CN111308682B - Super-resolution reconstruction method based on structured light illumination - Google Patents

Super-resolution reconstruction method based on structured light illumination Download PDF

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CN111308682B
CN111308682B CN201911126028.9A CN201911126028A CN111308682B CN 111308682 B CN111308682 B CN 111308682B CN 201911126028 A CN201911126028 A CN 201911126028A CN 111308682 B CN111308682 B CN 111308682B
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张尹馨
费建阳
杨怀栋
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Tianjin University
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Abstract

The invention relates to an optical super-resolution microscopic imaging technology, in order to provide a structured light illumination-based method, reduce the number of images required by reconstruction, reduce the complexity and improve the reconstruction rate, the invention uses a Spatial Light Modulator (SLM) to generate structured light, modulates a sample to be measured on an object plane, uses a CCD camera to collect the image for the first time, generates the structured light with the phase shift of pi through the spatial light modulator, collects the image for the second time after modulation, obtains a wide-field image by adding the first collected image and the second collected image, separates high-frequency information in the secondary collected image by using the frequency spectrum of the wide-field image and the frequency spectrum generated by carrying out wiener filtering on the frequency spectrum, carries out filtering and spectrum moving operations, moves back the high-frequency original position, carries out weighted averaging on the frequency spectrum through generalized wiener filtering to obtain the frequency spectrum, and finally, obtaining a super-resolution image through inverse Fourier transform. The invention is mainly applied to the microscopic imaging occasions.

Description

Super-resolution reconstruction method based on structured light illumination
Technical Field
The invention relates to the technical field of optical super-resolution microscopic imaging, in particular to a super-resolution imaging technology based on structured light illumination, which can be used for cell structure detection.
Background
The resolution of the traditional optical microscope is limited by diffraction limit, the limit resolution is about 200nm, and subcellular structures cannot be observed.
In order to break through the limit of diffraction limit, a series of super-resolution imaging techniques are proposed, in consideration of live cell imaging, the structured light super-resolution microscope imaging technique does not require any special sample preparation, has no special requirements for a fluorophore used for sample labeling, requires a small excitation light intensity, has small photobleaching property, can observe live cells for a long time, and has a high imaging speed and is used in large quantities.
The real-time dynamic living cell research is one of the main application directions of the structured light super-resolution microscope imaging technology, and the improvement of the time resolution is very important for the observation of the acting mechanism between organelles and inside. At present, the mainstream structure light super-resolution microscope imaging system is fully optimized on the aspects of hardware performance and system synchronization efficiency, the promotion space is limited, and the problem that a large amount of iteration approaches or parallel calculation is still needed in the current algorithm for reducing the number of reconstructed frames is solved, so that the reconstruction rate is not high, and the imaging real-time performance is influenced.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a super-resolution reconstruction method based on structured light illumination, which reduces the number of images required by reconstruction, reduces the complexity of the reconstruction method, greatly improves the reconstruction rate, and is particularly suitable for super-resolution cell imaging of structured light illumination. Therefore, the invention adopts the technical scheme that a super-resolution reconstruction method based on structured Light illumination utilizes a Spatial Light Modulator (SLM) to generate structured Light, modulates a sample to be detected on an object plane, introduces originally non-collectable high-frequency information after modulation, collects an image for the first time by a CCD camera, generating structured light with phase shift of pi by a spatial light modulator, secondarily acquiring images after modulation, adding the primarily acquired images and the secondarily acquired images to obtain a wide-field image, and the frequency spectrum of the wide field image and the frequency spectrum generated by carrying out wiener filtering on the frequency spectrum are utilized to separate high-frequency information in the secondary collected image, filtering and spectrum moving operations are carried out to move the high frequency back to the original position, and carrying out weighted average on the frequency spectrum through generalized wiener filtering to obtain the super-resolution frequency spectrum, and finally obtaining the super-resolution image through inverse Fourier transform.
The frequency of the structured light striations is estimated through an autocorrelation method, the solving of the structured light phase and the frequency of the structured light striations is accelerated by utilizing the result of solving the frequency of the structured light phase when the structured light phase is solved, a residual frequency spectrum is generated at the position where the frequency is close to the center in the separation process, the noise is suppressed through wiener filtering, and the quality of a super-resolution imaging result is ensured.
The method comprises the following specific steps:
the image 0 is collected by a CCD camera for the first time, high-frequency information exceeding the diffraction limit is introduced into the frequency spectrum of the image 0, so that an aliasing frequency spectrum is formed, structured light with the phase shift of pi is generated through a spatial light modulator, an image 1 is collected after modulation, and when the uniform illumination is carried out, an image space image collected by a wide-field imaging system is represented as follows:
D0(r)＝[S(r)·I(r)]*H(r) (1)
wherein r represents the two-dimensional coordinates of the spatial domain, S (r) represents the fluorescence concentration distribution, H (r) represents the point spread function of the imaging system, a represents the convolution symbol, D0(r) is image 0, which introduces high frequency information beyond the diffraction limit under modulation by the cosine structured light, which is illuminated as indicated by
Figure BDA00022768550900000218
I0The average light intensity of the structured light, m is the modulation degree, p is the spatial frequency of the structured light, phi is the phase of the structured light, and the frequency spectrum received after the structured light is modulated is as follows:
Figure BDA0002276855090000021
wherein
Figure BDA0002276855090000022
Is D0(r), S (r), representing the Fourier transform, k being the two-dimensional coordinates of the frequency domain,
Figure BDA0002276855090000023
for the optical transfer function OTF and shifting the phase of the structured light by pi, the image plane obtains an image 1 whose frequency spectrum is represented as:
Figure BDA0002276855090000024
Figure BDA0002276855090000025
is D1Fourier transform of (r). Frequency spectra 0 and1, there is a high frequency spectrum which is modulated by the structural light and then shifted into the OTF, the spectrograms of the images 0 and 1 are added, and the high frequency information is eliminated, so that the following result is obtained:
Figure BDA0002276855090000026
Figure BDA0002276855090000027
is the spectrum 2 of the wide-field image obtained after the addition, and the spectrum 1 and the spectrum 2 are subtracted to obtain a spectrum map 3 with the center low frequency removed, which can be expressed as:
Figure BDA0002276855090000028
the fringe frequency and the phase of the structured light acquire the frequency of the structured light fringes by utilizing an autocorrelation algorithm, the phase is solved by solving the result of the fringe frequency, the solving speed of the phase and the frequency of the structured light fringes is accelerated, and then the frequency of the structured light fringes is obtained
Figure BDA0002276855090000029
Wiener filtering is performed to obtain a spectrum diagram 4, which is represented as:
Figure BDA00022768550900000210
Figure BDA00022768550900000211
representing the frequency spectrum 4, NaRepresenting the noise power spectrum, A and alpha representing the coefficients of the estimated signal power spectrum, A2|k|-2αRepresenting the estimated power spectrum of the signal, spectrum 4 is shifted along-p and + p, respectively, to obtain spectrum 5 and spectrum 6, the corresponding spectra being represented as
Figure BDA00022768550900000212
Figure BDA00022768550900000213
Figure BDA00022768550900000214
And
Figure BDA00022768550900000215
respectively represented are a fourier transform and an inverse fourier transform,
Figure BDA00022768550900000216
and
Figure BDA00022768550900000217
representative spectrum 5 and representative spectrum 6. Respectively subtracting the frequency spectrum 3 from the frequency spectrum 5 to obtain a separated high-frequency spectrum at a position with negative frequency, generating a residual spectrum when the frequency is close to a zero value in the separation process, inhibiting the part of noise by wiener filtering, inhibiting the frequency spectrum value with the zero value close to k, and obtaining a high-frequency spectrum 7
Figure BDA0002276855090000031
Figure BDA0002276855090000032
For the high frequency spectrum 7, the spectrum 3 is subtracted from the spectrum 6, and a separate high frequency spectrum is obtained at a position where the frequency is positive, and wiener filtering is performed to suppress a spectrum value close to a zero value of k, so as to obtain a high frequency spectrum 8:
Figure BDA0002276855090000033
Figure BDA0002276855090000034
for the high frequency spectrum 8, I0And m is not required to be solved, the peak values of the high-frequency spectrums 7 and 8 are moved back to the positions where k is + p and-p from the center, the synthesized spread spectrum is obtained, the illumination direction of the structured light is changed by using the spatial light modulator, the super-resolution spectrums are obtained in different modulation directions, the super-resolution spectrums obtained in the three structured light illumination directions are synthesized after weighted averaging through the generalized wiener filtering, and then inverse Fourier transform is performed, so that the isotropic super-resolution image with the resolution is obtained.
The invention has the characteristics and beneficial effects that:
(1) the invention only needs to collect 2 images with phase shift of pi in each direction, can reduce the original images required by super-resolution reconstruction to 6 images, and greatly improves the time resolution.
(2) In the parameter solving process, the fringe frequency and the phase of one image only need to be solved in each direction, and the super-resolution image reconstruction rate is greatly improved.
(3) The invention mainly utilizes the step of frequency spectrum subtraction to separate out the high-frequency spectrum without iterative computation or parallel computation and excessively complicated reconstruction process, and has low requirement on the performance of a computer.
Description of the drawings:
FIG. 1 is a flow chart of a fast super-resolution imaging method based on structured light illumination according to the present invention.
Fig. 2 is a schematic diagram of the spectrum separation of the present invention, in which fig. 2(a) is a spectrum diagram 1 of a picture 1, fig. 2(b) is a spectrum diagram 2, fig. 2(c) is a spectrum 3 after separating a center low frequency, fig. 2(d) is a spectrum 5 shifted to the left, fig. 2(e) is a spectrum 6 shifted to the right, fig. 2(f) is an extracted left high frequency spectrum 7, fig. 2(g) is an extracted right high frequency spectrum 7, and fig. 2(h) is a synthesized super-resolution spectrum.
Detailed Description
The invention aims to overcome the defects of the existing reconstruction method, provides a super-resolution reconstruction method based on structured light illumination, reduces the number of images required by reconstruction, reduces the complexity of the reconstruction method, greatly improves the reconstruction rate, and is particularly suitable for super-resolution cell imaging of the structured light illumination.
The invention discloses a rapid super-resolution reconstruction method based on structured Light illumination, which comprises the steps of generating structured Light by utilizing a Spatial Light Modulator (SLM), modulating a sample to be measured on an object plane, collecting an image 0 by utilizing a CCD (charge coupled device) camera, introducing high-frequency information exceeding a diffraction limit into the frequency spectrum of the image 0 to form an aliasing frequency spectrum, generating the structured Light with a phase shift of pi by utilizing the SLM, collecting an image 1 after modulation, obtaining a wide-field image 2 by adding the image 0 and the image 1, and estimating a low-frequency spectrum by utilizing the frequency spectrum of the wide-field image 2 and the frequency spectrum generated by carrying out wiener filtering on the frequency spectrum, thereby separating two symmetrical parts of high-frequency information in the image 1. Carrying out wiener filtering and spectrum moving operation, moving the separated high-frequency spectrum back to the position where the high-frequency spectrum is not subjected to structural light modulation, carrying out weighted average on the spectrum through generalized wiener filtering, obtaining the super-resolution spectrum, and finally obtaining the super-resolution image through inverse Fourier transform (IFFT).
The method comprises the steps of generating structured light illumination patterns with different fringe periods through parameters of a spatial light modulator, collecting images by using a CCD camera, setting super-resolution image reconstruction parameters, and improving the parameters according to a super-resolution effect.
In order to ensure the effectiveness of super-resolution reconstruction, the method needs to meet the requirement that the generated image phase shift is close to pi, and the frequency spectrum 2 of the wide-field image 2 can be synthesized. In order to be able to obtain a high quality spectrum 3, the method processes the spectrum 2 by means of wiener filtering and estimates the signal and noise of the spectrum.
In order to increase the reconstruction efficiency, the structural light stripe frequency is obtained by utilizing an autocorrelation algorithm, and the phase is obtained by solving the result of the stripe frequency, so that the solving speed of the structural light phase and the structural light stripe frequency is increased. In the separation process, a residual frequency spectrum is generated at a position where the frequency is close to the center, and the part of noise is suppressed through wiener filtering, so that the quality of a super-resolution imaging result is ensured.
The present invention will be described with reference to the accompanying drawings.
The invention relates to a flow chart of a rapid super-resolution reconstruction method based on structured light illumination, which is shown in figure 1 and comprises the following specific steps:
when the illumination is uniform, the image space image acquired by the wide-field imaging system is represented as
D0(r)＝[S(r)·I(r)]*H(r) (12)
Wherein r represents the two-dimensional coordinates of the spatial domain, S (r) represents the fluorescence concentration distribution, H (r) represents the point spread function of the imaging system, a represents the convolution symbol, D0The (r) is an image 0, and the spectral information of the image 0 is limited by the diffraction limit, and only the spectral information within the cutoff frequency can be acquired. The illuminated cosine structured light can be represented as
Figure BDA0002276855090000041
I0The average light intensity of the structured light, m is the modulation degree, p is the spatial frequency of the structured light, phi is the phase of the structured light, and the frequency spectrum received after the structured light is modulated is as follows:
Figure BDA0002276855090000042
wherein
Figure BDA0002276855090000043
Is D0(r), S (r), representing the Fourier transform, k being the two-dimensional coordinates of the frequency domain,
Figure BDA0002276855090000044
is the Optical Transfer Function (OTF). And the phase of the structured light is shifted by pi, an image 1 is obtained on an imaging surface, and the frequency spectrum of the image is represented as:
Figure BDA0002276855090000045
Figure BDA0002276855090000046
is D1Fourier transform of (r). There are high frequency spectra in spectra 0 and 1 that are shifted into the OTF after structured light modulation. Image 0The spectrogram of sum 1 is added, and high frequency information is eliminated, so that the following result is obtained:
Figure BDA0002276855090000047
Figure BDA0002276855090000048
is the spectrum 2 of the wide-field image obtained after the addition, and the spectrum 1 and the spectrum 2 are subtracted to obtain a spectrum map 3 with the center low frequency removed, which can be expressed as:
Figure BDA0002276855090000049
the fringe frequency and the phase of the structured light acquire the frequency of the structured light fringes by utilizing an autocorrelation algorithm, and the phase is solved by solving the result when the fringe frequency is solved, so that the solving speed of the phase of the structured light and the frequency of the structured light fringes is accelerated. Then will be
Figure BDA0002276855090000051
Wiener filtering to obtain a spectrogram fig. 4, which can be expressed as:
Figure BDA0002276855090000052
Figure BDA0002276855090000053
representing the frequency spectrum 4, NaRepresenting the noise power spectrum, A and alpha representing the coefficients of the estimated signal power spectrum, A2|k|-2αRepresenting the estimated signal power spectrum. Moving spectrum 4 along-p and + p, respectively, a spectrum 5 and a spectrum 6 are obtained, the corresponding spectra can be represented as
Figure BDA0002276855090000054
Figure BDA0002276855090000055
Figure BDA0002276855090000056
And
Figure BDA0002276855090000057
respectively represented are a fourier transform and an inverse fourier transform,
Figure BDA0002276855090000058
and
Figure BDA0002276855090000059
representative spectrum 5 and representative spectrum 6. The frequency spectrum 3 is respectively differed from the frequency spectrum 5 to obtain a separated high-frequency spectrum at a position with negative frequency, a residual spectrum is generated when the frequency is close to a zero value in the separation process, the partial noise is restrained by wiener filtering, the frequency spectrum value close to a zero value of k is restrained, and a high-frequency spectrum 7 can be obtained
Figure BDA00022768550900000510
Then, the spectrum 3 is respectively subtracted from the spectrum 6, and a separate high-frequency spectrum is obtained at a position where the frequency is positive, and wiener filtering is performed to suppress a spectrum value where k is close to a zero value, so that a high-frequency spectrum 8 can be obtained.
Figure BDA00022768550900000511
I0And m need not be solved, and the peak values of the high-frequency spectrums 7 and 8 are moved back to the positions where k is + p and-p from the centers, so as to obtain the synthesized spread spectrum. The illumination direction of the structured light is changed by utilizing the spatial light modulator, super-resolution frequency spectrums are obtained in different modulation directions, and the super-resolution frequency spectrums are obtained from three structured light illumination directions after weighted averaging through generalized wiener filteringAnd synthesizing, and performing inverse Fourier transform to obtain the super-resolution image with isotropic resolution.
The invention only needs to collect 2 images with phase shift of pi in each direction, can reduce the original images required by super-resolution reconstruction to 6 images, and greatly improves the time resolution. In the parameter solving process, the frequency and the phase of the structured light striation of one image only need to be solved in each direction, and the super-resolution image reconstruction rate is greatly improved. The high-frequency spectrum is separated mainly through the step of spectrum subtraction, iterative computation or parallel computation is not needed, an excessively complex reconstruction process is not needed, and the requirement on the performance of a computer is not high.

Claims (3)

1. A super-resolution reconstruction method based on structured Light illumination is characterized in that a Spatial Light Modulator (SLM) is used for generating structured Light, a sample to be measured on an object plane is modulated, high-frequency information which cannot be acquired originally is introduced after modulation, a CCD camera is used for acquiring an image for the first time, the spatial Light modulator is used for generating structured Light with a phase shift of pi, an image is acquired for the second time after modulation, a wide-field image is obtained by adding the image acquired for the first time and the image acquired for the second time, the frequency spectrum of the wide-field image and the frequency spectrum generated by carrying out wiener filtering on the frequency spectrum are used for separating the high-frequency information in the image acquired for the second time, filtering and spectrum shifting operations are carried out, the high frequency is shifted back to an original position, the spatial Light modulator is used for changing the illumination direction of the structured Light, the frequency spectrum of super-resolution is acquired in different modulation directions, the super-resolution frequency spectrums acquired in three structured Light illumination directions are synthesized after weighted averaging through generalized wiener filtering, and performing inverse Fourier transform to obtain a super-resolution image with isotropic resolution.
2. The method as claimed in claim 1, wherein the structured light fringe frequency is estimated by autocorrelation method, and the result of solving the fringe frequency is used to speed up the solution of the structured light phase and the structured light fringe frequency when solving the structured light phase, and a residual spectrum is generated at the frequency near the center position during the separation process, and the noise is suppressed by wiener filtering to ensure the quality of the super-resolution imaging result.
3. The structured light illumination-based super-resolution reconstruction method according to claim 1, comprising the following steps:
the image 0 is collected by a CCD camera for the first time, high-frequency information exceeding the diffraction limit is introduced into the frequency spectrum of the image 0, so that an aliasing frequency spectrum is formed, structured light with the phase shift of pi is generated through a spatial light modulator, an image 1 is collected after modulation, and when the uniform illumination is carried out, an image space image collected by a wide-field imaging system is represented as follows:
D0(r)＝[S(r)·I(r)]*H(r) (1)
wherein r represents the two-dimensional coordinates of the spatial domain, S (r) represents the fluorescence concentration distribution, H (r) represents the point spread function of the imaging system, a represents the convolution symbol, D0(r) is image 0, which introduces high frequency information beyond the diffraction limit under modulation by the cosine structured light, which is illuminated as indicated by
Figure FDA0003351824360000011
I0Is the average light intensity of the structured light, m is the modulation degree, p is the spatial frequency of the structured light,
Figure FDA0003351824360000012
for structured light phase, the received spectrum after structured light modulation:
Figure FDA0003351824360000013
wherein
Figure FDA0003351824360000014
Is D0(r), S (r), representing the Fourier transform, k being the two-dimensional coordinates of the frequency domain,
Figure FDA0003351824360000015
for the optical transfer function OTF and shifting the phase of the structured light by pi, the image plane obtains an image 1 whose frequency spectrum is represented as:
Figure FDA0003351824360000016
Figure FDA0003351824360000017
is D1(r) Fourier transform, there is a high frequency spectrum in the frequency spectrums 0 and 1, which is modulated by the structural light and then shifted into the OTF, the frequency spectrums of the images 0 and 1 are added, and the high frequency information is eliminated, so as to obtain the following result:
Figure FDA0003351824360000018
Figure FDA0003351824360000019
is the spectrum 2 of the wide-field image obtained after the addition, and the spectrum 1 and the spectrum 2 are subtracted to obtain a spectrum map 3 with the center low frequency removed, which can be expressed as:
Figure FDA0003351824360000021
the fringe frequency and the phase of the structured light acquire the frequency of the structured light fringes by utilizing an autocorrelation algorithm, the phase is solved by solving the result of the fringe frequency, the solving speed of the phase and the frequency of the structured light fringes is accelerated, and then the frequency of the structured light fringes is obtained
Figure FDA0003351824360000022
Wiener filtering is performed to obtain a spectrum diagram 4, which is represented as:
Figure FDA0003351824360000023
Figure FDA0003351824360000024
representing the frequency spectrum 4, NaRepresenting the noise power spectrum, A and alpha representing the coefficients of the estimated signal power spectrum, A2|k|-2αRepresenting the estimated power spectrum of the signal, spectrum 4 is shifted along-p and + p, respectively, to obtain spectrum 5 and spectrum 6, the corresponding spectra being represented as
Figure FDA0003351824360000025
Figure FDA0003351824360000026
Figure FDA0003351824360000027
And
Figure FDA0003351824360000028
respectively represented are a fourier transform and an inverse fourier transform,
Figure FDA0003351824360000029
and
Figure FDA00033518243600000210
a representative frequency spectrum 5 and a representative frequency spectrum 6 are obtained by respectively subtracting the frequency spectrum 3 from the frequency spectrum 5 and obtaining a separated high-frequency spectrum at the position with negative frequency, a residual spectrum is generated when the frequency is close to a zero value in the separation process, the noise of the part is suppressed by wiener filtering, the frequency spectrum value with a zero value close to k is suppressed, and a high-frequency spectrum 7 is obtained
Figure FDA00033518243600000211
Figure FDA00033518243600000212
For the high frequency spectrum 7, the spectrum 3 is subtracted from the spectrum 6, and a separate high frequency spectrum is obtained at a position where the frequency is positive, and wiener filtering is performed to suppress a spectrum value close to a zero value of k, so as to obtain a high frequency spectrum 8:
Figure FDA00033518243600000213
Figure FDA00033518243600000214
for the high frequency spectrum 8, I0And m is not required to be solved, the peak values of the high-frequency spectrums 7 and 8 are moved back to the positions where k is + p and-p from the center, the synthesized spread spectrum is obtained, the illumination direction of the structured light is changed by using the spatial light modulator, the super-resolution spectrums are obtained in different modulation directions, the super-resolution spectrums obtained in the three structured light illumination directions are synthesized after weighted averaging through the generalized wiener filtering, and then inverse Fourier transform is performed, so that the isotropic super-resolution image with the resolution is obtained.
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