral transfer function calculation, and two-dimensional inverse Fourier transform are based on existing technologies and will not be elaborated further.

[0106] Specifically, Figure 3b This diagram illustrates a further embodiment of step S208 in another implementation of the holographic watermarking method of this application. Specifically, as shown... Figure 3b As shown, in one possible implementation, step S208 may include:

[0107] Step S2081b: Set the watermark hologram as the complex optical field at the source plane, and perform a two-dimensional Fourier transform on the complex optical field to obtain the corresponding frequency domain optical field;

[0108] Step S2082b: Based on the frequency domain light field, the preset visible light wavelength and the target propagation distance, the angular spectral transfer function is calculated. The angular spectral transfer function is used to characterize the phase accumulation characteristics of each spatial frequency component of the watermark hologram under the conditions of the visible light wavelength and the target propagation distance.

[0109] Step S2083b: Multiply the frequency domain optical field with the angular spectral transfer function, perform a two-dimensional inverse Fourier transform on the result of the multiplication, and transform the result of the multiplication to the spatial domain to obtain a watermarked reconstructed hologram.

[0110] Step S2084b: Perform attack simulation on the watermarked reconstructed hologram. The attack includes Cropout, Dropout, rotation, JPEG compression and / or Gaussian blur to obtain an attack simulation hologram.

[0111] Specifically, steps S208b1-S208b3 can refer to steps S208a1-S208a3. Specifically, in step S2084b, one or more of the following five attack types can be randomly selected: Cropout (cropping 10%-20% of the area and filling with zeros), Dropout (randomly discarding pixels), rotation (e.g., rotating 15°-45°), JPEG compression (quality factor can be set to 40), and Gaussian blur (σ can be set to 2) to simulate attacks on the watermarked reconstructed hologram, resulting in an attack simulation hologram. The attack simulation simultaneously affects both the real and imaginary parts of the watermarked reconstructed hologram to avoid omitting complex numerical key information. By simulating various attacks that the watermarked reconstructed hologram may encounter during actual storage, transmission, and display, the robustness of the watermark is verified and improved, ensuring that the watermark can still be accurately extracted after being attacked. Parameters for each attack can be set according to the intensity that may occur in actual scenarios to ensure the realism of the attack simulation.

[0112] Specifically, Figure 3c This illustrates a flowchart of yet another embodiment of step S208 in the holographic watermarking method of this application. Specifically, as shown... Figure 3c As shown, in one possible implementation, step S208 may include:

[0113] Step S2081c: Set the watermark hologram as the complex optical field at the source plane, and perform a two-dimensional Fourier transform on the complex optical field to obtain the corresponding frequency domain optical field;

[0114] Step S2082c: Based on the frequency domain light field, the preset visible light wavelength and the target propagation distance, the angular spectral transfer function is calculated. The angular spectral transfer function is used to characterize the phase accumulation characteristics of each spatial frequency component of the watermark hologram under the conditions of the visible light wavelength and the target propagation distance.

[0115] Step S2083c: Multiply the frequency domain optical field with the angular spectral transfer function, perform a two-dimensional inverse Fourier transform on the result of the multiplication, and transform the result of the multiplication to the spatial domain to obtain a watermarked reconstructed hologram.

[0116] Step S2084c: Perform attack simulation on the watermarked reconstructed hologram. The attack includes Cropout, Dropout, rotation, JPEG compression and / or Gaussian blur to obtain an attack simulation hologram.

[0117] Step S2085c: Use r consecutive 1×1 convolution kernels to extract complex numerical features from the attack simulation hologram, restore the attack simulation hologram to a 3×p×q complex feature map, and extend the lengths of the real and imaginary parts of the complex feature map to L / 2 respectively to obtain an extended complex feature map. Here, r is determined by multiple experiments and corresponds to the resolution of the original hologram. That is, by conducting experiments with original holograms of different resolutions, the optimal r value corresponding to different resolutions can be obtained. Thus, the corresponding optimal r value can be selected and preset according to the resolution of the original hologram. For example, when the resolution of the original hologram is 384×384, r is set to 6; when the resolution of the original hologram is 1920×1080, r is set to 9.

[0118] Step S2086c: Perform complex average pooling to reduce the dimensionality of the extended complex feature map to obtain a real part watermark feature map and an imaginary part watermark feature map, wherein the real part watermark feature map and the imaginary part watermark feature map are L / 2×1×1 respectively.

[0119] Step S2087c: Use linear mapping to map the real part watermark feature map and the imaginary part watermark feature map into a real part watermark vector and an imaginary part watermark vector, respectively. The lengths of the real part watermark vector and the imaginary part watermark vector are L / 2.

[0120] Step S2088c: The real watermark vector and the imaginary watermark vector are normalized and phase adjusted using a division layer (DIV layer) to obtain the real part Mr' and the imaginary part Mi' of the decoded watermark, and the corresponding decoded watermark is obtained. The DIV layer uses the global average complex value as the scale factor.

[0121] Step S2089c: Calculate the similarity between the decoded watermark and the watermark. If the similarity is greater than a preset first threshold, determine that the watermark extraction is accurate.

[0122] Specifically, steps S2081c-S2084c can refer to steps S2081b-S2084b.

[0123] Specifically, in steps S2085c-S2088c, watermark extraction is performed on the attack simulation hologram. In step S2085c, the attack simulation hologram is restored to a 3×p×q complex feature map through convolution calculation with r consecutive 1×1 convolution kernels and channel expansion. The lengths of the real and imaginary parts of the complex feature map are then expanded to L / 2 to obtain an expanded complex feature map. In step S2086c, dimensionality reduction is performed using complex average pooling to obtain a real part watermark feature map (L / 2×1×1) and an imaginary part watermark feature map (L / 2×1×1). This dimensionality reduction reduces computational pressure. The process involves several steps: First, the real watermark feature map and the imaginary watermark feature map are mapped using a linear mapping to vectors of the same length as the original watermark, resulting in a preliminary watermark vector (including a real watermark vector and an imaginary watermark vector). Second, a division layer is used to normalize the amplitude and adjust the phase of the real and imaginary watermark vectors, yielding the decoded watermark real part Mr' and the decoded watermark imaginary part Mi'. Specifically, ... ,in, This represents the real part watermark vector or the imaginary part watermark vector. For the corresponding scaling factor, This is a preset, small constant used to avoid division by zero. This represents the amplitude normalization part, used to eliminate amplitude scaling interference. The phase adjustment part is used to offset the phase shift effect. After amplitude normalization and phase adjustment, the real part Mr' and imaginary part Mi' of the decoded watermark are obtained, and the decoded watermark is obtained accordingly. The DIV layer uses the global average complex value as the scale factor to eliminate the amplitude scaling and phase rotation effects caused by complex scaling attacks, thereby completing the watermark extraction.

[0124] Specifically, in step S2089c, the similarity between the decoded watermark and the watermark is calculated. If the similarity is greater than a preset first threshold (e.g., 0.98), it is determined that the watermark extraction is accurate, so as to evaluate the accuracy of watermark extraction.

[0125] Specifically, Figure 3d This illustrates a flowchart of yet another embodiment of step S208 in the holographic watermarking method of this application. Specifically, as shown... Figure 3d As shown, in one possible implementation, step S208 may include:

[0126] Step S2081d: Set the watermark hologram as the complex optical field at the source plane, and perform a two-dimensional Fourier transform on the complex optical field to obtain the corresponding frequency domain optical field;

[0127] Step S2082d: Based on the frequency domain light field, the preset visible light wavelength and the target propagation distance, the angular spectral transfer function is calculated. The angular spectral transfer function is used to characterize the phase accumulation characteristics of each spatial frequency component of the watermark hologram under the conditions of the visible light wavelength and the target propagation distance.

[0128] Step S2083d: Multiply the frequency domain optical field with the angular spectral transfer function, perform a two-dimensional inverse Fourier transform on the result of the multiplication, and transform the result of the multiplication to the spatial domain to obtain a watermarked reconstructed hologram.

[0129] Step S2084d: Perform attack simulation on the watermarked reconstructed hologram. The attack includes Cropout, Dropout, rotation, JPEG compression and / or Gaussian blur to obtain the attack simulation hologram.

[0130] Step S2085d: Use r consecutive 1×1 convolution kernels to extract complex numerical features from the attack simulation hologram, restore the attack simulation hologram to a 3×p×q complex feature map, and extend the lengths of the real and imaginary parts of the complex feature map to L / 2 respectively to obtain an extended complex feature map. r is determined according to the resolution of the original hologram.

[0131] Step S2086d: Perform complex average pooling to reduce the dimensionality of the extended complex feature map to obtain a real part watermark feature map and an imaginary part watermark feature map, wherein the real part watermark feature map and the imaginary part watermark feature map are L / 2×1×1 respectively.

[0132] Step S2087d: Use linear mapping to map the real part watermark feature map and the imaginary part watermark feature map into a real part watermark vector and an imaginary part watermark vector, respectively. The lengths of the real part watermark vector and the imaginary part watermark vector are L / 2.

[0133] In step S2088d, the real watermark vector and the imaginary watermark vector are normalized in magnitude and adjusted in phase using a division layer to obtain the real part Mr' and the imaginary part Mi' of the decoded watermark, and the corresponding decoded watermark is obtained. The DIV layer uses the global average complex value as the scale factor.

[0134] Step S2089d: Calculate the similarity between the decoded watermark and the watermark. If the similarity is greater than a preset first threshold, determine that the watermark extraction is accurate.

[0135] Step S2090d: Use the generalized decoder to extract the decoded watermark from N watermark holograms, and calculate the watermark extraction accuracy R=S1 / N based on the similarity, where S1 is the number of similarities greater than or equal to the first threshold, and the watermarks corresponding to the N watermark holograms are all randomly generated and have the same length.

[0136] Step S2091d: If the accuracy is less than a preset second threshold, adjust the parameters of the generalized decoder until the accuracy is greater than or equal to the second threshold.

[0137] Specifically, steps S2081d-S2089d can refer to steps S208c1-S2089c. Steps S2090d-S2091d are used to optimize the generalized decoder, that is, to optimize the parameters in each step when the generalized decoder is executed. Specifically, in step S2090d, for the input N watermark holograms, steps S2081d-S2089d are executed to extract the decoded watermark from the N watermark holograms, and the similarity between the decoded watermark and the embedded watermark is calculated. The N watermark holograms are obtained by embedding watermarks through steps S201 to S207, and the watermarks corresponding to the N watermark holograms are all randomly generated and have the same length. The watermark extraction accuracy of the N watermark holograms is calculated based on the calculated similarity. In step S2091d, if the accuracy is less than a preset second threshold (e.g., 94%), the parameters of the generalized decoder are adjusted, i.e., the parameters in steps S2081d-S2089d, until the accuracy is greater than or equal to the second threshold. This involves repeatedly adjusting the parameters in steps S2081d-S2089d and executing steps S2081d-S2089d for N watermark holograms until the required accuracy is achieved, thus completing the optimization of the generalized decoder. It should be noted that which parameters are adjusted can be selected based on their importance in the calculation (which can be determined according to the conventional judgment of parameter importance in the algorithm used), combined with considerations of optimization complexity and resource consumption. N can be determined by considering both optimization resource consumption and accuracy requirements.

[0138] In one possible implementation, steps S2090d-S2091d can also be executed multiple times (a preset number of times) until the accuracy meets the requirements each time, finally resulting in a better generalized decoder.

[0139] In one possible implementation of the holographic watermarking method provided in this application, only the narrow decoder can be optimized. The narrow decoder is used to execute steps S2085d-S2088d, that is, only the parameters in steps S2085d-S2088d are optimized. Specifically, N attack simulation holograms are input to the narrow decoder, the decoded watermark is obtained through the narrow decoder, and then the optimization of the aforementioned generalized decoder is referenced. The decoding accuracy is calculated based on the similarity between the decoded watermark and the embedded watermark. The parameters of the narrow decoder are adjusted according to the accuracy until the accuracy reaches the threshold requirement.

[0140] The holographic watermarking method provided in this application significantly improves the adaptability, robustness, and extraction accuracy of watermarks by taking advantage of the complex characteristics of holograms. It employs a complex convolutional network for watermark embedding and extraction, deeply exploring the coupling relationship between the real and imaginary parts of the hologram, thus solving the problem of poor adaptability of existing real convolutional architectures. This allows for stable fusion of the watermark and holographic data, significantly improving robustness and extraction accuracy. Removing the bias term of conventional complex convolutions ensures that the holographic feature map maintains geometric equivariance even when subjected to complex scaling attacks, demonstrating outstanding robustness. Simultaneously, it reduces redundant parameters, lowering memory usage and inference time without sacrificing performance, adapting to the real-time processing needs of resource-constrained holographic terminals. An angular spectrum reconstruction module is introduced between the encoder and generalized decoder and incorporated into the training process, solving the problems of holographic quality degradation and watermark extraction failure after reconstruction in conventional methods, balancing visual effects and extraction accuracy. The modular architecture supports multi-resolution input, and end-to-end training requires no additional optimization for attack scenarios, significantly reducing computational overhead, operational complexity, and deployment and maintenance costs. In summary, the holographic watermarking processing method provided in this application fills the gap in complex convolutional watermarking technology adapted to the coupling characteristics of holograms, and has the advantages of high robustness, excellent image quality, high efficiency and deployment flexibility.

[0141] A second aspect of this application provides a holographic watermarking processing system. Figure 4 This diagram illustrates a structural block diagram of one embodiment of the holographic watermarking processing system of this application, as shown below. Figure 4 As shown, the holographic watermarking processing system of the third embodiment of this application includes an encoder 300, the encoder 300 comprising:

[0142] The complex convolution module 301 is used to convert the original hologram into a 3×p×q tensor. The real part Hr and the imaginary part Hi of the tensor are convolved by an n×n complex convolution kernel to obtain the real part Hjr and the imaginary part Hji, where 3 is the set number of channels, p×q is the resolution of the original hologram, and n is a preset value.

[0143] Normalization module 302 is used to normalize the real part Hjr and the imaginary part Hji respectively to obtain a standardized holographic feature map;

[0144] The real number convolution module 303 is used to convolve the real part Mr and the imaginary part Mi of the watermark using three consecutive 3×3 real number convolution layers to obtain the watermark feature map. The watermark is a binary complex watermark with a length of L.

[0145] The composite convolution module 304 is used to input the standardized holographic feature map into four consecutive 3×3 composite convolution layers to obtain a multiconvolutional holographic feature map. The first layer of the composite convolution layer is an equivariant multiconvolution, the second layer is a complex batch normalization, and the third layer is a generalized tangent ReLU. No bias parameter is introduced in the equivariant multiconvolution.

[0146] The splicing module 305 is used to splice the watermark feature map and the multiconvoluted holographic feature map to obtain a spliced ​​feature map;

[0147] The skip connection module 306 is used to stitch the spliced ​​feature map with the standardized holographic feature map to obtain a skip connection feature map;

[0148] The restoration module 307 is used to compress the number of channels of the skip connection feature map to 3, and to perform linear projection restoration on the compressed skip connection feature map to obtain a watermark hologram.

[0149] The restoration module can use m consecutive 3×3 composite convolutional layers to compress the number of channels of the skip connection feature map to 3, where m is determined according to the resolution of the original hologram.

[0150] Figure 5 A structural block diagram of another embodiment of the video hologram watermarking processing system of this application is shown, as follows: Figure 5 As shown, the holographic watermarking processing system of the fourth embodiment of this application includes an encoder 400A and a generalized decoder 400B. The encoder 400A includes:

[0151] The complex convolution module 401 is used to convert the original hologram into a 3×p×q tensor. The real part Hr and the imaginary part Hi of the tensor are convolved by an n×n complex convolution kernel to obtain the real part Hjr and the imaginary part Hji, where 3 is the set number of channels, p×q is the resolution of the original hologram, and n is a preset value.

[0152] Normalization module 402 is used to normalize the real part Hjr and the imaginary part Hji respectively to obtain a standardized holographic feature map;

[0153] The real number convolution module 403 is used to convolve the real part Mr and the imaginary part Mi of the watermark using three consecutive 3×3 real number convolution layers to obtain the watermark feature map. The watermark is a binary complex watermark with a length of L.

[0154] The compound convolution module 404 is used to input the standardized holographic feature map into four consecutive 3×3 compound convolution layers to obtain a multiconvolution holographic feature map. The first layer of the compound convolution layer is an equivariant multiconvolution, the second layer is a complex batch normalization, and the third layer is a generalized tangent ReLU. No bias parameter is introduced in the equivariant multiconvolution.

[0155] The splicing module 405 is used to splice the watermark feature map and the multiconvoluted holographic feature map to obtain a spliced ​​feature map;

[0156] The skip connection module 406 is used to stitch the spliced ​​feature map with the standardized holographic feature map to obtain a skip connection feature map;

[0157] The restoration module 407 is used to compress the number of channels of the skip connection feature map to 3, and to perform linear projection restoration on the compressed skip connection feature map to obtain a watermark hologram.

[0158] The restoration module 407 can use m consecutive 3×3 composite convolutional layers to compress the number of channels of the skip connection feature map to 3, where m is determined according to the resolution of the original hologram.

[0159] Generalized decoder 400B, the generalized decoder 400B comprising:

[0160] Reconstruction module 408, the reconstruction module includes:

[0161] The frequency domain conversion submodule 4081 is used to set the watermark hologram as a complex optical field at the source plane, and perform a two-dimensional Fourier transform on the complex optical field to obtain the corresponding frequency domain optical field.

[0162] The angular spectral transfer function calculation submodule 4082 is used to calculate the angular spectral transfer function based on the frequency domain light field, as well as the preset visible light wavelength and target propagation distance. The angular spectral transfer function is used to characterize the phase accumulation characteristics of each spatial frequency component of the watermark hologram under the conditions of the visible light wavelength and the target propagation distance.

[0163] The spatial domain transformation submodule 4083 is used to multiply the frequency domain optical field with the angular spectral transfer function, perform a two-dimensional inverse Fourier transform on the result of the multiplication, and transform the result of the multiplication to the spatial domain to obtain a watermarked reconstructed hologram.

[0164] The attack simulation module 409 is used to simulate an attack on the watermarked reconstructed hologram. The attack includes Cropout, Dropout, rotation, JPEG compression and / or Gaussian blur, to obtain an attack simulation hologram.

[0165] Watermark extraction module 4010, the watermark extraction module includes:

[0166] The complex feature restoration submodule 40101 is used to extract complex numerical features from the attack simulation hologram using r consecutive 1×1 convolution kernels, restore the attack simulation hologram to a 3×p×q complex feature map, and extend the lengths of the real and imaginary parts of the complex feature map to L / 2 respectively to obtain an extended complex feature map, where r is determined according to the resolution of the original hologram;

[0167] The dimensionality reduction submodule 40102 is used to perform complex average pooling dimensionality reduction on the extended complex feature map to obtain a real part watermark feature map and an imaginary part watermark feature map, wherein the real part watermark feature map and the imaginary part watermark feature map are L / 2×1×1 respectively.

[0168] The mapping submodule 40103 is used to map the real part watermark feature map and the imaginary part watermark feature map into a real part watermark vector and an imaginary part watermark vector respectively using a linear mapping, wherein the length of the real part watermark vector and the imaginary part watermark vector is L / 2.

[0169] The adjustment submodule 40104 is used to perform amplitude normalization and phase adjustment on the real part watermark vector and the imaginary part watermark vector using the division layer to obtain the real part Mr' and the imaginary part Mi' of the decoded watermark, and obtain the corresponding decoded watermark. The DIV layer uses the global average complex value as the scale factor.

[0170] The extraction evaluation submodule 40105 is used to calculate the similarity between the decoded watermark and the watermark. If the similarity is greater than a preset first threshold, it is determined that the watermark extraction is accurate.

[0171] Figure 6 This diagram illustrates a structural block diagram of yet another embodiment of the video hologram watermarking system of this application, as shown below. Figure 6 As shown, the holographic watermarking processing system of the fifth embodiment of this application includes an encoder 500A, a generalized decoder 500B, and an optimization unit 500C. The encoder 500A includes:

[0172] The complex convolution module 501 is used to convert the original hologram into a 3×p×q tensor. The real part Hr and the imaginary part Hi of the tensor are convolved by an n×n complex convolution kernel to obtain the real part Hjr and the imaginary part Hji, where 3 is the set number of channels, p×q is the resolution of the original hologram, and n is a preset value.

[0173] Normalization module 502 is used to normalize the real part Hjr and the imaginary part Hji respectively to obtain a standardized holographic feature map;

[0174] The real number convolution module 503 is used to convolve the real part Mr and the imaginary part Mi of the watermark using three consecutive 3×3 real number convolution layers to obtain the watermark feature map. The watermark is a binary complex watermark with a length of L.

[0175] The composite convolution module 504 is used to input the standardized holographic feature map into four consecutive 3×3 composite convolution layers to obtain a multiconvolutional holographic feature map. The first layer of the composite convolution layer is an equivariant multiconvolution, the second layer is a complex batch normalization, and the third layer is a generalized tangent ReLU. No bias parameter is introduced in the equivariant multiconvolution.

[0176] The splicing module 505 is used to splice the watermark feature map and the multiconvoluted holographic feature map to obtain a spliced ​​feature map;

[0177] The skip connection module 506 is used to stitch the spliced ​​feature map with the standardized holographic feature map to obtain a skip connection feature map;

[0178] The restoration module 507 is used to compress the number of channels of the skip connection feature map to 3, and to perform linear projection restoration on the compressed skip connection feature map to obtain a watermark hologram.

[0179] The restoration module can use m consecutive 3×3 composite convolutional layers to compress the number of channels of the skip connection feature map to 3, where m is determined according to the resolution of the original hologram.

[0180] Generalized decoder 500B, the generalized decoder 500B comprising:

[0181] Reconstruction module 508, the reconstruction module includes:

[0182] The frequency domain conversion submodule 5081 is used to set the watermark hologram as a complex optical field at the source plane, and perform a two-dimensional Fourier transform on the complex optical field to obtain the corresponding frequency domain optical field.

[0183] The angular spectral transfer function calculation submodule 5082 is used to calculate the angular spectral transfer function based on the frequency domain light field, as well as the preset visible light wavelength and target propagation distance. The angular spectral transfer function is used to characterize the phase accumulation characteristics of each spatial frequency component of the watermark hologram under the conditions of the visible light wavelength and the target propagation distance.

[0184] The spatial domain transformation submodule 5083 is used to multiply the frequency domain optical field with the angular spectral transfer function, perform a two-dimensional inverse Fourier transform on the result of the multiplication, and transform the result of the multiplication to the spatial domain to obtain a watermarked reconstructed hologram.

[0185] Attack simulation module 509 is used to simulate attacks on the watermarked reconstructed hologram, the attacks including Cropout, Dropout, rotation, JPEG compression and / or Gaussian blur, to obtain an attack simulation hologram;

[0186] Watermark extraction module 5010, the watermark extraction module includes:

[0187] The complex feature restoration submodule 50101 is used to extract complex numerical features from the attack simulation hologram using r consecutive 1×1 convolution kernels, restore the attack simulation hologram to a 3×p×q complex feature map, and extend the lengths of the real and imaginary parts of the complex feature map to L / 2 respectively to obtain an extended complex feature map, where r is determined according to the resolution of the original hologram;

[0188] The dimensionality reduction submodule 50102 is used to perform complex average pooling dimensionality reduction on the extended complex feature map to obtain a real part watermark feature map and an imaginary part watermark feature map, wherein the real part watermark feature map and the imaginary part watermark feature map are L / 2×1×1 respectively.

[0189] The mapping submodule 50103 is used to map the real part watermark feature map and the imaginary part watermark feature map into a real part watermark vector and an imaginary part watermark vector respectively using a linear mapping, wherein the length of the real part watermark vector and the imaginary part watermark vector is L / 2.

[0190] The adjustment submodule 50104 is used to perform amplitude normalization and phase adjustment on the real part watermark vector and the imaginary part watermark vector using the division layer to obtain the real part Mr' and the imaginary part Mi' of the decoded watermark, and obtain the corresponding decoded watermark. The DIV layer uses the global average complex value as the scale factor.

[0191] The extraction evaluation submodule 50105 is used to calculate the similarity between the decoded watermark and the watermark. If the similarity is greater than a preset first threshold, it is determined that the watermark extraction is accurate.

[0192] Optimization unit 500C, the optimization unit 500C is used for:

[0193] The decoded watermark is obtained by extracting the watermark from the N watermark holograms using the generalized decoder. The accuracy of watermark extraction is calculated as R=S1 / N based on the similarity, where S1 is the number of similarities greater than or equal to the first threshold. The watermarks corresponding to the N watermark holograms are all randomly generated and have the same length.

[0194] If the accuracy is less than a preset second threshold, the parameters of the generalized decoder are adjusted until the accuracy is greater than or equal to the second threshold.

[0195] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process and related descriptions of the system described above can be referred to the corresponding processes in the foregoing method embodiments, and therefore will not be repeated here.

[0196] This application provides a holographic watermarking processing system that employs a complex convolutional network to process the watermark. It deeply explores the coupling characteristics of the real and imaginary parts of holograms, solving the adaptation problem of real convolution and enabling stable fusion of the watermark and holographic data, thus improving robustness and extraction accuracy. The system removes the complex convolutional bias term to ensure that the holographic feature map retains geometric equivariance even under complex scaling attacks. An angular spectrum reconstruction module is introduced between the encoder and the generalized decoder and incorporated into the training, solving the problems of image quality degradation and watermark failure after reconstruction using conventional methods, balancing visual effects and extraction accuracy. Without sacrificing performance, redundant parameters are reduced, lowering memory usage and inference time, adapting to real-time processing on resource-constrained terminals. The modular architecture supports multi-resolution input, requiring no additional tuning during training, significantly reducing computational and operational costs.

[0197] It should be noted that the holographic watermarking system provided in the above embodiments is only illustrated by the division of the above functional modules / units. In practical applications, the above functions can be assigned to different functional modules / units as needed, that is, the modules / units or steps in the embodiments of this application can be further decomposed or combined. For example, the modules / units in the above embodiments can be merged into one module / unit, or further divided into multiple sub-modules to complete all or part of the functions described above. The names of the modules / units and steps involved in the embodiments of this application are only for distinguishing each module or step and are not considered as an improper limitation of this application.

[0198] In a third aspect of this application, an electronic device is also provided, the electronic device comprising: at least one processor; and a memory communicatively connected to at least one of the processors; wherein the memory stores instructions executable by the processor, the instructions being executed by the processor to implement the holographic watermarking processing method described above.

[0199] In a fourth aspect of this application, a computer-readable storage medium is also provided, the computer-readable storage medium storing computer instructions for execution by the computer to implement the above-described holographic watermarking processing method.

[0200] In a fifth aspect of this application, a computer program product comprising instructions is also provided, which, when executed by a computer device, cause the computer device to perform the holographic watermarking processing method described above.

[0201] Those skilled in the art will recognize that the modules / units and method steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. The programs corresponding to the software modules and method steps can be placed in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disks, removable disks, CD-ROMs, or any other form of storage medium known in the art. To clearly illustrate the interchangeability of electronic hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in electronic hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0202] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0203] The terms “first”, “second”, etc., are used to distinguish similar objects, not to describe or indicate a specific order or sequence.

[0204] The term "comprising" or any other similar term is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus / device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent in such process, method, article, or apparatus / device.

[0205] The technical solutions of this application have been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of this application is obviously not limited to these specific embodiments. Without departing from the principles of this application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of this application.

Claims

1. A holographic watermarking processing method, characterized in that, include: The original hologram is converted into a 3×p×q tensor. The real part Hr and the imaginary part Hi of the tensor are convolved using an n×n complex convolution kernel to obtain the real part Hjr and the imaginary part Hji. Here, 3 is the set number of channels, p×q is the resolution of the original hologram, and n is a preset value. The real part Hjr and the imaginary part Hji are normalized respectively to obtain a standardized holographic feature map; The real part Mr and the imaginary part Mi of the watermark are convolved by three consecutive 3×3 real number convolution layers to obtain the watermark feature map. The watermark is a binary complex watermark with a length of L. The standardized holographic feature map is input into s consecutive 3×3 composite convolutional layers to obtain a multiconvolutional holographic feature map. The first layer of the composite convolutional layer is an equivariant multiconvolution, the second layer is a complex-valued batch normalization, and the third layer is a generalized tangent ReLU. No bias parameter is introduced in the equivariant multiconvolution, where s is preset. The watermark feature map and the multiconvoluted holographic feature map are spliced ​​together to obtain a spliced ​​feature map; The spliced ​​feature map is spliced ​​with the standardized holographic feature map to obtain a skip connection feature map; The number of channels in the skip connection feature map is compressed to 3, and the compressed skip connection feature map is linearly projected back to obtain a watermark hologram.

2. The method as described in claim 1, characterized in that, It also includes extracting the watermark from the watermark hologram using a generalized decoder, wherein the watermark extraction using the generalized decoder includes: The watermark hologram is set as the complex optical field at the source plane, and a two-dimensional Fourier transform is performed on the complex optical field to obtain the corresponding frequency domain optical field. Based on the frequency domain light field, the preset visible light wavelength and the target propagation distance, the angular spectral transfer function is calculated. The angular spectral transfer function is used to characterize the phase accumulation characteristics of each spatial frequency component of the watermark hologram under the conditions of the visible light wavelength and the target propagation distance. The frequency domain optical field is multiplied by the angular spectral transfer function, and the result of the multiplication is subjected to a two-dimensional inverse Fourier transform to transform the result of the multiplication to the spatial domain, thereby obtaining a watermarked reconstructed hologram.

3. The method as described in claim 2, characterized in that, The step of extracting the watermark from the watermark hologram using a generalized decoder also includes: The watermarked reconstructed hologram is subjected to an attack simulation to obtain an attack simulation hologram. The attack includes Cropout, Dropout, rotation, JPEG compression and / or Gaussian blur. The attack simulation hologram is extracted with r consecutive 1×1 convolution kernels to extract complex numerical features, and the attack simulation hologram is restored to a 3×p×q complex feature map. The lengths of the real and imaginary parts of the complex feature map are extended to L / 2 respectively to obtain an extended complex feature map, where r is preset. The extended complex feature map is subjected to complex average pooling for dimensionality reduction to obtain a real part watermark feature map and an imaginary part watermark feature map, wherein the real part watermark feature map and the imaginary part watermark feature map are L / 2×1×1 respectively; The real part watermark feature map and the imaginary part watermark feature map are mapped to real part watermark vector and imaginary part watermark vector respectively using linear mapping, and the length of the real part watermark vector and the imaginary part watermark vector is L / 2. The real and imaginary watermark vectors are normalized and phase-adjusted using a division layer to obtain the real watermark Mr' and imaginary watermark Mi', and the corresponding decoded watermark is obtained. The division layer uses the global average complex value as the scale factor. Calculate the similarity between the decoded watermark and the watermark. If the similarity is greater than a preset first threshold, the watermark extraction is determined to be accurate.

4. The method as described in claim 3, characterized in that, Also includes: The decoded watermark is obtained by extracting the watermark from the N watermark holograms using the generalized decoder. The accuracy of watermark extraction is calculated as R=S1 / N based on the similarity, where S1 is the number of similarities greater than or equal to the first threshold. The watermarks corresponding to the N watermark holograms are all randomly generated and have the same length. If the accuracy is less than a preset second threshold, the parameters of the generalized decoder are adjusted until the accuracy is greater than or equal to the second threshold.

5. A holographic watermarking processing system, characterized in that, Includes an encoder, the encoder being used for: The original hologram is converted into a 3×p×q tensor. The real part Hr and the imaginary part Hi of the tensor are convolved using an n×n complex convolution kernel to obtain the real part Hjr and the imaginary part Hji. Here, 3 is the set number of channels, p×q is the resolution of the original hologram, and n is a preset value. The real part Hjr and the imaginary part Hji are normalized respectively to obtain a standardized holographic feature map; The real part Mr and the imaginary part Mi of the watermark are convolved by three consecutive 3×3 real number convolution layers to obtain the watermark feature map. The watermark is a binary complex watermark with a length of L. The standardized holographic feature map is input into s consecutive 3×3 composite convolutional layers to obtain a multiconvolutional holographic feature map. The first layer of the composite convolutional layer is an equivariant multiconvolution, the second layer is a complex-valued batch normalization, and the third layer is a generalized tangent ReLU. No bias parameter is introduced in the equivariant multiconvolution, where s is preset. The watermark feature map and the multiconvoluted holographic feature map are spliced ​​together to obtain a spliced ​​feature map; The spliced ​​feature map is spliced ​​with the standardized holographic feature map to obtain a skip connection feature map; The number of channels in the skip connection feature map is compressed to 3, and the compressed skip connection feature map is linearly projected back to obtain a watermark hologram.

6. The system as described in claim 5, characterized in that, It also includes a generalized decoder, which is used to extract the watermark from the watermark hologram. Specifically, the generalized decoder is used for: The watermark hologram is set as the complex optical field at the source plane, and a two-dimensional Fourier transform is performed on the complex optical field to obtain the corresponding frequency domain optical field. Based on the frequency domain light field, the preset visible light wavelength and the target propagation distance, the angular spectral transfer function is calculated. The angular spectral transfer function is used to characterize the phase accumulation characteristics of each spatial frequency component of the watermark hologram under the conditions of the visible light wavelength and the target propagation distance. The frequency domain optical field is multiplied by the angular spectral transfer function, and the result of the multiplication is subjected to a two-dimensional inverse Fourier transform to transform the result of the multiplication to the spatial domain, thereby obtaining a watermarked reconstructed hologram.

7. The system as described in claim 6, characterized in that, The generalized decoder is also specifically used for: The watermarked reconstructed hologram is subjected to an attack simulation, the attack including Cropout, Dropout, rotation, JPEG compression and / or Gaussian blur, to obtain an attack simulation hologram; The attack simulation hologram is extracted with r consecutive 1×1 convolution kernels to extract complex numerical features, and the attack simulation hologram is restored to a 3×p×q complex feature map. The lengths of the real and imaginary parts of the complex feature map are extended to L / 2 respectively to obtain an extended complex feature map, where r is preset. The extended complex feature map is subjected to complex average pooling for dimensionality reduction to obtain a real part watermark feature map and an imaginary part watermark feature map, wherein the real part watermark feature map and the imaginary part watermark feature map are L / 2×1×1 respectively; The real part watermark feature map and the imaginary part watermark feature map are mapped to real part watermark vector and imaginary part watermark vector respectively using linear mapping, and the length of the real part watermark vector and the imaginary part watermark vector is L / 2. The real and imaginary watermark vectors are normalized and phase-adjusted using a division layer to obtain the real watermark Mr' and imaginary watermark Mi', and the corresponding decoded watermark is obtained. The division layer uses the global average complex value as the scale factor. Calculate the similarity between the decoded watermark and the watermark. If the similarity is greater than a preset first threshold, the watermark extraction is determined to be accurate.

8. The system as described in claim 7, characterized in that, It also includes an optimization unit, which is used to: The decoded watermark is obtained by extracting the watermark from the N watermark holograms using the generalized decoder. The accuracy of watermark extraction is calculated as R=S1 / N based on the similarity, where S1 is the number of similarities greater than or equal to the first threshold. The watermarks corresponding to the N watermark holograms are all randomly generated and have the same length. If the accuracy is less than a preset second threshold, the parameters of the generalized decoder are adjusted until the accuracy is greater than or equal to the second threshold.

9. An electronic device, characterized in that, include: At least one processor; as well as A memory communicatively connected to at least one of the processors; wherein, The memory stores instructions that can be executed by the processor to implement the holographic watermarking processing method as described in any one of claims 1-4.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that are executed by the computer to implement the holographic watermarking processing method as described in any one of claims 1-4.

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