Lightweight coaxial holographic reconstruction method based on double-domain complex valued neural network

Abstract

The invention belongs to the field of holographic phase reconstruction, and discloses a lightweight coaxial holographic reconstruction method based on a double-domain complex-valued neural network, which achieves the same reconstruction effect under the condition that model parameters and calculated amount are greatly reduced, and adopts a physical process based on a double-domain complex-valued neural network architecture in combination with an optical coaxial holographic imaging model. Firstly, a hologram A and an initial phase construct a complex amplitude, the complex amplitude is input into a double-domain complex-valued neural network, an output complex-valued field C is obtained through spatial domain convolution and frequency domain learning, then a coaxial holographic forward propagation process is simulated, and the intensity is taken as a reconstructed hologram D; and then calculating the similarity between the hologram A and the reconstructed hologram D, and realizing phase reconstruction through a gradient descent optimization algorithm of a complex valued neural network. The invention provides a method for directly reconstructing a complex-valued field by combining a lightweight double-domain complex-valued neural network with physical constraints.

Description

Technical Field

[0001] The invention relates to a hologram phase reconstruction method, and in particular to a lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network. Background Art

[0002] Coaxial hologram is a holographic imaging technology. It is based on the light beam generated by a coherent light source, which is divided into reference light and object light. The object light reaches the detector after passing through the object to be measured, and meets the reference light to form an interference pattern to record the phase and amplitude information of the object, which can achieve high-precision three-dimensional reconstruction. Modern holographic phase reconstruction uses high-resolution digital detectors and advanced image processing algorithms to achieve high-resolution three-dimensional imaging, record and reconstruct the phase information of the object, and show richer physical characteristics. Unlike traditional imaging methods, it does not require labeling or staining, and is suitable for real-time observation and non-destructive testing of dynamic processes. The system design is simple and compact, does not require complex optical path adjustment, has good stability, and is widely used in many fields.

[0003] The application of complex-valued neural network (CVNN) in the field of phase reconstruction combines the essence of machine learning and optical imaging technology. With deep learning algorithms, it can efficiently reconstruct high-quality phase information from holograms. Based on complex expression, CVNN is good at processing the coupling information between the amplitude and phase components of the wavefront, and realizes the high-dimensional intrinsic representation of the complex wavefront. Compared with the real-valued neural network (RVNN), CVNN provides richer representation capabilities, especially good at processing complex amplitude information composed of amplitude and phase. In terms of processing highly nonlinear and complex relationships, CVNN shows excellent performance, and its effect is particularly significant for complex structures and nonlinear problems encountered in phase reconstruction. At the same time, CVNN has strong robustness to noise, good generalization ability, and can adapt to different data and application scenarios, thereby significantly improving the accuracy and effect of reconstruction. The core advantage of this technology is that it makes full use of the powerful nonlinear mapping ability and data-driven methods of neural networks, and successfully overcomes the limitations of traditional iterative algorithms in processing complex situations and high-noise data.

[0004] Lightweight network structures are of great significance in engineering and practical applications. By optimizing the model structure and reducing the number of parameters, it significantly improves computing efficiency and reduces the demand for hardware resources, enabling deep learning technology to run efficiently in resource-constrained devices such as mobile devices and embedded systems. This advantage has promoted the continuous innovation and development of artificial intelligence technology. Summary of the invention

[0005] The present invention provides a lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network. The phase reconstruction method can accurately retain and reconstruct phase information by learning in the spatial domain and the frequency domain, integrating the features in two different spatial domains. The method is based on a complex-valued neural network and can directly process complex data, and more naturally represent and process information in the hologram. By directly processing complex data, it has a higher representation capability and can capture the phase and amplitude changes in the data. Combining physical constraints and regularization effects can effectively suppress overfitting, better retain phase relationships, and thus improve reconstruction accuracy.

[0006] The technical solution of the present invention for simultaneously reconstructing the complex amplitude is:

[0007] A lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network comprises the following steps:

[0008] (S1), based on the coaxial holography theory, a camera is selected to shoot a set of pure phase coaxial holograms as network input, i.e., hologram A;

[0009] (S2), after reading the collected hologram A, performing a square root operation to obtain the amplitude, and generating a random matrix of the same size as the hologram A as the initial phase, and constructing an initial complex-valued field with the amplitude and the initial phase as the input of the dual-domain complex-valued neural network;

[0010] (S3), perform complex-valued convolution in the spatial domain, perform frequency-domain learning after Fourier transformation, and then add in the spatial domain, and then add nonlinearity through the sp lit-re lu activation function, and repeat this process multiple times to obtain the output complex-valued field C;

[0011] (S4) softly constraining the amplitude of the output complex-valued field C so that the value of each point is not greater than the value specified by the absorption constraint, and the range of the value is related to the object being recorded;

[0012] (S5) Forward propagate the complex-valued field C to the distance z, take the intensity of the reconstructed complex-valued field at z to obtain the reconstructed hologram D, take the phase to update the phase of the input complex-valued field B, and the updated complex-valued field B is the next round of network input;

[0013] (S6) Calculate the data fidelity term, that is, the similarity between hologram A and the reconstructed hologram D, calculate the complex-valued regularization term comp l ex total variation (CTV), assign the sum of the two weights as the loss function, back-propagate the gradient of the loss function value to update the parameters of the network model, and obtain a trained dual-domain complex-valued neural network.

[0014] Preferably, in step (S1), the collected hologram is a pure phase hologram, and the amplitude of the original object wave is set to 1.

[0015] Preferably, in step (S4), the forward propagation method includes an angular spectrum method, a Fresnel diffraction method, a convolution method, and the like.

[0016] Preferably, the spatial domain convolution is a two-dimensional complex-valued convolution, wherein the complex-valued convolution is implemented by a convolution kernel of 3×3, and the frequency domain learning is to establish a learnable matrix of the same size as the input image, multiply the matrix by the frequency spectrum, and continuously optimize the parameters of the learnable matrix.

[0017] Preferably, in step (S3), the complex-valued activation function includes a sp lit type activation function and a fuly type activation function.

[0018] Preferably, the loss function of the lightweight coaxial holographic reconstruction method based on dual-domain complex-valued neural network adopts a loss function for comparing image structure similarity, and the loss function is an SSIM loss function.

[0019] Preferably, the physical constraints adopted include soft constraints on the output complex-valued field C, complex-valued regularization constraints and a forward propagation part.

[0020] Preferably, in step (S5), the reconstructed hologram D is also obtained by simulating the diffraction process of the collected hologram A after passing through the network output, and the loss back propagation of the two is calculated to guide the network training. The entire process of network training is a self-supervised learning process, and the method is self-supervised learning.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] 1. The present invention introduces a lightweight coaxial holographic reconstruction method of a dual-domain complex-valued neural network. This method cleverly combines the rigor of the physical model with the richness of dual-domain information. Through the powerful learning ability of the deep learning model, it can not only effectively capture the complex nonlinear dynamics and noise characteristics of the physical process, but also significantly improve the accuracy of image reconstruction through dual-domain learning. Furthermore, this scheme brings unprecedented high precision to phase reconstruction.

[0023] 2. The lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network of the present invention can directly and efficiently process complex data in the hologram, breaking through the limitation that traditional real-valued neural networks need to decompose complex numbers into real and imaginary parts for independent processing when processing complex data. By directly operating on data in complex form, the present invention not only simplifies the processing flow, but more importantly, it completely retains the key phase and amplitude information in the hologram. This direct processing method shows significant advantages in phase reconstruction tasks, because the hologram is essentially in complex form, and the phase information it contains is crucial to the reconstruction accuracy. By directly processing complex data, accurate capture and reconstruction of the phase information is achieved, making the reconstruction result closer to the true value.

[0024] 3. The lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network of the present invention adopts a lightweight network design, and can autonomously discover and generate effective training labels from large-scale unlabeled data, overcoming the problems of difficulty in obtaining high-quality labeled data and high application costs in phase reconstruction tasks. The lightweight network structure is of great significance in engineering and practical applications. It significantly improves computing efficiency and reduces the demand for hardware resources by optimizing the model structure and reducing the number of parameters, enabling deep learning technology to be used in resource-constrained devices. The present invention significantly reduces the demand for labeled data and hardware resources, thereby reducing the cost of data labeling. Not only does it reduce costs, it also makes phase reconstruction technology easier to promote and apply. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a flowchart of the lightweight coaxial holographic reconstruction method based on dual-domain complex-valued neural network of the present invention.

[0026] Figure 2 This is a network structure diagram of the lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network of the present invention. DETAILED DESCRIPTION

[0027] The present invention is further described in detail below in conjunction with embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0028] See also Figure 1-Figure 2 The lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network of the present invention comprises the following steps:

[0029] (S1), based on the coaxial holography theory, a camera is selected to shoot a set of pure phase coaxial holograms as network input, i.e., hologram A;

[0030] (S2), after reading the collected hologram A, performing a square root operation to obtain the amplitude, and generating a random matrix of the same size as the hologram A as the initial phase, and constructing an initial complex-valued field with the amplitude and the initial phase as the input of the dual-domain complex-valued neural network;

[0031] (S3), perform complex-valued convolution in the spatial domain, perform frequency-domain learning after Fourier transformation, and then add in the spatial domain, and then add nonlinearity through the sp lit-re lu activation function, and repeat this process multiple times to obtain the output complex-valued field C;

[0032] (S4) softly constraining the amplitude of the output complex-valued field C so that the value of each point is not greater than the value specified by the absorption constraint, and the range of the value is related to the object being recorded;

[0033] (S5) Forward propagate the complex-valued field C to the distance z, take the intensity of the reconstructed complex-valued field at z to obtain the reconstructed hologram D, take the phase to update the phase of the input complex-valued field B, and the updated complex-valued field B is the next round of network input;

[0034] (S6) Calculate the data fidelity term, that is, the similarity between hologram A and the reconstructed hologram D, calculate the complex-valued regularization term comp l ex total variation (CTV), assign the sum of the two weights as the loss function, back-propagate the gradient of the loss function value to update the parameters of the network model, and obtain a trained dual-domain complex-valued neural network.

[0035] See also Figure 1-Figure 2 In step (S4), the propagation method of the lightweight coaxial holographic reconstruction method based on the dual-domain complex-valued neural network includes angular spectrum method, Fresnel diffraction method, convolution method, etc. The angular spectrum method is used in this embodiment.

[0036] In step (S4), the value of z in this embodiment is 15 mm.

[0037] In step (S5), the optimization algorithm includes a structural similarity algorithm, an average error square sum algorithm, an error square sum algorithm, etc. In this embodiment, the structural similarity algorithm is used.

[0038] The above is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited to the above content. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network, comprising the following steps: (S1), based on the coaxial holography theory, a camera is selected to shoot a set of pure phase coaxial holograms as network input, i.e., hologram A; (S2), after reading the collected hologram A, performing a square root operation to obtain the amplitude, and generating a random matrix of the same size as the hologram A as the initial phase, and constructing an initial complex-valued field with the amplitude and the initial phase as the input of the dual-domain complex-valued neural network; (S3), perform complex-valued convolution in the spatial domain, perform frequency-domain learning after Fourier transformation, and then add in the spatial domain, and then add nonlinearity through the split-relu activation function. Repeat this process multiple times to obtain the output complex-valued field C; (S4) softly constraining the amplitude of the output complex-valued field C so that the value of each point is not greater than the value specified by the absorption constraint, and the range of the value is related to the object being recorded; (S5) Forward propagate the complex-valued field C to the distance z, take the intensity of the reconstructed complex-valued field at z to obtain the reconstructed hologram D, take the phase to update the phase of the input complex-valued field B, and the updated complex-valued field B is the next round of network input; (S6) Calculate the data fidelity term, that is, the similarity between hologram A and reconstructed hologram D, calculate the complex-valued regularization term complex total variation (CTV), assign the sum of the two weights as the loss function, back-propagate the gradient of the loss function value to update the parameters of the network model, and obtain a trained dual-domain complex-valued neural network.

2. The lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network according to claim 1 is characterized in that: In step (S1), the collected hologram A is a pure phase hologram, and the amplitude of the original object wave is set to 1.

3. The lightweight coaxial holographic reconstruction method based on dual-domain complex-valued neural network according to claim 1 is characterized in that: In step (S5), the diffraction forward propagation method includes angular spectrum method, Fresnel diffraction method, convolution method, etc.

4. The lightweight coaxial holographic reconstruction method based on dual-domain complex-valued neural network according to claim 1 is characterized in that: The spatial domain convolution is a two-dimensional complex-valued convolution, in which the complex-valued convolution is realized by a 3×3 convolution kernel. The frequency domain learning is to establish a learnable matrix with the same size as the input image, multiply the matrix with the spectrum, and continuously optimize the parameters of the learnable matrix.

5. The lightweight coaxial holographic reconstruction method based on dual-domain complex-valued neural network according to claim 1 is characterized in that: In step (S3), the complex-valued activation function includes a split-type activation function and a fully-type activation function.

6. The lightweight coaxial holographic reconstruction method based on dual-domain complex-valued neural network according to claim 1 is characterized in that: The lightweight coaxial holographic reconstruction method of the dual-domain complex-valued neural network adopts a loss function that can reflect the similarity of two images and CTV to form a loss function, and assigns appropriate weights. The loss function that reflects the similarity of two images includes a mean square error MSE function and a structural similarity index SSIM function.

7. The lightweight coaxial holographic reconstruction method based on dual-domain complex-valued neural network according to claim 1 is characterized in that: In steps (S3), (S4) and (S5), the physical constraints adopted include soft constraints on the output complex-valued field C, complex-valued regularization constraints and the forward propagation part.

8. The lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network according to claim 1 is characterized in that: Self-supervised learning is adopted. In step (S5), the reconstructed hologram D is also obtained by simulating the diffraction process of the collected hologram A after passing through the network output. The loss back propagation of the two is calculated to guide the network training.

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