A complex amplitude reconstruction method based on a frequency domain self-supervised complex neural network

Abstract

The application belongs to the field of holographic phase reconstruction, and discloses a complex amplitude reconstruction method based on a frequency domain self-supervised complex neural network, which provides a reconstruction method learned from the frequency domain while getting rid of the dependence of an end-to-end network on a large amount of labeled data, and adopts a network architecture based on a complex neural network to combine the physical process of an optical coaxial holographic imaging model, so that the collected hologram is subjected to Fourier transform to obtain a frequency spectrum B, the frequency spectrum B is put into the complex neural network, an object field frequency spectrum C is output, inverse Fourier transform is performed, a coaxial holographic forward propagation process is simulated to obtain a diffraction complex amplitude D, the intensity is taken as a reconstructed hologram E and a frequency spectrum F; subsequently, the similarity between the collected hologram and the reconstructed hologram E and between the frequency spectrum B and the frequency spectrum F is calculated, and the phase reconstruction is realized through a gradient descent optimization algorithm of the complex neural network. The application provides a holographic complex amplitude reconstruction method based on frequency spectrum learning of a complex neural network.

Description

TECHNICAL FIELD

[0001] The present application relates to a hologram phase reconstruction method, in particular to a complex amplitude reconstruction method based on a frequency domain self-supervised complex-valued neural network. BACKGROUND

[0002] Coaxial holography is a holographic imaging technology based on the principle of coherent light interference. It mainly divides the coherent light source into two parts: one part as reference light directly reaches the detector, and the other part as object light after passing through the object to be measured also reaches the detector. On the detector, the two beams meet and produce interference patterns, recording the amplitude and phase information of the object. This technology can record the amplitude and phase data of the object in the same hologram, thereby realizing high-precision three-dimensional reconstruction. Compared with traditional imaging techniques, modern holographic phase reconstruction combines high-resolution digital detectors and advanced image processing algorithms, and can realize high-resolution three-dimensional imaging without the need for labeling or staining, recording and reconstructing the detailed physical characteristics of the object. In addition, the system design of holographic phase reconstruction is relatively simple and compact, without the need for complex optical path adjustment, with good stability and easy operation. This makes the technology particularly suitable for real-time observation and non-destructive testing of dynamic processes, and has been widely used in biomedical imaging, material science and industrial detection. With the development of modern technology, coaxial holography shows great potential in providing more rich physical information and realizing higher precision imaging, becoming an important tool in scientific research and application.

[0003] The application of complex-valued neural network (CVNN) in phase reconstruction combines optical imaging technology and machine learning to achieve the goal of extracting and reconstructing high-quality phase information from holograms. The core advantage of CVNN lies in its powerful nonlinear mapping ability and data-driven method, which can overcome the limitations of traditional iterative algorithms in dealing with complex structures and high noise data. Compared with real-valued neural network (RVNN), CVNN is based on complex number representation, which is more suitable for processing complex amplitude data containing amplitude and phase information, thus performing better in phase reconstruction tasks. Because of its intrinsic representation of the coupling relationship between wavefront amplitude and phase components, CVNN can handle the complexity of phase reconstruction and has strong robustness to noise, further improving the accuracy of reconstruction. Through these characteristics, CVNN shows good generalization ability, adapts to different data sets and application scenarios, and provides more rich and efficient solutions in the field of phase reconstruction. SUMMARY

[0004] The application provides a complex amplitude reconstruction method based on a frequency domain self-supervised complex neural network.

[0005] The technical scheme of the application can simultaneously reconstruct complex amplitude, and has the advantages that:

[0006] A complex amplitude reconstruction method based on a frequency domain self-supervised complex neural network comprises the following steps:

[0007] (S1) On the basis of the on-axis holography theory, a plurality of pure phase on-axis holograms are selected by using a camera as network input, namely, a hologram A;

[0008] (S2) The collected hologram A is read in and subjected to Fourier transform to obtain a frequency spectrum B, which is used as input of the complex convolution neural network, and the network outputs an original object field frequency spectrum C;

[0009] (S3) The object field frequency spectrum C is subjected to inverse Fourier transform, and the amplitude thereof is subjected to soft constraint and forward propagation to a z distance to obtain a diffraction field complex amplitude D, wherein the soft constraint is to limit the amplitude of each point to be not greater than a value specified by the absorption constraint, and the value range is related to the recorded object;

[0010] (S4) The diffraction field complex amplitude D is subjected to intensity to obtain a reconstructed hologram E, and a frequency spectrum F is calculated;

[0011] (S5) An empty domain loss term, namely, the similarity of the hologram A and the reconstructed hologram E, is calculated; a frequency domain loss term, namely, the similarity of the frequency spectrum B and the frequency spectrum F, is calculated; appropriate weights are respectively given to the empty domain loss term and the frequency domain loss term, and then the two loss terms are added to obtain a loss function, the gradient of the loss function value is subjected to back propagation to update the parameters of the network model, a trained complex neural network is obtained, the collected on-axis hologram is converted into a frequency spectrum domain and input into the trained network, and the complex amplitude distribution can be reconstructed.

[0012] Preferably, in the step (S1), the collected hologram is a pure phase hologram, and the amplitude of the original object wave is set to 1.

[0013] Preferably, in the step (S1), the hologram A is collected to prepare a data set, and the number of the hologram A is not less than 100.

[0014] Preferably, in the step (S4), the forward propagation method comprises an angular spectrum method, a Fresnel diffraction method and a convolution method.

[0015] Preferably, the complex-valued neural network has a U-shaped structure of a complex-valued network structure, comprising complex-valued convolution, complex-valued deconvolution, and complex-valued activation function, wherein the complex-valued convolution and deconvolution are respectively realized by a 3*3 convolution kernel and a 2*2 deconvolution kernel; the complex-valued activation function includes a split-type activation function and a fully-type activation function.

[0016] Preferably, the complex-valued neural network adopts an encoder-decoder U-shaped structure, and the depth of the encoder-decoder is more than 2 layers.

[0017] Preferably, the loss function of the complex amplitude reconstruction method based on the frequency domain self-supervised complex-valued neural network adopts a loss function for comparing the structural similarity of images, and the loss function is an SSIM loss function and an L1 norm.

[0018] Preferably, in step (S5), the reconstructed hologram E and the spectrum F are also obtained by simulating the diffraction process after the hologram A collected is output by the network, and the corresponding loss back propagation is calculated to guide the network training. The whole process of network training is a self-supervised learning process, and the method is a self-supervised learning method.

[0019] Compared with the prior art, the present application has the following beneficial effects:

[0020] 1. The present application introduces a frequency domain learning algorithm that fuses physical constraints, which focuses on the accurate reconstruction of complex amplitude images. The phase reconstruction method starts from the frequency domain and deeply explores the characteristic relationship between the hologram and the original phase in the frequency domain. By converting the data of the hologram into the frequency domain for analysis, this method can more effectively capture the frequency characteristics of the phase information and reveal the complex mapping relationship between the hologram and the phase. By taking advantage of the frequency domain, this method can reduce the interference of redundant information in the spatial domain and highlight the core features of the phase, thereby improving the reconstruction accuracy. This method provides a new way of thinking for phase reconstruction, which helps to better understand the relationship between the hologram and the original phase and achieve higher quality phase reconstruction.

[0021] 2、The application provides a complex amplitude reconstruction method based on a frequency domain self-supervised complex neural network, which focuses on conveniently processing complex information in the frequency domain. The method directly operates complex data of a hologram in the frequency domain, avoiding the complex process of independently processing real and imaginary parts of the complex number in traditional real neural networks. Through this frequency domain processing method, the application not only simplifies the operation steps, but also fully retains the key phase and amplitude information in the hologram. By taking advantage of the frequency domain, the complex relationship between the hologram and the original phase can be more naturally captured and characterized, thereby significantly improving the accuracy and efficiency of phase reconstruction. By directly processing complex information in the frequency domain, the method realizes accurate capture and efficient reconstruction of the phase, making the result closer to the true value, and provides a simple and powerful solution for the phase reconstruction task.

[0022] 3、The application provides a complex amplitude reconstruction method based on a frequency domain self-supervised complex neural network, which can autonomously mine and generate effective training labels from large-scale unlabeled data, solving the problem of high-quality labeled data being difficult to obtain and high cost in the phase reconstruction task. In the traditional supervised learning framework, model training is heavily dependent on accurately labeled data sets, while self-supervised learning trains by mining the internal structure and pattern of unlabeled data. The application greatly reduces the dependence on labeled data, not only reducing the cost of data labeling, but also significantly improving the training efficiency. This method reduces the threshold of the phase reconstruction technology, making it easier to popularize and apply, and showing stronger flexibility and adaptability in actual operation. BRIEF DESCRIPTION OF DRAWINGS

[0023] Fig. 1 The flowchart of the complex amplitude reconstruction method based on the frequency domain self-supervised complex neural network of the application.

[0024] Fig. 2 The algorithm framework diagram of the complex amplitude reconstruction method based on the frequency domain self-supervised complex neural network of the application. DETAILED DESCRIPTION

[0025] The application will be described in further detail below in conjunction with the embodiments and the accompanying drawings, but the embodiments of the application are not limited thereto.

[0026] Referring to Figs. 1-2 The complex amplitude reconstruction method based on the frequency domain self-supervised complex neural network of the application includes the following steps:

[0027] (S1), based on the on-axis holography theory, a plurality of pure phase on-axis holograms are selected by a camera for shooting as network input, that is, a hologram A;

[0028] (S2), the collected hologram A is read in and Fourier transformed to obtain a frequency spectrum B, which is input into a complex convolutional neural network, and the original object field frequency spectrum C is output after the network.

[0029] (S3), after the object field spectrum C is inversely Fourier transformed, the amplitude thereof is subjected to soft constraint and is positively propagated to the z distance to obtain the diffraction field complex amplitude D, wherein the soft constraint is to limit the amplitude of each point to be not greater than a value defined by the absorption constraint, and the value range is related to the recorded object;

[0030] (S4), the reconstructed hologram E is obtained by taking the intensity of the diffraction field complex amplitude D, and the spectrum F is calculated;

[0031] (S5), the spatial domain loss term, i.e., the similarity of the hologram A and the reconstructed hologram E, is calculated; the frequency domain loss term, i.e., the similarity of the spectrum B and the spectrum F, is calculated; appropriate weights are respectively given to the spatial domain loss term and the frequency domain loss term, and then the two loss terms are added to obtain a loss function, the gradient of the loss function value is reversely propagated to update the parameters of the network model, a trained complex neural network is obtained, the coaxial hologram collected is converted into the spectrum domain and input into the trained network, and the complex amplitude distribution can be reconstructed.

[0032] Referring to Figs. 1-2 In step (S4), the propagation method of the complex amplitude reconstruction method based on the frequency domain self-supervised complex neural network includes an angular spectrum method, a Fresnel diffraction method and a convolution method, and the angular spectrum method is used in the embodiment.

[0033] In step (S4), the value of z in the embodiment is 15 mm.

[0034] In step (S5), the optimization algorithm includes a structural similarity algorithm, a mean error square sum algorithm and an error square sum algorithm, and the structural similarity algorithm and the L1 norm are used in the embodiment.

[0035] The complex neural network with the encoder-decoder structure used in the application has 3 layers and a maximum channel number of 256.

[0036] The above is the preferred embodiment of the application, but the embodiment of the application is not limited by the above, and any change, modification, substitution, combination, simplification made without departing from the spirit and principle of the application should be an equivalent replacement, which is included in the protection scope of the application.

Claims

1. A method for complex amplitude reconstruction based on a frequency domain self-supervised complex-valued neural network, comprising the following steps: (S1) Based on the theory of coaxial holography, multiple sets of pure phase coaxial holograms are captured by a camera and used as network input, i.e., hologram A; (S2) After reading the acquired hologram A, perform a Fourier transform to obtain the spectrum B, which is used as the input of the complex-valued convolutional neural network. After passing through the network, the original object field spectrum C is output. (S3) After the inverse Fourier transform of the object field spectrum C, its amplitude is softly constrained and propagated forward to a distance z to obtain the complex amplitude D of the diffraction field. The soft constraint is to limit the amplitude value at each point to be no greater than the value specified by the absorption constraint. The range of this value is related to the object being recorded. (S4) Take the intensity of the complex amplitude D of the diffraction field to obtain the reconstructed hologram E, and calculate its spectrum F; (S5) Calculate the spatial domain loss term, i.e., the similarity between hologram A and reconstructed hologram E; calculate the frequency domain loss term, i.e., the similarity between spectrum B and spectrum F; assign appropriate weights to the spatial domain loss term and the frequency domain loss term respectively, and then add the two loss terms together as the loss function. Backpropagate the gradient of the loss function value to update the parameters of the network model to obtain the trained complex valued neural network. Convert the acquired coaxial hologram into the frequency domain and input it into the trained network to reconstruct the complex amplitude distribution.

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

3. The complex amplitude reconstruction method based on a frequency domain self-supervised complex-valued neural network according to claim 1, characterized in that, In step (S1), a dataset of at least 100 holograms A is collected.

4. The complex amplitude reconstruction method based on a frequency domain self-supervised complex-valued neural network according to claim 1, characterized in that, In step (S4), the forward propagation diffraction methods include angular spectroscopy, Fresnel diffraction, and convolution.

5. The complex amplitude reconstruction method based on a frequency domain self-supervised complex valued neural network according to claim 1, characterized in that, Complex-valued neural networks have a U-shaped network structure, which includes complex-valued convolution, complex-valued deconvolution, and complex-valued activation functions. The complex-valued convolution and deconvolution are implemented by a 3×3 convolutional layer and a 2×2 deconvolutional kernel, respectively. The complex-valued activation functions include split activation functions and fully activation functions.

6. The complex amplitude reconstruction method based on a frequency domain self-supervised complex-valued neural network according to claim 5, characterized in that, The complex value neural network adopts a U-shaped encoder-decoder structure, with a depth of more than 2 layers.

7. The method for complex amplitude reconstruction based on a frequency domain self-supervised complex-valued neural network according to claim 1, characterized in that, The frequency domain self-supervised complex value neural network complex amplitude reconstruction method adopts a loss function that can reflect the similarity between two images, and assigns appropriate weights to the spatial domain loss term and the frequency domain loss term respectively. The loss function that reflects the similarity between two images includes the L1 norm, the mean square error (MSE) function, and the structural similarity index (SSIM) function.

8. The method for complex amplitude reconstruction based on a frequency domain self-supervised complex-valued neural network according to claim 1, characterized in that, Self-supervised learning is adopted. In step (S4), the reconstructed hologram E and spectrum F are obtained by simulating the diffraction process after the acquired hologram A is output by the network. The corresponding loss is calculated and backpropagated to guide the network training.

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