A lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network

Abstract

The present invention belongs to the field of holographic phase reconstruction, and discloses a lightweight in-line holographic reconstruction method based on a dual-domain complex-valued neural network, which achieves the same reconstruction effect with greatly reduced model parameters and computational complexity. The present invention adopts a physical process combining a dual-domain complex-valued neural network architecture with an optical in-line holographic imaging model. First, a complex amplitude is constructed from a hologram A and an initial phase and input into the dual-domain complex-valued neural network, and an output complex-valued field C is obtained through spatial domain convolution and frequency domain learning respectively. Then, the in-line holographic forward propagation process is simulated, and the intensity is taken as the reconstructed hologram D. Subsequently, the similarity between the hologram A and the reconstructed hologram D is calculated, and phase reconstruction is realized through the gradient descent optimization algorithm of the complex-valued neural network. The present invention provides a method for directly reconstructing a complex-valued field by combining a lightweight dual-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 in-line holographic reconstruction method based on a dual-domain complex-valued neural network. This phase reconstruction method can learn in the spatial domain and the frequency domain, integrate features in two different spatial domains, accurately retain and reconstruct phase information. This method is based on a complex-valued neural network, which can directly process complex data and more naturally represent and process information in holography. By directly processing complex data, it has higher representation ability and can capture phase and amplitude changes in the data. Combining physical constraints and regularization effects can effectively suppress overfitting, better retain phase relationships, and thus improve the reconstruction accuracy.

[0006] The technical solution for the present invention to simultaneously reconstruct the complex amplitude is as follows:

[0007] A lightweight in-line holographic reconstruction method based on a dual-domain complex-valued neural network, comprising the following steps:

[0008] (S1), Based on the in-line holography theory, select a camera to capture a set of pure-phase in-line holograms as the network input, namely hologram A;

[0009] (S2), After reading the captured hologram A, perform a square root operation to obtain the amplitude, and generate a random matrix of the same size as hologram A as the initial phase. Construct 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 transform, add in the spatial domain, and then add non-linearity through the split-relu activation function. Repeat this process multiple times to obtain the output complex-valued field C;

[0011] (S4), Soft-constrain the amplitude of the output complex-valued field C so that the value of each point does not exceed the value specified by the absorption constraint. The range of this value is related to the object being recorded;

[0012] (S5), Propagate the complex-valued field C forward to a 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. The updated complex-valued field B is the input of the next round of the network;

[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 complex total variation (CTV). Assign weights to the two terms and add them as the loss function. Perform backpropagation of the gradient of the loss function value to update the parameters of the network model to obtain a trained dual-domain complex-valued neural network.

[0014] Preferably, in step (S1), the captured 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 the angular spectrum method, the Fresnel diffraction method, the convolution method, etc.

[0016] Preferably, the spatial domain convolution is a two-dimensional complex-valued convolution, where the complex-valued convolution is implemented 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 by the spectral points, and continuously optimize the parameters of the learnable matrix.

[0017] Preferably, in step (S3), the complex-valued activation functions include the split-type activation function and the fully-type activation function.

[0018] Preferably, the loss function of the lightweight in-line holographic reconstruction method based on the dual-domain complex-valued neural network adopts a loss function for comparing the structural similarity of images, and the loss function is the SSIM loss function.

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

[0020] Preferably, in step (S5), the reconstructed hologram D is also obtained by simulating the diffraction process after the collected hologram A passes through the network output. Calculate the loss of the two and backpropagate 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] The present invention has the following beneficial effects compared with the prior art:

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

[0023] 2. The lightweight in-line holographic reconstruction method based on the dual-domain complex-valued neural network of the present invention can directly and efficiently process the 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 dealing with complex data. By directly operating on complex-form data, 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 the phase reconstruction task because holography is essentially in complex form, and the phase information it contains is crucial for the reconstruction accuracy. By directly processing complex data, the accurate capture and reconstruction of phase information are realized, making the reconstruction result closer to the true value.

[0024] 3. The lightweight coaxial holographic reconstruction method based on the 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 difficult acquisition and high application cost of high-quality labeled data in the phase reconstruction task. The lightweight network structure is of great significance in engineering and practical applications. By optimizing the model structure and reducing the number of parameters, it significantly improves the computing efficiency, reduces the demand for hardware resources, and enables 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 annotation. It not only reduces the cost but also makes the 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 the dual-domain complex-valued neural network of the present invention.

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

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

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

[0029] (S1) Select a camera to take a set of pure-phase coaxial holograms based on the coaxial holography theory as the network input, that is, hologram A;

[0030] (S2) After reading the collected hologram A, perform a square root operation to obtain the amplitude, and generate a random matrix of the same size as hologram A as the initial phase. Construct the 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 transform, add in the spatial domain, and then add non-linearity through the split-relu activation function. Repeat multiple such processes to obtain the output complex-valued field C;

[0032] (S4) Soft-constrain the amplitude of the output complex-valued field C so that the value of each point does not exceed the value specified by the absorption constraint. The range of this value is related to the object to be recorded;

[0033] (S5) Propagate the complex-valued field C forward to a 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 input for the next round of the network;

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

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

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

[0037] In step (S5), the optimization algorithms include the structural similarity algorithm, the mean squared error algorithm, the sum of squared errors algorithm, etc. In this embodiment, the structural similarity algorithm is used.

[0038] The above is a preferred embodiment of the present invention, but the embodiments of the present invention are not limited to the above content. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all 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), select a camera to capture a set of pure-phase coaxial holograms based on coaxial holography theory as the network input, namely hologram A; (S2), after reading the captured hologram A, perform a square root operation to obtain the amplitude, and generate a random matrix of the same size as hologram A as the initial phase. Construct 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 transform, add in the spatial domain, and then add non-linearity through the split-relu activation function. Repeat this process multiple times to obtain the output complex-valued field C; (S4), perform soft constraint on the amplitude of the output complex-valued field C so that the value of each point does not exceed the value specified by the absorption constraint. The range of this value is related to the recorded object; (S5), propagate the complex-valued field C forward to a 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. The updated complex-valued field B is the input for the next round of the network; (S6), calculate the data fidelity term, that is, the similarity between hologram A and the reconstructed hologram D, calculate the complex-valued regularization term complex total variation, namely CTV, assign weights to the two terms and add them as the loss function. Perform backpropagation on the gradient of the loss function value to update the parameters of the network model, and obtain the 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, wherein In step (S1), the captured 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 a dual-domain complex-valued neural network according to claim 1, characterized in that In step (S5), the forward propagation method includes the angular spectrum method, the Fresnel diffraction method, and the convolution method.

4. The lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network according to claim 1, wherein The spatial domain convolution is a two-dimensional complex-valued convolution, where the complex-valued convolution is implemented by a convolution kernel of 3×3. The frequency-domain learning is to establish a learnable matrix of the same size as the input image, multiply the matrix by the spectral points, and continuously optimize the parameters of the learnable matrix.

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

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

7. The lightweight coaxial holographic reconstruction method based on a dual-domain complex-valued neural network according to claim 1, wherein 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, characterized in that, Adopt self-supervised learning. In step (S5), the reconstructed hologram D is also obtained by simulating the diffraction process after the captured hologram A passes through the network output. Calculate the loss between the two and perform backpropagation to guide the network training.

Images