WO2021097916A1 - Method and system for reconstructing high-fidelity image, computer device, and storage medium - Google Patents

Abstract

A method and system for reconstructing a high-fidelity image, a computer device, and a storage medium. The method comprises: reading a SIM image; generating or reading the measured PSF; estimating a structured light fringe parameter; and reconstructing a high-fidelity super-resolution SIM image by using a spectrum optimization method. The system comprises: an image acquisition module, a parameter estimation module, (a PSF generation module), and an image reconstruction module. The computer device and the storage medium can implement the processes of the method by executing a computer program. The method or system can effectively solve the artifact problem in the super-resolution SIM image, achieve high-fidelity reconstruction of the super-resolution SIM image, greatly improve the axial layer cutting capability of the 2D-SIM technology, so that the 2D-SIM technology can obtain the layer cutting capability comparable with the 3D-SIM technology, and effectively expand the application scenario of the 2D-SIM technology. In addition, the method or system can still reconstruct a high-fidelity super-resolution SR-SIM image by using the theory to generate the PSF to replace the complicated PSF measurement process. The method or system is suitable for data processing of almost all SIM systems based on the structured illumination technology principle.

Description

High-fidelity image reconstruction method, system, computer equipment and storage medium Technical field

The invention relates to the field of super-resolution microscopic imaging and three-dimensional surface measurement using structured light illumination technology, and in particular to a high-fidelity image reconstruction method, system, computer equipment and storage medium of a super-resolution structured light illumination microscope.

Background technique

Super-resolution Structured Illumination Microscopy (SR-SIM) is a wide-field microscopy imaging technology that can break through the Abbe diffraction limit due to its non-invasiveness, fast imaging speed, and low light damage. The advantages have been widely used in biomedical research. The SIM technology uses structured light with a sinusoidal distribution of intensity to illuminate the observed sample to produce a "Moiré effect", which can encode high-frequency information that cannot be directly detected within the optical transfer function of the microscope objective into the low-frequency area of the detection objective to be collected, and then collected by The image reconstruction algorithm decodes the high-frequency component information from the collected multiple original images, and reconstructs the final super-resolution image (as shown in Figure 1). Theoretically, linear SIM (Linear SIM, L-SIM) can achieve a resolution increase of about 2 times, and nonlinear SIM (Nonlinear SIM, NL-SIM) can further improve the resolution on the basis of L-SIM.

It is particularly emphasized that the final super-resolution image obtained by the SIM microscope relies heavily on post-processing image reconstruction algorithms. At present, although various versions of SIM algorithms have been developed including commercial SIM systems (Ge, Nikon, and Zeiss) and the SIM system built by the laboratory, almost all SIM algorithms still follow the classic Wiener-SIM refactoring proposed by Gustafsson et al. The two-step process of the construction algorithm: Step1: Estimate the structured light fringe parameters from the collected raw data (including the spatial frequency of the illumination fringe (strip wave vector) k _θ , the initial phase

And modulation m); Step2: Use the estimated fringe parameters to separate and extract the 0-level spectrum and the high-level sub-spectrum from the original image (2D-SIM: ±1 level; 3D-SIM and NL-SIM: ±1 level and ±2 Level), and translate the high-level spectrum to the correct position, and use the Wiener filter deconvolution algorithm to achieve spectrum fusion, so as to obtain the final super-resolution image.

However, the super-resolution image reconstruction process of SIM is essentially an ill-conditioned inverse problem that is extremely prone to artifacts. Since the invention of the SIM technology, the fidelity of the SIM technology has been challenged due to the typical artifacts contained in the SIM super-resolution image. Artifacts are often found in SIM super-resolution images in many published articles, and these artifacts in super-resolution images have caused some high-level research results to be questioned. Typical artifacts commonly seen in SIM images include honeycomb artifacts, “sidelobe” artifacts, “snowflake” artifacts, and “hammerstroke” artifacts. artifacts) and so on. At present, although most of the sources of these typical artifacts have been clearly studied, there is still no effective SIM algorithm that can completely eliminate these artifacts.

At present, the development of SIM technology is moving towards the pursuit of minimizing artifacts or even no artifacts. In the early days, researchers mostly focused on step 1 of the SIM reconstruction process-optimizing the structured light parameter estimation algorithm to determine accurate illumination fringe parameters from the original image to reduce reconstruction artifacts. However, even if the illumination parameters are accurately estimated, the artifacts in the reconstructed super-resolution image cannot be effectively avoided. In recent years, some deconvolution algorithms, including RL-SIM, TV-SIM and Hession-SIM, have been developed to suppress artifacts, but these methods are only used for specific types of data (such as high modulation and low signal noise). Compared with the original data), the effect is more obvious, and it is still unable to effectively suppress the artifacts for some original data with strong background or sub-optimal modulation. Up to now, there is no general algorithm that can effectively remove the typical artifacts in the reconstructed SIM image.

At the same time, the conventional two-dimensional SIM (2D-SIM) has poor axial optical slice cutting capability, resulting in all current 2D-SIM super-resolution images usually containing obvious residual defocus background and artifacts related to defocus signals. shadow. In addition, the poor axial slice ability will also cause 2D-SIM technology to image strong background samples or thick samples, the artifacts in the super-resolution image reconstructed by the algorithm will be aggravated, and the spatial resolution and contrast of the reconstructed image will also be increased. Lower. Therefore, the problem of the weak axial layer cutting capability of 2D-SIM has limited the application of SIM technology in more fields.

In addition, most of the existing SIM algorithms are very sensitive to the point spread function (PSF) used by the algorithm. In order to ensure that the algorithm reconstructs the SIM super-resolution image with minimal artifacts, the SIM algorithm usually requires the use of real PSF that matches the imaging conditions of the original image acquisition. However, in the actual imaging process, it is very difficult to simultaneously measure the PSF that matches the imaging conditions. On the one hand, measuring the matched PSF usually requires very complicated steps and requires professionals to complete; on the other hand, the measurement process of the real PSF increases the difficulty of using SIM technology, which will make some ordinary users unacceptable. Currently, most of the literature uses PSF measured by fluorescent beads as the real PSF for algorithm reconstruction. However, the PSF measured using fluorescent microspheres is only an approximate PSF, which still cannot be strictly matched to the imaging conditions.

Summary of the invention

Based on this, it is necessary to solve the above technical problems and provide a high-fidelity reconstruction method for realizing SIM super-resolution images that can take into account the removal of artifacts and the improvement of the slice cutting ability, and reduce the difficulty of using the SIM technology.

The technical solution to achieve the objective of the present invention is: a high-fidelity image reconstruction method, the method includes:

Read multiple frames of original images collected by the SIM imaging system;

Estimate structured light fringe parameters, including estimating structured light fringe wave vector k _θ , estimating fringe modulation degree m and initial phase

Based on the result of the structured light fringe parameter estimation, the spectrum optimization method is used to reconstruct the high-fidelity SIM super-resolution image.

Further, before the method for reconstructing a high-fidelity SIM super-resolution image using the spectrum optimization method, the method further includes: generating a point spread function PSF based on a theoretical model, which specifically includes:

Use the optical parameters of the SIM imaging system to generate the optical transfer function OTF:

In the formula, k _c is the cut-off frequency of the imaging objective lens;

For the optical transfer function

Perform the inverse Fourier transform to generate the point spread function PSF(r).

Further, the estimated structured light fringe wave vector k _θ specifically includes:

The original image is preprocessed to eliminate out-of-focus signals, 0-level spectrum signals, and

The influence of the attenuation of high-frequency signals in the original image on the estimated structured light fringe wave vector k _θ ;

Based on the preprocessed original image, cross-correlation is performed to estimate the structured light fringe wave vector k _θ .

Further, the preprocessing of the original image specifically includes:

Sum and average the read multiple original images D _θ,n (r) to obtain the equivalent wide-field image D _EWF,θ (r);

Introduce the constant weight factor α _θ , and combine the equivalent wide-field image D _EWF,θ (r) to process the single frame original image D _θ,n (r) to obtain a new single frame original image D' _θ,n (r ), the formula used is:

D' _θ,n (r)=D _θ,n (r)-α _θ □D _EWF,θ (r) (2)

In the formula, α _θ ∈[0,1], θ represents the direction angle, and n represents the phase;

Taking α _θ = 1, then the above formula (2) becomes:

D' _θ,n (r)=D _θ,n (r)-D _EWF,θ (r) (3)

The above formula (3) is subjected to deconvolution processing to obtain a new single-frame original image D' _θ,n (r) after the final preprocessing.

Further, the cross-correlation based on the preprocessed original image to estimate the structured light fringe wave vector k _θ specifically includes:

Perform SIM spectrum separation calculation on the new single-frame original image D' _θ,n (r) after the preprocessing, to obtain separated multi-level spectrum, including 0-level spectrum, 1-level spectrum, ..., L-level spectrum, The spectrum of each level is expressed as

among them,

Respectively represent +l level and -l level spectrum, the value of l is 0～L, k _θ represents the period of structured light;

Perform Fourier transform on the equivalent wide-field image D _EWF,θ (r) to obtain the equivalent wide-field image spectrum

For all spectrums except the 0-level spectrum and equivalent wide-field image spectrum

All perform spectral amplitude normalization processing;

Using a Gaussian function to perform notch processing on the central regions of all the normalized frequency spectra;

The equivalent wide-field image spectrum after the notch processing

And L-level spectrum

or

Perform cross-correlation calculation to obtain the peak position of the structured light fringe wave vector;

The sub-pixel precision fitting positioning is performed near the peak position to complete the estimation of the _{structured light fringe wave vector k θ.}

Further, the estimated fringe modulation degree m and the initial phase

Specifically:

Perform deconvolution preprocessing on the original image to obtain an image D" _θ,n (r);

Perform SIM spectrum separation calculation on the image D" _θ,n (r) to obtain separated multi-level spectrum, including 0-level spectrum, 1-level spectrum,..., L'-level spectrum, and each level of spectrum is expressed as

among them,

Respectively represent +l'-level and -l'-level spectra, the value of l'is 0～L', and k _θ represents the period of structured light;

Performing spectral amplitude normalization processing on all frequency spectra, and using Gaussian function to perform notch processing on the central area of all normalized frequency spectra;

Shift all the frequency spectra after the notch processing until the zero frequency of each level spectrum is consistent with the zero frequency of the 0 level spectrum; wherein, the shifted l'level spectrum is denoted as

For the equivalent wide-field image spectrum

Perform spectral amplitude normalization processing, and use Gaussian function to perform notch processing on the center area of the normalized equivalent wide-field image spectrum, denoted as

For each spectrum after translation

or

It and said

Cross-correlation calculation is performed on the overlapping area of, and the corresponding fringe modulation degree m _{l is obtained} ; the shifted level 1 spectrum

or

With said

Cross-correlation calculation for the overlapping area to obtain the initial phase

Further, the reconstruction of a high-fidelity SIM super-resolution image based on the structured light fringe parameter estimation result using a spectrum optimization method specifically includes:

Based on the result of the structured light fringe parameter estimation, reconstruct the initial SIM image spectrum

Use Gaussian function to analyze the spectrum of the initial SIM image

Notch processing in the central area of the sensor to obtain the frequency spectrum

Construct a composite filter

The frequency spectrum

With the composite filter

Multiply and perform inverse Fourier transform to obtain the final high-fidelity SIM super-resolution image.

Further, the reconstruction of the initial SIM image spectrum based on the structured light fringe parameter estimation result specifically includes:

Perform deconvolution preprocessing on the original image to obtain an image D"' _θ,n (r);

Based on the estimation results of the structured light fringe parameters, _{perform SIM spectrum separation calculation on the image D"' θ,n} (r) to obtain separated multi-level spectra, including level 0 spectrum, level 1 spectrum,..., L" level Spectrum, each level of spectrum is expressed as

among them,

Respectively represent +l” level and -l” level spectra, the value of l” is 0～L”, k _θ represents the period of structured light;

Shift all spectrums except the 0-level spectrum until the zero frequency of each level of the spectrum is consistent with the zero frequency of the 0-level spectrum; among them, the shifted l"-level spectrum is denoted as

Multiply the shifted spectrum of each level and the complex conjugate of its corresponding OTF and sum them, and reconstruct the spectrum of the initial SIM image as

Where

Indicates that the shifted l"-level spectrum corresponds to OTF, and "*" indicates conjugate;

The use of Gaussian function on the spectrum of the initial SIM image

Notch processing in the central area of the, to obtain the frequency spectrum

The formula used is:

Where

Represents the Gaussian function.

Further, the structured composite filter

The formula used is:

Where

It is the first composite sub-filter or the first single sub-filter, which is used to initially restore the zero-level spectrum, the first-level spectrum, ..., the L"-level spectrum that has been collapsed after the notch and translation processing;

It is the second composite sub-filter or the second single-sub filter, which is used to further restore the first-level spectrum,..., L"-level spectrum after the preliminary restoration, and at the same time, to reduce the amplitude of the 0-level spectrum after the preliminary restoration.

A high-fidelity image reconstruction system, the system includes:

Image acquisition module, used to read multiple frames of original images acquired by the SIM imaging system;

Parameter estimation module for estimating structured light fringe parameters, including estimating structured light fringe wave vector k _θ , estimating fringe modulation degree m and initial phase

The image reconstruction module is used to reconstruct a high-fidelity SIM super-resolution image based on the structured light fringe parameter estimation result by using a spectrum optimization method.

Further, the system further includes:

The point spread function PSF generation module is used to generate the point spread function PSF based on the theoretical model; the module specifically includes:

The OTF generating unit is used to generate the optical transfer function OTF using the optical parameters of the SIM imaging system. The formula used is:

In the formula, k _c is the cut-off frequency of the imaging objective lens;

PSF generating unit, used to compare the optical transfer function

Perform the inverse Fourier transform to generate the point spread function PSF(r).

A computer device includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The processor implements the following steps when the processor executes the computer program:

Read multiple frames of original images collected by the SIM imaging system;

Estimate structured light fringe parameters, including estimating structured light fringe wave vector k _θ , estimating fringe modulation degree m and initial phase

Based on the result of the structured light fringe parameter estimation, the spectrum optimization method is used to reconstruct the high-fidelity SIM super-resolution image.

A computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the following steps are implemented:

Read multiple frames of original images collected by the SIM imaging system;

Estimate structured light fringe parameters, including estimating structured light fringe wave vector k _θ , estimating fringe modulation degree m and initial phase

Based on the result of the structured light fringe parameter estimation, the spectrum optimization method is used to reconstruct the high-fidelity SIM super-resolution image.

Compared with the prior art, the present invention has significant advantages as follows: 1) Effectively solve a variety of typical artifacts that are easily generated in SIM super-resolution images, and realize high-fidelity reconstruction of SIM super-resolution images; 2) Effectively solve two-dimensional The problem of poor axial slice cutting capability of SIM technology (2D-SIM) makes 2D-SIM technology comparable to 3D-SIM technology to improve the quality of current 2D-SIM super-resolution images, thereby expanding the capabilities of SIM technology. Application scenarios; 3) Effectively solve the problem that the current SIM reconstruction algorithm is sensitive to the used PSF, use the PSF generated by the theoretical model to replace the complex process of measuring the real PSF, and use the generated rough PSF to still reconstruct the high-fidelity SIM ultra Resolving images reduces the difficulty of using SIM technology to a certain extent.

The present invention will be described in further detail below in conjunction with the accompanying drawings.

Description of the drawings

Figure 1 is a schematic diagram of the principle of linear SIM technology, in which Figure (a) is a schematic diagram of Moiré fringe generated by the Moiré effect, Figure (b) is a schematic diagram of the traditional wide-field imaging technology to detect the image spectrum range; Figure (c) is a unidirectional illumination Schematic diagram of the spectrum range of the SIM image; Figure (d) is a schematic diagram of the SIM spectrum range with three-directional angular illumination.

Fig. 2 is a flowchart of a high-fidelity image reconstruction method of a super-resolution structured light illumination microscope in an embodiment.

Figure 3 is a schematic diagram of the estimation principle of structured light fringe parameters in an embodiment, in which Figures (a) ~ (b) are _{schematic diagrams of the estimation principle of structured light fringe wave vector k θ} , combined on the basis of Figures (a) and (b) Figure (c) shows the fringe modulation degree m and the initial phase

Schematic diagram of estimation principle.

Figure 4 is a schematic diagram of spectrum optimization in an embodiment, where Figure (a) is the theoretical equivalent OTF of SIM, Figure (b) OTF of Gaussian notch modulation, Figure (c) ~ Figure (e) are the first sub filter

Second subfilter

Composite filter

Schematic diagram.

Figure 5 is a schematic diagram of the results of reconstructing a high-fidelity SIM super-resolution image using a spectrum optimization method in an embodiment, where Figures (a1) to (a3) are schematic diagrams of the reconstructed initial SR-SIM spectrum and the implementation of the initial spectrum Schematic diagram of Gaussian notch modulation and schematic diagram of spectrum optimization. Figures (b1) to (b3) are SR-SIM images corresponding to Figures (a1) to (a3), and Figures (c1) to (c4) are wide respectively. An enlarged view of the field image, and an enlarged schematic view of the sub-image of the rectangular box area in the diagrams (b1) to (b3).

Fig. 6 is a structural diagram of a high-fidelity image reconstruction system of a super-resolution structured light illumination microscope in an embodiment.

Figure 7 is a schematic diagram of the comparison of the results of the reconstruction of the HiFi-SIM algorithm and the conventional Wiener-SIM algorithm in an embodiment, where Figures (a1) to (a3) are the wide-field equivalent image and the conventional Wiener-SIM algorithm reconstruction respectively. The SIM image and the SIM image reconstructed by the HiFi-SIM algorithm of the present invention. Figures (b1) to (b3) are the wide-field equivalent image spectrum, the conventional Wiener-SIM algorithm reconstruction spectrum, and the HiFi-SIM algorithm reconstruction spectrum, respectively. .

Detailed ways

In order to make the purpose, technical solutions, and advantages of this application clearer, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present application, and are not used to limit the present application.

The high-fidelity image reconstruction method of the super-resolution structured light illumination microscope provided by the present invention is not only suitable for the reconstruction of 2D-SIM and 3D-SIM data, but also suitable for the non-linear structured light illumination microscope (NL-SIM). Super-resolution image reconstruction is suitable for almost all data processing of SIM systems based on the principle of structured light illumination technology.

In one embodiment, as shown in FIG. 2, a high-fidelity image reconstruction method (HiFi-SIM) for a super-resolution structured light microscope is provided, and the method includes:

Step S101: Read multiple frames of original images collected by the SIM imaging system;

Here, for different SIM technologies, the way to collect the original image is different. For 2D-SIM, usually 3 different phases of 9 original images are collected under 3 different illumination angles; for single-layer 3D-SIM, usually 5 different phases are collected under 3 different illumination angles, a total of 15 Frame image.

Step S103, estimating structured light fringe parameters, including estimating structured light fringe wave vector k _θ , estimating fringe modulation degree m and initial phase

Step S104: Based on the structured light fringe parameter estimation result, the high-fidelity SIM super-resolution image is reconstructed using a spectrum optimization method.

The above-mentioned high-fidelity image reconstruction method of super-resolution structured light illumination microscope is to estimate structured light fringe parameters by reading multiple frames of original images collected by SIM imaging system, including estimating structured light fringe wave vector k _θ and estimating fringe modulation degree m And initial phase

Based on the estimation results of the structured light fringe parameters, the high-fidelity SIM super-resolution image is reconstructed using the spectrum optimization method. In this way, the high-fidelity reconstruction of the SIM super-resolution image can be realized, and the removal of artifacts and the enhancement of the slice cutting ability can be taken into account.

Further, in one of the embodiments, the method further includes before reconstructing the high-fidelity SIM super-resolution image by using the spectrum optimization method:

Step S102: Generate a point spread function PSF based on the theoretical model;

Here, the point spread function PSF generated by the theoretical model can be realized based on the optical parameters of the SIM imaging system, and the optical parameters can include, but are not limited to, the microscope magnification, the numerical aperture of the microscope objective, and the fluorescence emission wavelength.

With the solution of this embodiment, not only the measured PSF can be directly used, but also the PSF generated based on the theoretical model can be used, which is more flexible. The deviation of PSF is likely to cause obvious artifacts. The solution of this embodiment overcomes the problem that the conventional SIM algorithm is more sensitive to PSF. In addition, even if non-professionals cannot complete the PSF measurement, the solution of the present invention can also be used to achieve SIM ultra The high-fidelity reconstruction of the resolved image overcomes the complexity and difficulty of the PSF measurement process and reduces the difficulty of using the SIM technology.

It should be noted that step S102 and step S103 may not be limited to the above-mentioned order of execution, and may also be executed at the same time.

Further, in one of the embodiments, the aforementioned generating of the point spread function PSF based on the theoretical model specifically includes:

Use the optical parameters of the SIM imaging system to generate the optical transfer function OTF:

In the formula, k _c is the cut-off frequency of the imaging objective lens;

Pair optical transfer function

Perform the inverse Fourier transform to generate the point spread function PSF(r).

Further, in one of the embodiments, the above-mentioned estimating structured light fringe wave vector k _θ specifically includes:

Step S201, preprocessing the original image to eliminate the out-of-focus signal, the 0-level spectrum signal, and

The influence of the attenuation of high-frequency signals in the original image on the estimated structured light fringe wave vector k _θ ;

Here, take 2D-SIM as an example to describe and analyze the proposed preprocessing:

For 2D-SIM, the original single frame image can be expressed as:

In the formula, S _in (r) is the real sample, m _θ is the modulation degree of the illumination fringe, and k _θ is the wave vector of the illumination fringe,

Is the initial phase of the illumination fringe, PSF(r) is the point spread function of the microscope, S _out (r) is the out-of-focus signal, and N(r) is the noise.

In the frequency domain space, the Fourier transform of equation (2) can obtain the spectrum of the original SIM image:

Where

Is the optical transfer function of the microscope system, which is the result of the Fourier transform of PSF(r);

Is the spectrum of the sample at the focal plane of the microscope, corresponding to the 0-level spectrum;

It is the undecoded high-frequency information encoded by the structured light into the low-frequency region of the microscope objective OTF, corresponding to the ±1 level spectrum;

Is the out-of-focus signal spectrum;

Is the noise spectrum.

For the traditional SIM algorithm, the 0-level and ±1-level spectrum are usually directly separated from the original image, and the cross-key of the 0-level and 1-level spectrum is directly used to estimate the key parameters of the illumination fringe, including the fringe wave vector k _θ and the modulation degree m And initial phase

Wait. However, from the SIM microscopic imaging process shown in Equation 1, it can be seen that the convolution of the PSF of the detection objective, the defocus signal, and noise will cause the modulation of the collected SIM raw data to be greater than that at the focal plane of the objective (Equation 1 in

) To be low. Therefore, the present invention proposes an original image preprocessing method based on the inverse process of microscopic imaging.

Step S202: Perform cross-correlation based on the preprocessed original image to estimate the structured light fringe wave vector k _θ .

Further, in one of the embodiments, the foregoing preprocessing of the original image specifically includes:

Step S301, summing and averaging the read multiple frames of original images D _θ,n (r) to obtain an equivalent wide-field image D _EWF,θ (r);

Here, taking 2D-SIM as an example, the equivalent wide-field image D _EWF,θ (r) obtained is:

In the formula, N'(r) is the residual noise after average noise reduction. The above summation step is beneficial to noise reduction.

Comparing formulas 2 and 4, it can be seen that the acquired SIM original image D _θ,n (r) and the equivalent wide-field image D _EWF,θ (r) contain approximately equivalent defocused background signals and zero-level spectrum components. Therefore, in order to remove the influence of the out-of-focus signal and the 0-level spectrum component, step S302 is performed.

Step S302: Introduce a constant weight factor α _θ , and combine the equivalent wide-field image D _EWF,θ (r) to process the single frame original image D _θ,n (r) to obtain a new single frame original image D' _{θ, n} (r), the formula used is:

D' _θ,n (r)=D _θ,n (r)-α _θ □D _EWF,θ (r) (5)

In the formula, α _θ ∈[0,1], θ represents the direction angle, and n represents the phase;

Here, taking 2D-SIM as an example, a new single-frame original image D' _θ,n (r) is obtained as:

In the formula, N"(r) is the residual defocus signal. Comparing formulas 2 and 6, it can be seen that the 0-level spectrum signal and defocus contained in the processed image are attenuated by 1-α _θ times, while the ±1-level signal spectrum constant.

Step S303, taking α _θ =1, then the above formula (5) becomes:

D' _θ,n (r)=D _θ,n (r)-D _EWF,θ (r) (7)

Here, taking 2D-SIM as an example, the above equation (6) becomes:

It can be seen from the above formula 8 that the preprocessed image only contains ±1 level spectrum signal and residual noise signal. However, the high-frequency signal in the ±1-level spectrum is still attenuated due to the convolution of the PSF, which is not conducive to the estimation of the peak position of the _{structured light fringe wave vector k θ. Therefore, step S304 is executed.}

Step S304: Perform deconvolution processing on the above formula (7) to obtain a new single frame original image D′ _θ,n (r) after the final preprocessing.

Here, taking 2D-SIM as an example, the above formula (8) after deconvolution becomes:

In the formula, N"'(r) is the residual defocus signal after deconvolution.

By adopting the solution of this embodiment, it is possible to eliminate out-of-focus signals, 0-level spectrum signals, and

The effect of the attenuation of the high-frequency signal in the original image on the estimation of the structured light fringe wave vector k _θ is improved, and the estimation accuracy of the structured light fringe wave vector k _{θ is improved.}

Further, in one of the embodiments, in conjunction with FIG. 3, the above-mentioned cross-correlation is performed based on the preprocessed original image to estimate the structured light fringe wave vector k _θ , which specifically includes:

Step S401: Perform SIM spectrum separation calculation on the new single-frame original image D' _θ,n (r) after preprocessing, to obtain separated multi-level spectrum, including 0-level spectrum, 1-level spectrum,..., L-level spectrum , Each level of spectrum is expressed as

among them,

Respectively represent +l level and -l level spectrum, the value of l is 0～L, k _θ represents the period of structured light;

Here, taking 2D-SIM as an example, _{perform SIM spectrum separation calculation on the new single-frame original image D'θ,n} (r) after preprocessing, and obtain the separated 2-level spectrum, including the 0-level spectrum and the 1-level spectrum, respectively for

Here, taking 3D-SIM as an example, the _{SIM spectrum separation calculation is performed on the new single frame original image D'θ,n} (r) after preprocessing, and the separated three-level spectrum is obtained, including the 0-level spectrum, the 1-level spectrum and the second-level spectrum. Grade spectrum, respectively

Step S402: Perform Fourier transform on the equivalent wide-field image D _EWF,θ (r) to obtain the equivalent wide-field image spectrum

Step S403: For all spectrums except the 0-level spectrum and the equivalent wide-field image spectrum

All perform spectral amplitude normalization processing;

Step S404, using a Gaussian function to perform notch processing on the center regions of all normalized frequency spectra;

Step S405, the equivalent wide-field image spectrum after notch processing

And L-level spectrum

or

Perform cross-correlation calculation to obtain the peak position of the structured light fringe wave vector;

Here, taking 2D-SIM as an example, the equivalent wide-field image spectrum after notch processing

And level 1 spectrum

or

Perform cross-correlation calculations.

Here, taking 3D-SIM as an example, the equivalent wide-field image spectrum after notch processing

And level 2 spectrum

or

Perform cross-correlation calculations.

Step S406: Perform sub-pixel precision fitting positioning near the peak position to complete the estimation of the _{structured light fringe wave vector k θ.}

By adopting the solution of this embodiment, the estimation accuracy _{of the structured light fringe wave vector k θ can be further improved.}

Further, in one of the embodiments, in conjunction with FIG. 3, the above-mentioned estimated fringe modulation degree m and the initial phase

Specifically:

Step S501: Perform deconvolution preprocessing on the original image to obtain an image D" _θ,n (r);

Step S502: Perform SIM spectrum separation calculation on the image D" _θ,n (r) to obtain separated multi-level spectra, including the 0-level spectrum, the 1-level spectrum,..., the L'-level spectrum, and each level of spectrum is expressed as

among them,

Respectively represent +l'-level and -l'-level spectra, the value of l'is 0～L', and k _θ represents the period of structured light;

Here, taking 2D-SIM as an example, the _{SIM spectrum separation calculation is performed on the image D" θ,n} (r), and the separated 2-level spectra are obtained, including the 0-level spectrum and the 1-level spectrum, which are respectively

Here, taking 3D-SIM as an example, the _{SIM spectrum separation calculation is performed on the image D" θ,n} (r), and the separated 3-level spectrum is obtained, including the 0-level spectrum, the 1-level spectrum and the 2-level spectrum, which are respectively

Step S503: Perform spectrum amplitude normalization processing on all frequency spectra, and use Gaussian function to perform notch processing on the center area of all normalized frequency spectra;

Step S504: Shift all the frequency spectra after the notch processing until the zero frequency of each level of the spectrum is consistent with the zero frequency of the 0-level spectrum; where the shifted l'-level spectrum is denoted as

Step S505: Analyze the equivalent wide-field image frequency spectrum

Perform spectral amplitude normalization processing, and use Gaussian function to trap the center area of the normalized equivalent wide-field image spectrum, denoted as

Step S506, for each frequency spectrum after translation

or

It and

Cross-correlation calculation is performed on the overlapping area of, and the corresponding fringe modulation degree m _{l is obtained} ; the shifted level 1 spectrum

or

versus

Cross-correlation calculation for the overlapping area to obtain the initial phase

Here, taking 2D-SIM as an example, the

or

versus

Cross-correlation calculation is carried out on the overlapping area of, and the fringe modulation degree m and initial phase

Here, taking 3D-SIM as an example, the

or

versus

Cross-correlation calculation is carried out on the overlapping area of, and the fringe modulation degree m ₁ and the initial phase are obtained

will

or

versus

Cross-correlation calculation is performed on the overlapping area of, and the fringe modulation degree m _{2 is obtained} .

By adopting the scheme of this embodiment, the fringe modulation degree m and the initial phase can be improved

The estimation accuracy.

Further, in one of the embodiments, in conjunction with FIG. 4, the above-mentioned structured light fringe parameter estimation results are used to reconstruct the high-fidelity SIM super-resolution image using the spectrum optimization method, which specifically includes:

Step S601: Based on the structured light fringe parameter estimation result, reconstruct the spectrum of the initial SIM image

Step S602: Use Gaussian function to analyze the spectrum of the initial SIM image

Notch processing in the central area of the sensor to obtain the frequency spectrum

Eliminate the residual out-of-focus signal spectrum at the center of the spectrum by notching;

However, the Gaussian notch will cause a spectral notch at the center of the corresponding spectral component, which will cause the true signal corresponding to these spectral regions to be lost in the reconstructed image. In addition, the "hexagon-like" unnatural structure in the reconstructed spectrum may cause obvious sidelobe artifacts and snowflake artifacts in the reconstructed image. In addition, the Wiener filtering step adopted by most existing SIM algorithms cannot effectively balance the trade-off between "removing residual out-of-focus signals" and "retaining real sample signals", so step S603 is executed.

Step S603, construct a composite filter

Step S604, the frequency spectrum

With composite filter

Multiply and perform inverse Fourier transform to obtain the final high-fidelity SIM super-resolution image.

Using the solution of this embodiment and in conjunction with Fig. 5, it can be seen that the present invention can take into account both the removal of artifacts and the improvement of the slice cutting ability, and realize the high-fidelity reconstruction of the SIM super-resolution image.

Further, in one of the embodiments, with reference to FIG. 4, the above step S601 reconstructs the initial SIM image spectrum based on the structured light fringe parameter estimation result, which specifically includes:

Step S701: Perform deconvolution preprocessing on the original image to obtain an image D"' _θ,n (r);

Step S702: Based on the estimation result of the structured light fringe parameters, _{perform SIM spectrum separation calculation on the image D"' θ,n} (r) to obtain separated multi-level spectra, including the 0-level spectrum, the 1-level spectrum, ..., L" Level spectrum, each level of spectrum is expressed as

among them,

Respectively represent +l” level and -l” level spectra, the value of l” is 0～L”, k _θ represents the period of structured light;

Step S703: Shift all spectrums except the 0-level spectrum until the zero frequency of each level of the spectrum is consistent with the zero frequency of the 0-level spectrum; where the shifted l"-level spectrum is denoted as

Step S704: Multiply and sum each level of the shifted spectrum with the complex conjugate of its corresponding OTF, and reconstruct the initial SIM image spectrum as

Where

Indicates that the shifted l"-level spectrum corresponds to OTF, and "*" indicates conjugate.

Further, in one of the embodiments, the Gaussian function is used to calculate the spectrum of the initial SIM image in step S602.

Notch processing in the central area of the sensor to obtain the frequency spectrum

The formula used is:

Where

Represents the Gaussian function, specifically:

In the formula, A'is the intensity of the Gaussian notch, and B'is the width of the notch area.

Further, in one of the embodiments, the above-mentioned structured composite filter

The formula used is:

Where

It is the first composite sub-filter or the first single sub-filter, which is used to initially restore the zero-level spectrum, the first-level spectrum, ..., the L"-level spectrum that has been collapsed after the notch and translation processing;

It is the second composite sub-filter or the second single-sub filter, which is used to further restore the first-level spectrum,..., L"-level spectrum after the preliminary restoration, and at the same time, to reduce the amplitude of the 0-level spectrum after the preliminary restoration.

The analysis of this embodiment is as follows:

The designed composite filter is mainly used to solve the following three problems:

1. Due to the Gaussian notch or the related regions in the 0-level and ±l”-level spectrum after translation, spectral depressions are generated, which causes the real sample signals corresponding to the spectra of these recessed regions to be attenuated or even lost from the image;

2. There is a strong spectral peak in the center of the spectrum of the SR-SIM obtained by the conventional Wiener-SIM algorithm, which causes the residual out-of-focus background signal and related artifacts in the reconstructed SR image to be amplified, Cause the image quality to deteriorate. This limits the axial layer cutting capability of the conventional 2D-SIM, making the 2D-SIM layer cutting capability poor. In addition, conventional Wiener-SIM cannot effectively balance the trade-off between removing the out-of-focus signal and retaining the real sample signal. Therefore, if you want to retain more real sample signals, the artifacts in the reconstructed image will be aggravated; if you want to remove the artifacts as much as possible, some of the real sample signals will be attenuated or even lost;

3. In the reconstructed spectrum obtained by conventional Wiener-SIM, for 2D-SIM, the overlapping area of the 0-level spectrum and the ±1 spectrum is often prone to "hexagon-like" unnatural spectrum structure, and cause "sidelobe artifacts". "Shadow" or "snow-like artifact".

The composite filter of the scheme of this embodiment takes into account the collapsed spectrum area caused by the Gaussian notch in the recovery formula (11), and suppresses the strong spectrum peak in the center of the spectrum obtained by conventional Wiener-SIM to improve the layer of 2D-SIM. Cut ability, and correct the unnatural spectrum structure in the reconstructed spectrum to eliminate the artifacts. Here, the sub-filter of the composite filter

The characteristic of is: an upwardly convex peak is generated at the position corresponding to the notched area of the center of ±1 level after level 0 and translation, which is used to restore the collapsed spectrum area to prevent the loss of real signal; sub-filter

The characteristic of is: the position corresponding to the notched area of the ±1 level center after the translation produces an upwardly convex peak, which is used to further restore the cashed spectrum area; and the position corresponding to the collapsed area of the 0 level spectrum center produces a Peaks sunken down for adjustment

The intensity of the peak value in the central area of level 0, so as to achieve the function of adjusting the SIM layer cutting ability. In addition,

with

Multiplied composite filter

It is also possible to correct the "hexagon-like" unnatural structure in the initial reconstructed spectrum, thereby suppressing or even eliminating the corresponding artifacts. In a word, the idea of generating a composite filter with spectrum optimization in the present invention revolves around solving the above-mentioned problems and has the above-mentioned features at the same time.

Here, taking 2D-SIM as an example, the first sub-filter

for:

Second subfilter

Specifically:

Here, taking 3D-SIM as an example, the first sub-filter

for:

Second subfilter

Specifically:

among them,

In the formula, α, β, α', β'are all constants; w ₁ , w ₂ are all Wiener constants;

with

All are Gaussian notch functions, A ₁ (k) is the OTF-shaped apodization function, A ₂ (k) is the Gaussian apodization function; A, B, C, and D are all constants, and _rapo is the apodization radius, ApoFWHM is a constant parameter of the Gaussian apodization function A ₂ (k).

In one embodiment, in conjunction with FIG. 6, a high-fidelity image reconstruction system for a super-resolution structured light illumination microscope is provided, including:

The image acquisition module 101 is used to read multiple frames of original images acquired by the SIM imaging system;

The parameter estimation module 103 is used to estimate structured light fringe parameters, including estimating structured light fringe wave vector k _θ , estimating fringe modulation degree m and initial phase

The image reconstruction module 104 is configured to reconstruct a high-fidelity SIM super-resolution image based on the structured light fringe parameter estimation result and using a spectrum optimization method.

Further, in one of the embodiments, the system further includes:

The point spread function PSF generating module 102 is used to generate the point spread function PSF based on the theoretical model; the module specifically includes:

The OTF generating unit is used to generate the optical transfer function OTF using the optical parameters of the SIM imaging system. The formula used is:

In the formula, k _c is the cut-off frequency of the imaging objective lens;

PSF generating unit for the optical transfer function

Perform the inverse Fourier transform to generate the point spread function PSF(r).

For the specific definition of the high-fidelity image reconstruction system of the super-resolution structured light illumination microscope, please refer to the above definition of the high-fidelity image reconstruction method of the super-resolution structured light illumination microscope, which will not be repeated here. The various modules in the high-fidelity image reconstruction system of the above-mentioned super-resolution structured light illumination microscope can be implemented in whole or in part by software, hardware, and a combination thereof. The above-mentioned modules may be embedded in the form of hardware or independent of the processor in the computer equipment, or may be stored in the memory of the computer equipment in the form of software, so that the processor can call and execute the operations corresponding to the above-mentioned modules.

In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, and the processor implements the following steps when the processor executes the computer program:

Read multiple frames of original images collected by the SIM imaging system;

Estimate structured light fringe parameters, including estimating structured light fringe wave vector k _θ , estimating fringe modulation degree m and initial phase

Based on the estimation results of the structured light fringe parameters, the high-fidelity SIM super-resolution image is reconstructed using the spectrum optimization method.

For the specific definition of each step, please refer to the above definition of the high-fidelity image reconstruction method of the super-resolution structured light illumination microscope, which will not be repeated here.

Further, in one of the embodiments, the processor further implements the following steps when executing the computer program:

Generate the point spread function PSF based on the theoretical model, including:

For the specific definition of this step, please refer to the above definition of the high-fidelity image reconstruction method of the super-resolution structured light illumination microscope, which will not be repeated here.

In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the following steps are implemented:

Read multiple frames of original images collected by the SIM imaging system;

Estimate structured light fringe parameters, including estimating structured light fringe wave vector k _θ , estimating fringe modulation degree m and initial phase

Based on the estimation results of the structured light fringe parameters, the high-fidelity SIM super-resolution image is reconstructed using the spectrum optimization method.

For the specific definition of each step, please refer to the above definition of the high-fidelity image reconstruction method of the super-resolution structured light illumination microscope, which will not be repeated here.

Further, in one of the embodiments, the computer program further implements the following steps when being executed by the processor:

Generate the point spread function PSF based on the theoretical model, including:

For the specific definition of this step, please refer to the above definition of the high-fidelity image reconstruction method of the super-resolution structured light illumination microscope, which will not be repeated here.

Using the HiFi-SIM algorithm of the present invention and the conventional Wiener-SIM algorithm to reconstruct the same wide-field equivalent image respectively, the result is shown in Figure 7. It can be seen from the figure that there are "class six" in the conventional Wiener-SIM reconstruction spectrum. The unnatural spectral structure of the “edge” feature causes obvious sidelobe artifacts in the reconstructed image, and the hammer artifacts in the reconstructed image are more serious. The method of the present invention can effectively solve the problem of SIM super-resolution images. A variety of typical artifacts that are extremely easy to produce, to achieve high-fidelity reconstruction of SIM super-resolution images.

The invention can effectively solve the problem of artifacts that have plagued the fidelity and credibility of the SIM super-resolution image for a long time, and realizes the high-fidelity reconstruction (HiFi-SIM) of the SIM super-resolution image. In addition, the present invention can greatly improve the axial layer cutting capability of the 2D-SIM technology, enable the 2D-SIM technology to obtain the layer cutting capability comparable to the 3D-SIM technology, and effectively expand the application scenarios of the 2D-SIM technology. In addition, HiFi-SIM uses theoretical PSF generation instead of the complex process of measuring real PSF, and can still reconstruct high-fidelity SR-SIM super-resolution images.

The high-fidelity image reconstruction method of the super-resolution structured light illumination microscope provided by the present invention is not only suitable for the reconstruction of 2D-SIM and 3D-SIM data, but also suitable for the non-linear structured light illumination microscope (NL-SIM). Super-resolution image reconstruction is suitable for almost all data processing of SIM systems based on the principle of structured light illumination technology.

The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above embodiments are not described. However, as long as there is no contradiction in the combination of these technical features, they should be It is considered as the range described in this specification.

The above-mentioned embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the invention patent. It should be pointed out that for those of ordinary skill in the art, without departing from the concept of this application, several modifications and improvements can be made, and these all fall within the protection scope of this application. Therefore, the scope of protection of the patent of this application shall be subject to the appended claims.

Claims (14)

1. A high-fidelity image reconstruction method, characterized in that the method includes:

   Read multiple frames of original images collected by the SIM imaging system;

   Estimate structured light fringe parameters, including estimating structured light fringe wave vector k _θ , estimating fringe modulation degree m and initial phase

   

   Based on the result of the structured light fringe parameter estimation, the spectrum optimization method is used to reconstruct the high-fidelity SIM super-resolution image.
2. The high-fidelity image reconstruction method according to claim 1, characterized in that, before said using the spectrum optimization method to reconstruct a high-fidelity SIM super-resolution image, the method further comprises: generating a point spread function (PSF) based on a theoretical model, specifically include:

   Use the optical parameters of the SIM imaging system to generate the optical transfer function OTF:

   

   In the formula, k _c is the cut-off frequency of the imaging objective lens;

   For the optical transfer function

   

   Perform the inverse Fourier transform to generate the point spread function PSF(r).
3. The high-fidelity image reconstruction method according to claim 1, wherein the estimated structured light fringe wave vector k _θ specifically includes:

   The original image is preprocessed to eliminate out-of-focus signals, 0-level spectrum signals, and

   

   The influence of the attenuation of high-frequency signals in the original image on the estimated structured light fringe wave vector k _θ ;

   Based on the preprocessed original image, cross-correlation is performed to estimate the structured light fringe wave vector k _θ .
4. The high-fidelity image reconstruction method according to claim 3, wherein said preprocessing the original image specifically comprises:

   Sum and average the read multiple original images D _θ,n (r) to obtain the equivalent wide-field image D _EWF,θ (r);

   Introduce the constant weight factor α _θ , and combine the equivalent wide-field image D _EWF,θ (r) to process the single frame original image D _θ,n (r) to obtain a new single frame original image D' _θ,n (r ), the formula used is:

   D' _θ,n (r)=D _θ,n (r)-α _θ □D _EWF,θ (r) (2)

   In the formula, α _θ ∈[0,1], θ represents the direction angle, and n represents the phase;

   Taking α _θ = 1, then the above formula (2) becomes:

   D' _θ,n (r)=D _θ,n (r)-D _EWF,θ (r) (3) Deconvolve the above formula (3) to obtain the new single frame original after final preprocessing Image D' _θ,n (r).
5. The high-fidelity image reconstruction method according to claim 4, wherein the cross-correlation based on the preprocessed original image to estimate the structured light fringe wave vector k _θ specifically includes:

   Perform SIM spectrum separation calculation on the new single-frame original image D' _θ,n (r) after the preprocessing, to obtain separated multi-level spectrum, including 0-level spectrum, 1-level spectrum, ..., L-level spectrum, The spectrum of each level is expressed as

   

   among them,

   

   Respectively represent +l level and -l level spectrum, the value of l is 0～L, k _θ represents the period of structured light;

   Perform Fourier transform on the equivalent wide-field image D _EWF,θ (r) to obtain the equivalent wide-field image spectrum

   

   For all spectrums except the 0-level spectrum and equivalent wide-field image spectrum

   

   All perform spectral amplitude normalization processing;

   Using a Gaussian function to perform notch processing on the central regions of all the normalized frequency spectra;

   The equivalent wide-field image spectrum after the notch processing

   

   And L-level spectrum

   

   or

   

   Perform cross-correlation calculation to obtain the peak position of the structured light fringe wave vector;

   The sub-pixel precision fitting positioning is performed near the peak position to complete the estimation of the _{structured light fringe wave vector k θ.}
6. The high-fidelity image reconstruction method according to claim 1, wherein the estimated fringe modulation degree m and the initial phase

   

   Specifically:

   Perform deconvolution preprocessing on the original image to obtain an image D" _θ,n (r);

   Perform SIM spectrum separation calculation on the image D" _θ,n (r) to obtain separated multi-level spectrum, including 0-level spectrum, 1-level spectrum,..., L'-level spectrum, and each level of spectrum is expressed as

   

   among them,

   

   Respectively represent +l'-level and -l'-level spectra, the value of l'is 0～L', and k _θ represents the period of structured light;

   Performing spectral amplitude normalization processing on all frequency spectra, and using Gaussian function to perform notch processing on the central area of all normalized frequency spectra;

   Shift all the frequency spectra after the notch processing until the zero frequency of each level spectrum is consistent with the zero frequency of the 0 level spectrum; wherein, the shifted l'level spectrum is denoted as

   

   For the equivalent wide-field image spectrum

   

   Perform spectral amplitude normalization processing, and use Gaussian function to perform notch processing on the center area of the normalized equivalent wide-field image spectrum, denoted as

   

   For each spectrum after translation

   

   or

   

   It and said

   

   Cross-correlation calculation is performed on the overlapping area of, and the corresponding fringe modulation degree m _{l is obtained} ; the shifted level 1 spectrum

   

   or

   

   With said

   

   Cross-correlation calculation for the overlapping area to obtain the initial phase

   
7. The high-fidelity image reconstruction method according to claim 5 or 6, wherein the reconstruction of a high-fidelity SIM super-resolution image based on the structured light fringe parameter estimation result using a spectrum optimization method specifically includes:

   Based on the result of the structured light fringe parameter estimation, reconstruct the initial SIM image spectrum

   

   Use Gaussian function to analyze the spectrum of the initial SIM image

   

   Notch processing in the central area of the sensor to obtain the frequency spectrum

   

   Construct a composite filter

   

   The frequency spectrum

   

   With the composite filter

   

   Multiply and perform inverse Fourier transform to obtain the final high-fidelity SIM super-resolution image.
8. The high-fidelity image reconstruction method according to claim 7, wherein the reconstruction of the initial SIM image spectrum based on the structured light fringe parameter estimation result specifically comprises:

   Perform deconvolution preprocessing on the original image to obtain an image D"' _θ,n (r);

   Based on the estimation results of the structured light fringe parameters, _{perform SIM spectrum separation calculation on the image D"' θ,n} (r) to obtain separated multi-level spectra, including level 0 spectrum, level 1 spectrum,..., L" level Spectrum, each level of spectrum is expressed as

   

   among them,

   

   Respectively represent +l” level and -l” level spectra, the value of l” is 0～L”, k _θ represents the period of structured light;

   Shift all spectrums except the 0-level spectrum until the zero frequency of each level of the spectrum is consistent with the zero frequency of the 0-level spectrum; among them, the shifted l"-level spectrum is denoted as

   

   Multiply the shifted spectrum of each level and the complex conjugate of its corresponding OTF and sum them, and reconstruct the spectrum of the initial SIM image as

   

   

   Where

   

   Indicates that the shifted l"-level spectrum corresponds to OTF, and "*" indicates conjugate;

   The use of Gaussian function on the spectrum of the initial SIM image

   

   Notch processing in the central area of the sensor to obtain the frequency spectrum

   

   The formula used is:

   

   Where

   

   Represents the Gaussian function.
9. The high-fidelity image reconstruction method according to claim 8, wherein the structured composite filter

   

   The formula used is:

   

   Where

   

   It is the first composite sub-filter or the first single sub-filter, which is used to initially restore the zero-level spectrum, the first-level spectrum, ..., the L"-level spectrum that has been collapsed after the notch and translation processing;

   

   It is the second composite sub-filter or the second single-sub filter, which is used to further restore the first-level spectrum,..., L"-level spectrum after the preliminary restoration, and at the same time, to reduce the amplitude of the 0-level spectrum after the preliminary restoration.
10. The high-fidelity image reconstruction method according to claim 9, wherein the first sub-filter

    

    Specifically:

    (1) For 2D-SIM:

    

    (2) For 3D-SIM:

    

    The second sub-filter

    

    Specifically:

    (1) For 2D-SIM:

    

    (2) For 3D-SIM:

    

    among them,

    

    

    

    

    In the formula, α, β, α', β'are all constants; w ₁ , w ₂ are all Wiener constants;

    

    with

    

    All are Gaussian notch functions, A ₁ (k) is the OTF-shaped apodization function, A ₂ (k) is the Gaussian apodization function; A, B, C, and D are all constants, and _rapo is the apodization radius, ApoFWHM is a constant parameter of the Gaussian apodization function A ₂ (k).
11. A high-fidelity image reconstruction system, characterized in that the system includes:

    Image acquisition module, used to read multiple frames of original images acquired by the SIM imaging system;

    Parameter estimation module for estimating structured light fringe parameters, including estimating structured light fringe wave vector k _θ , estimating fringe modulation degree m and initial phase

    

    The image reconstruction module is used to reconstruct a high-fidelity SIM super-resolution image based on the structured light fringe parameter estimation result by using a spectrum optimization method.
12. The high-fidelity image reconstruction system according to claim 11, wherein the system further comprises:

    The point spread function PSF generation module is used to generate the point spread function PSF based on the theoretical model; the module specifically includes:

    The OTF generating unit is used to generate the optical transfer function OTF using the optical parameters of the SIM imaging system. The formula used is:

    

    In the formula, k _c is the cut-off frequency of the imaging objective lens;

    PSF generating unit, used to compare the optical transfer function

    

    Perform the inverse Fourier transform to generate the point spread function PSF(r).
13. A computer device, comprising a memory, a processor, and a computer program stored on the memory and running on the processor, wherein the processor implements any one of claims 1 to 10 when the computer program is executed The steps of the method.
14. A computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the steps of the method according to any one of claims 1 to 10 when the computer program is executed by a processor.

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