High-robustness Fourier lamination imaging method based on wavelet transform

Abstract

The invention discloses a high-robustness Fourier lamination imaging method based on wavelet transform. The method comprises the following steps: acquiring a low-resolution image in a Fourier lamination imaging system; reconstructing a prediction image; according to the initially collected LED illumination image, generating a predicted complex amplitude light field under the current LED illumination wave vector; setting the number of iteration updating times, and performing a non-convex optimization process in a single LED iteration reconstruction process; carrying out two-dimensional wavelet transformation on the difference between the obtained initial prediction image and the original acquisition image, and introducing the two-dimensional wavelet transformation to different types of wavelet bases for decomposition; processing the information of each dimension in a wavelet domain; replacing original information with gradient information obtained by estimation in a feature domain, then updating the initial complex field, and carrying out iterative reconstruction until all LED illumination light fields are traversed; after traversal is completed, gradient information under all LED wave vectors is obtained, an optimizer is added to carry out an accelerated optimization process on the gradient information, and meanwhile local minimum is avoided.

Description

Technical Field

[0001] The invention relates to the technical fields of computational optical imaging and quantitative phase imaging, and in particular to a high-robustness Fourier stack imaging method based on wavelet transform. Background Art

[0002] Pathological analysis is the gold standard for disease detection and diagnosis. Whole slide imaging (WSI) is widely used by doctors in clinics for pathological detection. The stitching is completed by scanning the slices with a high-precision electronically controlled platform. Unavoidable problems such as high hardware requirements, stitching artifacts and misalignment of WSI will directly affect the accuracy of diagnosis. Fourier ptychographic microscopy (FPM) is a non-interferometric computational imaging technology that combines angle-varying illumination and synthetic aperture technology. It traditionally uses a ptychographic iterative engine (PIE) algorithm to correct optical system aberrations, providing a large field of view, wide depth of field and high resolution without the need for additional mechanical scanning or optical elements. Due to these advantages, FPM has been widely used in various fields, including WSI, biomedicine and materials engineering. In addition, more technologies have been derived, such as far-field FPM, 3D FPM, color FPM, fast FPM, etc. These methods recognize the advantages of FPM and are committed to improving imaging performance to expand its biomedical applications.

[0003] In addition to those promising achievements of FPM, there are a large number of publications reporting how to solve FPM system problems, including but not limited to LED position mismatch, significant aberration compensation, noise signal suppression, and how to solve vignetting effects. This fact means that FPM is not actually user-friendly, which limits its acceptance in fields outside of optics, such as biomedicine and pathology. However, the reported improvements involve trade-offs between correction efficiency, data redundancy, and reconstruction accuracy. In addition, the linear time-invariant imaging model in FPM deals with the actual nonlinear time-varying optical system, resulting in forward model mismatch. In short, the naive FPM forward model simplifies the actual process of FPM imaging and cannot effectively solve outliers, especially systematic errors. Since the first demonstration of FPM in 2013, the FPM recovery framework developed based on PIE has remained unchanged for decades. The old-school L2 norm loss function used in most reported FPM implementations has been proven to be inefficient because they ignore the advantages of the non-convex nature of phase retrieval. Therefore, a new computational framework is needed to bring a breakthrough to FPM technology. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a highly robust Fourier stack imaging method based on wavelet transform, which can achieve non-stitching, highly robust, and high-resolution imaging.

[0005] In order to solve the above technical problems, a technical solution adopted by the present invention is to provide a highly robust Fourier stack imaging method based on wavelet transform, comprising the following steps:

[0006] Step 1: In the Fourier stack imaging system, lighting units in the programmable LED lighting array are sequentially illuminated to complete low-resolution image acquisition;

[0007] Step 2: Simulate and generate the position of the actual LED lighting array and the lighting order of the LED light source in step 1, and record the spatial position coordinates under the corresponding LED lighting to reconstruct the predicted image;

[0008] Step 3: Generate a predicted complex amplitude light field under the current LED lighting wave vector based on the initially collected LED lighting image;

[0009] Step 4: Set the number of iteration updates. During the iterative reconstruction of a single LED, evaluate the difference between the complex amplitude of the actual collected light field and the predicted complex amplitude light field obtained under the current LED simulated pupil position. This process is a non-convex optimization process.

[0010] Step 5: In the non-convex optimization process of a single LED, the difference between the initial predicted image and the original collected image is transformed into a two-dimensional wavelet transform, and introduced into different types of wavelet bases for decomposition to obtain the information of each dimension of the specified number of layers;

[0011] Step 6: Process the information of each dimension in the wavelet domain;

[0012] Step 7: Obtain the initial complex field from the original image, replace the original information with the estimated gradient information in the feature domain, and then update the initial complex field. Use the wavelet loss function to restore the complex amplitude U and pupil P. Finally, reconstruct the updated complex field iteratively until all LED lighting light fields are traversed.

[0013] Step 8: After the traversal is completed, the gradient information of all LED wave vectors is obtained, and an optimizer is added to accelerate the optimization process of the gradient information to avoid the reconstruction process falling into the local minimum;

[0014] Step 9: After reaching the preset number of iterations, the reconstruction is completed to obtain the sample amplitude and phase information, and the system aberration is reconstructed.

[0015] In a preferred embodiment of the present invention, in step 1, the entire Fourier stack imaging process can be expressed by formula I n =|F -1 PM n FU|2 +η represents; where U is the target complex amplitude to be reconstructed and restored, M n is the selection matrix of the nth LED lighting, recording the frequency domain coordinates of the current LED lighting position, F and F-1 are the Fourier transform and inverse Fourier transform, P is the pupil function under the current objective lens parameters of the system, and η is the noise signal existing in the collected image.

[0016] In a preferred embodiment of the present invention, in step 4, the non-convex optimization process minimizes the difference between the complex amplitude of the generated predicted image and the complex amplitude of the original acquired image, and its loss function is expressed as:

[0017]

[0018] Among them, U is the target complex amplitude to be reconstructed and restored, M n is the selection matrix for the nth LED lighting, recording the frequency domain coordinates of the current LED lighting position, F and F -1 is the Fourier transform and inverse Fourier transform, P is the pupil function under the current objective lens parameters of the system, I n To actually collect the light field.

[0019] Furthermore, in step five, the difference between the initial predicted image and the original captured image is subjected to a two-dimensional wavelet transform, and the loss function is rewritten as:

[0020]

[0021] in, It is a wavelet transform. It is assumed that the noise signal in the wavelet domain is a super-Laplace distribution, and the loss function of the wavelet FPM is taken as the P norm of the model prediction difference.

[0022] In a preferred embodiment of the present invention, in step five, the dimensional information includes four components contained in each decomposed layer: wavelet approximation details, diagonal details, horizontal details and vertical detail coefficients.

[0023] In a preferred embodiment of the present invention, in step six, each dimensional information is processed in the wavelet domain including noise reduction and smoothing.

[0024] In a preferred embodiment of the present invention, in step 7, in the feature domain, the error image after wavelet processing is transformed into the frequency domain, its feature domain multi-scale parameters are calculated, and the complex amplitude is restored using the wavelet loss function U and pupil P , which is expressed as follows:

[0025]

[0026] Among them, k x and ky Indicates the current LED lighting wave vector edge x ,y components in both directions; represents the complex amplitude in the frequency domain at the wave vector k x and k y The difference is calculated; the gradient adjustment wavefront parameter of the complex amplitude U and pupil function P is w1(k x ,k y ) and w2(k x ,k y ).

[0027] The beneficial effects of the present invention are:

[0028] In order to reduce model mismatch and enhance the practical application of FPM in biomedicine, the present invention redesigns the loss function to handle nonlinear and time-varying systems. Wavelet transform has attracted widespread attention due to its ability to effectively analyze the rapid changes of transient signals and thus provide accurate local time and frequency information. Wavelet transform can decompose data into different frequency components. This ability is particularly effective in processing discontinuous and bursty information.

[0029] Therefore, the present invention proposes a set of highly robust FPM algorithms based on wavelet transform, called WL-FPM. This method can better adapt to the complexity of natural systems and solve practical problems such as LED position mismatch, LED intensity fluctuation, various noises, vignetting effects, etc. The wavelet forward model takes into account the influence of the feature domain on the reconstructed image and utilizes the multi-scale translation and expansion of the basis function. The model works in a multi-scale feature domain and has unique scale characteristics. The wavelet basis is selected efficiently and flexibly according to different system environments, so that the model can better capture the local features and detail information of the image. The high flexibility of WL-FPM greatly enhances its versatility, and this feature makes WL-FPM suitable for robust and high-resolution imaging of various biomedical samples. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of the highly robust Fourier stack imaging method based on wavelet transform of the present invention;

[0031] Figure 2 Schematic diagram of the resolution comparison between the present invention and the traditional ePIE algorithm;

[0032] Figure 3 The method of the present invention is used to reconstruct the phase image of the entire field of view of L929 cells. DETAILED DESCRIPTION

[0033] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making a clearer and more definite definition of the protection scope of the present invention.

[0034] See also Figure 1 , the embodiment of the present invention includes:

[0035] A highly robust Fourier stack imaging method based on wavelet transform comprises the following steps:

[0036] Step 1: In the Fourier stack imaging system, lighting units in the programmable LED lighting array are sequentially illuminated to complete low-resolution image acquisition;

[0037] After the FPM system is built, the programmable circular LED illumination array is controlled by a single-chip microcomputer to light up one by one, and the intensity of each LED is switched by the serial port input value. In the Fourier stack imaging system, lighting up a specific LED unit in the illumination array is equivalent to translating its objective lens pupil in the corresponding direction in the spectrum. When the LED light source illuminates the sample, the incident light is assumed to be a plane wave. In general, the sample is weakly absorbed. The transmitted light waves carry information of different frequencies, but the ideal objective lens pupil is a circular low-pass filter that only collects limited light wave information. After the light wave passes through the tube lens, it is equivalent to performing an inverse Fourier transform in the focal plane. Then, the camera sensor collects the intensity information to obtain a low-resolution image. This process can be described as:

[0038] I n =|F -1 PM n FU| 2 +η n ,

[0039] Where U is the target complex amplitude to be reconstructed, M n is the selection matrix of the nth LED lighting. F represents Fourier transform, F -1 represents the inverse Fourier transform. P is the system pupil function. Generally, the ideal pupil function is set to 1 at the cutoff frequency of the objective lens and 0 at the external frequency. η n Represents the image domain noise signal.

[0040] Step 2: Simulate and generate the position of the actual LED lighting array and the lighting order of the LED light source in step 1, and record the spatial position coordinates under the corresponding LED lighting to reconstruct the predicted image;

[0041] Step 3: Generate a predicted complex amplitude light field under the current LED lighting wave vector based on the initially collected LED lighting image;

[0042] Step 4: Set the number of iteration updates. During the iterative reconstruction of a single LED, evaluate the difference between the complex amplitude of the actual collected light field and the predicted complex amplitude light field obtained under the current LED simulated pupil position. This process is a non-convex optimization process.

[0043] The iteration starts with the reconstruction of amplitude and phase, evaluating the difference in complex amplitude between the actual collected light field and the predicted light field under the current LED illumination wave vector. The traditional FPM technology hopes to minimize the gap between the predicted image and the actual collected image. Its loss function can be expressed as:

[0044]

[0045] Among them, U is the target complex amplitude to be reconstructed and restored, M n is the selection matrix of the nth LED lighting, recording the frequency domain coordinates of the current LED lighting position, F and F -1 is the Fourier transform and inverse Fourier transform, P is the pupil function under the current objective lens parameters of the system, I n To actually collect the light field.

[0046] Step 5: In the non-convex optimization process of a single LED, the difference between the initial predicted image and the original collected image is transformed into a two-dimensional wavelet transform, and introduced into different types of wavelet bases for decomposition to obtain the information of each dimension of the specified number of layers;

[0047] Since the reconstruction process is a non-convex optimization problem, wavelet transform has excellent local characteristics of time, space and frequency, and the image difference can be accurately evaluated by shrinking and translating the wavelet basis. The loss function of equation (1) is rewritten as follows through two-dimensional wavelet transform:

[0048]

[0049] in is the wavelet transform. Batch is a batch. Since the wavelet transform is reversible, the "=" sign is valid and will not cause data loss. Assuming that the noise signal in the wavelet domain is a super-Laplace distribution, the loss function of the wavelet FPM is taken as the P norm of the model prediction difference.

[0050] Step 6: Process the information of each dimension in the wavelet domain. In this step, the initial difference image can be denoised and smoothed;

[0051] After wavelet decomposition, the wavelet basis carries different image information. Here we take the Daubechies (db) wavelet basis as an example, which has a scaling function and a wavelet function. It can be expressed as:

[0052]

[0053] Where φ (x) is the scaling function, ψ (x) is the wavelet function. k and b kThey are expressed as scaling coefficients and wavelet coefficients respectively. N represents the filter length. φ(θx-k) is used to control the translation and scaling of the wavelet, where θ is the scaling factor and k In multi-resolution analysis, the scaling function φ(x) represents the low-frequency contour component of the signal and is determined by the low-pass filter factor a. k The wavelet function ψ(x) represents the high-frequency detail component.

[0054] In FPM using the db wavelet basis, the one-dimensional wavelet decomposition of rows and columns is expressed as

[0055]

[0056] Combining the one-dimensional wavelet basis function with the tensor product (Kronecker product), the basis function of the two-dimensional wavelet transform can be constructed. The two-dimensional wavelet basis function can be divided into four coefficients, namely the approximate detail coefficient (A), the diagonal detail coefficient (D), the horizontal detail coefficient (H) and the vertical detail coefficient (V):

[0057]

[0058] Combining the above one-dimensional wavelet decomposition, we can get the specific formula of two-dimensional wavelet decomposition:

[0059]

[0060] In this step, the wavelet decomposition coefficients can be processed. In order to update the coefficients of the above equation in iteration, the soft threshold method can be used:

[0061] a′ i,j,k,l =sign(a i,j,k,l )·max(|a i,j,k,l |-λ,0),

[0062] b′ i,j,k,l =sign(b i,j,k,l )·max(|b i,j,k,l |-λ,0),

[0063] c′ i,j,k,l =sign(c i,j,k,l )·max(|c i,j,k,l |-λ,0),

[0064] d′ i,j,k,l =sign(d i,j,k,l )·max(|d i,j,k,l |-λ,0).

[0065] Step 7: Obtain the initial complex field from the original image, replace the original information with the estimated gradient information in the feature domain, and then update the initial complex field. Use the wavelet loss function to restore the complex amplitude U and pupil P. Finally, reconstruct the updated complex field iteratively until all LED lighting light fields are traversed.

[0066] Due to the reversibility of wavelets, the signal can be decomposed and reconstructed. Different from the traditional image domain, the feature domain framework needs to transform the error image after wavelet processing into the frequency domain, calculate its feature domain multi-scale parameters, and use the wavelet loss function to restore the complex amplitude U and pupil P, which is expressed as follows:

[0067]

[0068] Among them, k x and k y Indicates the current LED lighting wave vector edge x ,y components in both directions; represents the complex amplitude in the frequency domain at the wave vector k x and k y The difference is calculated; the gradient adjustment wavefront parameter of the complex amplitude U and pupil function P is w1(k x ,k y ) and w2(k x ,k y ).

[0069] The feature domain inversion updates the gradient under the current illumination wave vector. Since the feature domain gradient information is insensitive to the global intensity image, its robustness to various system errors is greatly increased. After completing the reconstruction of the current LED wave vector, repeat this process until all LED illumination light fields are traversed.

[0070] Step 8: After the traversal is completed, the gradient information of all LED wave vectors is obtained, and an optimizer is added to accelerate the optimization process of the gradient information to avoid the reconstruction process falling into the local minimum;

[0071] After the traversal is completed, the gradient information of all LED wave vectors is obtained and added to the optimizer to speed up the optimization convergence process and avoid falling into the local minimum. One of the commonly used optimizers is RMSprop, which can handle non-stationary objective functions well. RMSprop adaptively adjusts the learning rate to effectively reduce oscillation and speed up convergence. Update the complex amplitude in this iteration U and pupil function P :

[0072] E[dw1 2 ] t =ρE[dw1 2 ] t-1 +(1-ρ)((dw1) t ) 2

[0073]

[0074] E[dw2 2 ] t =ρE[dw2 2 ] t-1 +(1-ρ)((dw2) t ) 2

[0075]

[0076] E[dw1 2 ] and E[dw2 2 ] is the mean square of the gradient shift. ρ is the decay rate. And dw1 and dw2 are the gradients of the current target, and η is the learning rate. Parameter U t+1 (k x ,k y ) and P t+1 (k x ,k y ) is updated in each iteration based on the learning rate, momentum, and other information. For each LED lighting, the complex amplitude of the object is updated using the gradient information U And the pupil function P:

[0077]

[0078] Step 9: After reaching the preset number of iterations, the reconstruction is completed to obtain the sample amplitude and phase information, and the system aberration is reconstructed.

[0079] In order to verify the effect of the algorithm described in the present invention, the resolution of the present invention and the traditional ePIE algorithm are compared. Figure 2 The bright field image is shown in Figure 2 (a) shows the enlarged areas of the red and green boxes. Figure 2 (b) As shown in Figure 2, the green area shows higher contrast due to the change in the LED incident angle. However, the image details are affected by the vignetting effect. Figure 2 (c) shows their Fourier spectra. The theoretical value of the synthetic NA of the system is about 0.64 (red circle), which is determined by the sum of the objective lens NA and the illumination NA. The comparison shows the loss of high-frequency regions in the ePIE spectrum. In WL-FPM, the edge and detail information of the reconstructed image can be better preserved and enhanced by using a two-dimensional wavelet transform. Compared with the traditional ePIE algorithm, WL-FPM shows higher spectral values ​​in these areas. This means that WL-FPM can reconstruct more resolution within a limited data range. Figure 2(d) Reconstructed aberrations for WL-FPM and ePIE. Under these distortions, traditional PIE methods are prone to falling into local minima, resulting in reconstruction failures using these methods without prior knowledge. Since ePIE is sensitive to systematic errors in the image domain, it cannot reconstruct systematic aberrations. In contrast, WL-FPM avoids these problems and performs well in aberration reconstruction. Figure 2 (e) shows the reconstruction of the quantitative phase target (QPT, benchmark, USAF). In the ePIE reconstruction, the FPM performance is affected by the noise of the industrial camera, which causes some edge areas to fall into local minima, produce artifacts, and have poor reconstruction. In WL-FPM, an optimizer is used to avoid falling into local minima during the iteration process. In addition, the flexibility of choosing the wavelet basis makes it more adaptable to various environments. Therefore, WL-FPM shows better reconstruction performance with a uniform background, distinct edges, and clearer details. We use the USAF1951 target plate to measure the resolution of the system, which consists of groups and elements. According to the Rayleigh criterion, for an objective lens with a NA of 0.1, the effective resolution is limited to 3.25μm. Figure 2 (f) shows Figure 2 In the enlarged area of ​​the yellow box in (e), the second element of group 10 can be observed. The quantitative phase profiles along the M1 line of group 9 and the M2 line of group 10 are shown in Figure 2. Figure 2 (g1) and 2(g2). In group 9, the ePIE curve shows that the peak of element 5 is not clear, indicating that the resolution of ePIE is 615nm. However, the WL-FPM we proposed can show all the details of group 9. When we plotted the profile of group 10, element 2 showed three clear peaks in WL-FPM, indicating that a resolution of 435nm was achieved. Compared with the Rayleigh criterion, the lateral resolution is improved by about 7.46 times. The experimental results confirm that WL-FPM has high robustness and good resolution.

[0080] At the same time, the FPM algorithm of the present invention is used to reconstruct L929 cells, and the phase image is as follows Figure 3 As shown, Figure 3(a) is a bright field image acquired under central LED illumination. Only low-frequency sample information can be observed at this NA. In the lower right corner of the image, for the same image data, the image is reconstructed using three conventional algorithms (ePIE, rPIE, and tPIE). When the entire field of view is reconstructed using the rPIE and ePIE algorithms, artifacts shown by red arrows appear. These artifacts are caused by inherent noise interference and other systematic errors, causing these algorithms to fall into local minima. Since the iterations of tPIE can be calibrated by deviations and normalization factors, cellular details can be clearly observed without artifacts. Compared with the previous three phase images of the same field of view, our WL-FPM has higher contrast and resolution, as shown in Figure 2. Figure 3 (b) Compared with the tPIE phase image, there are no artifacts in the WL-FPM reconstructed image, and the edge details and cell nuclei are clearly visible. For the bright field image after magnification in the green frame area, as shown in Figure 3 (c) shows that the subcellular structure of the original bright field image is blurred. Figure 3 In each reconstructed image in (d1)-(d4), the phase profile drawn along the yellow dashed line is shown in the figure. The distortion caused by LED light intensity fluctuations and position offsets limits the robustness of the three traditional FPM reconstruction results in practical applications. Among the four reconstruction methods, WL-FPM shows a clear peak in the phase spectrum, indicating a large number of well-defined lipid droplets in the cytoplasm. The other three methods only provide fuzzy clustering without clear subcellular boundaries. In the WL-FPM reconstruction process, wavelet transform and optimizer are used to retain both low-frequency information and high-frequency details in the iterative process. Due to its high resolution and robustness, WL-FPM is more suitable for the observation of biological cells and can provide a new method for studying cell proliferation, migration and dynamics.

[0081] Different from the traditional image domain optimization method, this technology adds wavelet transform to the basic iterative process of Fourier stack imaging to broaden its spectrum range, and through the reversibility of wavelet transform, it significantly reduces the algorithm's dependence on image quality. The complex back diffraction method is used to solve the non-convex optimization problem. This method iteratively reconstructs in the multi-dimensional feature domain and uses wavelet multi-scale translation to calculate the loss function of each LED lighting. Wavelets are used to learn gradient information and then use optimizers to accelerate the optimization process, while avoiding local minima to achieve high-fidelity, high-resolution feature domain reconstruction. For different system environments, the wavelet basis and wavelet decomposition layer number are effectively and flexibly selected to focus on the local features and detail information of the reconstructed image, so that it can adapt to different system environments.

[0082] As a general Fourier stack imaging system framework, the method can simultaneously solve various practical problems such as correction of large aberrations, reconstruction under vignetting effects, and large-scale position deviation of LEDs, which are difficult to solve with traditional image domain algorithms, without adding algorithms or making additional optical system modifications. This feature makes it suitable for high-robustness and high-resolution imaging of various biological samples.

[0083] Such a unique computational framework can immediately benefit a wide range of applications related to phase retrieval, including biomedical imaging, remote sensing, and pattern recognition, and have profound implications for optical computing and wavefront shaping.

[0084] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above embodiments can be implemented by software, or by means of software plus necessary general hardware platforms. Based on such understanding, the technical solutions of the above embodiments can be embodied in the form of software products, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.), including several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of various embodiments of the present invention.

[0085] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A highly robust Fourier stack imaging method based on wavelet transform, characterized in that: The following steps are involved: Step 1: In the Fourier stack imaging system, lighting units in the programmable LED lighting array are sequentially illuminated to complete low-resolution image acquisition; Step 2: Simulate and generate the position of the actual LED lighting array and the lighting order of the LED light source in step 1, and record the spatial position coordinates under the corresponding LED lighting to reconstruct the predicted image; Step 3: Generate a predicted complex amplitude light field under the current LED lighting wave vector based on the initially collected LED lighting image; Step 4: Set the number of iteration updates. During the iterative reconstruction of a single LED, evaluate the difference between the complex amplitude of the actual collected light field and the predicted complex amplitude light field obtained under the current LED simulated pupil position. This process is a non-convex optimization process. Step 5: In the non-convex optimization process of a single LED, the difference between the initial predicted image and the original collected image is transformed into a two-dimensional wavelet transform, and introduced into different types of wavelet bases for decomposition to obtain the information of each dimension of the specified number of layers; Step 6: Process the information of each dimension in the wavelet domain; Step 7: Obtain the initial complex field from the original image, replace the original information with the estimated gradient information in the feature domain, update the initial complex field, and restore the complex amplitude using the wavelet loss function U and pupil P , and finally the updated complex field is iteratively reconstructed until all LED lighting light fields are traversed; Step 8: After the traversal is completed, the gradient information of all LED wave vectors is obtained, and an optimizer is added to accelerate the optimization process of the gradient information to avoid the reconstruction process falling into the local minimum; Step 9: After reaching the preset number of iterations, the reconstruction is completed to obtain the sample amplitude and phase information, and the system aberration is reconstructed.

2. The highly robust Fourier stack imaging method based on wavelet transform according to claim 1, characterized in that: In step 1, the entire Fourier stack imaging process can be expressed by formula I n =|F -1 PM n FU| 2 +η represents; where U is the target complex amplitude to be reconstructed and restored, M n is the selection matrix of the nth LED lighting, recording the frequency domain coordinates of the current LED lighting position, F and F -1 is the Fourier transform and inverse Fourier transform, P is the pupil function under the current objective lens parameters of the system, η is the noise signal existing in the acquired image.

3. The highly robust Fourier stack imaging method based on wavelet transform according to claim 1, characterized in that: In step 4, the non-convex optimization process minimizes the difference between the complex amplitude of the generated predicted image and the complex amplitude of the original acquired image. The loss function is expressed as: Among them, U is the target complex amplitude to be reconstructed and restored, M n is the selection matrix of the nth LED lighting, recording the frequency domain coordinates of the current LED lighting position, F and F -1 is the Fourier transform and inverse Fourier transform, P is the pupil function under the current objective lens parameters of the system, I n To actually collect the light field.

4. The highly robust Fourier stack imaging method based on wavelet transform according to claim 3, characterized in that: In step 5, the difference between the initial predicted image and the original captured image is transformed into a two-dimensional wavelet transform, and the loss function is rewritten as: in, It is a wavelet transform. It is assumed that the noise signal in the wavelet domain is a super-Laplace distribution, and the loss function of the wavelet FPM is taken as the P norm of the model prediction difference.

5. The highly robust Fourier stack imaging method based on wavelet transform according to claim 1, characterized in that: In step five, the various dimensional information includes four components contained in each decomposed layer: wavelet approximation details, diagonal details, horizontal details and vertical detail coefficients.

6. The highly robust Fourier stack imaging method based on wavelet transform according to claim 1, characterized in that: In step six, each dimension of information is processed in the wavelet domain including noise reduction and smoothing.

7. The highly robust Fourier stack imaging method based on wavelet transform according to claim 1, characterized in that: In step 7, in the feature domain, the error image after wavelet processing is transformed into the frequency domain, its feature domain multi-scale parameters are calculated, and the complex amplitude is restored using the wavelet loss function. U and pupil P , which is expressed as follows: Among them, k x and k y Indicates the current LED lighting wave vector edge x ,y components in both directions; represents the complex amplitude in the frequency domain at the wave vector k x and k y The difference is calculated; the gradient adjustment wavefront parameter of the complex amplitude U and pupil function P is w1(k x ,k y ) and w2(k x ,k y ).

Images