CN114022583B - OCT image reconstruction method based on non-uniform discrete Fourier transform - Google Patents
OCT image reconstruction method based on non-uniform discrete Fourier transform Download PDFInfo
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Abstract
According to the non-uniform discrete Fourier transform-based OCT image reconstruction method, a discrete Fourier transform method of non-uniform time sampling points and non-uniform frequency sampling points is used, so that loss of high-frequency signals in the discrete Fourier transform process is reduced, and the phenomenon of sensitivity reduction at a large depth is improved; conversion and interpolation of lambda space and k space of the traditional reconstruction method are not needed, and the operation process and the calculated amount of the reconstruction depth information are simplified; the frequency domain expansion can be realized by resampling the frequency domain, so that huge calculated amount caused by zero padding of front and rear data is avoided; the method for selecting the non-uniform time sampling points eliminates the influence of linear array CCD on the original signal non-linear sampling on the reconstructed image quality; half of the frequency domain space is selected, and the interference of complex conjugate pair imaging quality is eliminated, like Hilbert transformation.
Description
Technical Field
The invention belongs to the technical field of optical coherence tomography, and particularly relates to an OCT image reconstruction method based on non-uniform discrete Fourier transform.
Background
Optical coherence tomography (Optical coherence tomography, OCT) is a non-invasive, non-contact imaging method that uses a michelson interferometer optical path to obtain high resolution cross-sectional images of tissue microstructures. OCT has revolutionized ophthalmic diagnostics by its ability to non-invasively and generate micron resolution cross-sectional and volumetric imaging. OCT is a shallow imaging method, which is suitable for the optical diagnosis technology of 2-3mm shallow biological tissue imaging. In contrast to conventional time domain OCT based on scanning optical delay lines, fourier domain OCT is capable of fourier transforming reconstructed depth profile of biological tissue from the acquired raw spectral data. There are mainly two types of frequency domain OCT, one is spectral domain OCT (SD-OCT) with a spectrometer and a linear array CCD, and the other is swept source OCT (SS-OCT) with a swept source and point detection. Compared with SS-OCT, the SD-OCT has the advantages of high resolution, high phase stability. The current depth information reconstruction method mainly applied to SD-OCT is mainly discrete Fourier transform. While there is no patent related to an OCT image reconstruction method based on non-uniform discrete fourier transform.
The SD-OCT system adopts a broadband light source, a Michelson interferometer and a fast multichannel spectrometer to acquire interference information. The reflected light from the reference arm is delayed and the backscattered light from the sample arm contains structural information within the sample, which modulates the interference spectrum signal. The interference spectrum is received by the fast linear array camera after grating light splitting, and the signal is collected by the image collecting card. The collected interference signals can reconstruct the reflection coefficient envelope of the sample light in the depth direction through Discrete Fourier Transform (DFT).
Maximum imaging depth of SD-OCT systemWherein δλ=Δλ/N, Δλ represents the spectral bandwidth of the broadband light source, N represents the number of pixels of the linear array CCD, and δλ represents the spectral sampling interval of the CCD. Theoretically the maximum imaging depth is determined by the resolution/>, of the spectrometerAnd (5) determining. As the imaging depth increases, the depth dependent sensitivity decay (fall-off) also limits the actual imaging depth. Another factor affecting the axial resolution and depth dependent sensitivity decay is the image reconstruction method. The main image reconstruction method at present is to correct the original spectrum, reduce the DC term, interpolate the original data after converting the lambda space into k space, compensate the dispersion, make Fourier transform and take the modulus of the index term to obtain the chromatographic signal of the sample. Whereas the application of Discrete Fourier Transform (DFT) to reconstruct the tomographic signal requires wavenumber k linear sampling of the spectral data. Since the optical signal received by the spectrometer is λ -space, and the interference signal actually processed is k-space, it is necessary to convert the λ -space signal into a k-space interference signal. Also, because λ is inversely related to k, the short wavelength portion of the spectrum is more sparsely sampled than the long wavelength portion. This means that if the resampled spectrum is interpolated to uniformly sample k, the high frequency signal of the spectral fringes is lost, resulting in a reduced sensitivity. That is, the DFT reconstruction of the image is performed at equal intervals, so that the data of the short wavelength part (high frequency signal) cannot be more completely sampled, thus resulting in the loss of the high frequency signal. Resampling and interpolation are required, otherwise resolution is reduced. Or irregularly sampling the spectrum data and directly carrying out NDFT on the spectrum data without resampling and interpolation, and reconstructing the depth information without causing resolution degradation.
In addition, a larger operation amount is needed for converting the original spectrum from lambda space to k space for re-interpolation, and in order to meet the requirement of high-speed operation, interpolation is needed for the whole image repeatedly scanned during OCTA blood flow imaging, GPU acceleration is often used, and the complexity of algorithm program is increased.
The existing method for reconstructing an image by using non-uniform fourier transform mainly performs NDFT on spectral data of k space, which means that the system can be directly used if the system is a swept OCT system, and the conversion between λ and k space is needed in SD-OCT. In fact, in SD-OCT systems, the signal received by the linear CCD in the spectrometer is not ideally uniformly distributed in λ space, but rather should be non-uniformly sampled in the time domain of the non-uniform fourier transform due to the non-uniform distribution of the original spectrum in λ space caused by grating spectroscopy, i.e. the original spectral signal of SD-OCT is non-linearly sampled. In addition, the existing non-uniform Fourier transform algorithm reconstructs all k-space data, so that interference of complex conjugate images exists.
Disclosure of Invention
The invention overcomes the defects in the prior art, reduces the loss of high-frequency signals in the discrete Fourier transform process, improves the phenomenon of sensitivity reduction at a larger depth, simplifies the operation process and the calculation amount of reconstruction depth information, eliminates the influence of linear array CCD on the original signal nonlinear sampling on the reconstruction image quality, and eliminates the interference of complex conjugate pair imaging quality.
In order to solve the technical problems, the invention is realized by the following technical scheme:
the OCT image reconstruction method based on the non-uniform discrete Fourier transform comprises the following steps:
Step 1, placing reflectors on a reference arm and a sample arm, adjusting interference signals in an OCT system, enabling a light source to reach the reference arm and the sample arm after being split by a coupler, wherein the return light of the reference arm is A R exp (ik.2r), k is wave number, 2r is the optical path of the reference arm, and A R is the reflection coefficient of the reference light;
In the sample arm, backward scattering or refraction can occur on different depth layers after sample light enters the sample, the superimposed sample light sigma ZAS (z) exp (ik.2z) of backward scattering light of scattering tissues of different layers in the depth direction, wherein A S (z) is backward scattering coefficient of scattering tissues of different layers in the depth direction, and the interference spectrum signal is
Where S (k) is the power spectrum of the light source, where r is set to 0 and A R is set to 1 for ease of calculation, then the formula (1-1) can be written as:
In the above description, the two "=" are a first term, a second term and a third term respectively, wherein the first term is the autocorrelation spectrum of the reference light, is a direct current term, and belongs to background information; the interference signals of the second reference light and the backward scattered light of different layers, including the depth information of the sample, are the superposition of cosine signals of different frequencies; the third term is the autocorrelation signal of the backward scattered light of different layers of the sample arm, and the signal weakness is negligible;
Performing a DFT on the raw data requires that the signal be discrete, discontinuous, and that the fourier transform is also defined only at regular points in the frequency domain as a function of time frequency, yielding the formula:
X F (m) represents the discrete Fourier transform result of the original signal X (N), wherein F represents Fourier, N represents the number of sampling points in the frequency domain, and N represents the index;
Step 2, subtracting a background direct current term from the acquired interference spectrum signal to eliminate interference of an original spectrum and a detector on the interference signal;
step 3, multiplying the interference signal after background removal by a window function, and shaping and correcting the spectrum;
step 4, performing dispersion compensation on the shaped spectrum signal;
Step 5, resampling a frequency domain interval of the spectrum signal after dispersion compensation, carrying out band-pass filtering on a depth z space of the spectrum signal, thinning the interval, selecting a depth range of a sample, selecting a half of images to carry out Fourier transform, which is equivalent to Hilbert transform, so that the influence of complex conjugate on image reconstruction is avoided;
Step6, constructing an index term of the non-uniform Fourier transform M, n=0, 1, …, N-1, and calculating the fourier transform result.
Further, the light source is a broadband light source, and a fiber-optic OCT light path system is used.
Further, in said step 1), the original data is subjected to DFT, the desired signal is discrete and discontinuous, and the Fourier transform is defined only at regular points in the frequency domain as a function of time frequency, i.e. the intervals of X (ω) after the discrete Fourier transform are regular, so that all samples ω m are the dominant frequencyMultiples of/>Wherein m=0, 1, …, N-1; t is the finite time for which the signal x (T) continues, during which time the DFT of x (T) is defined, assuming that the number of samples in the frequency domain is equal to the number of samples in the time domain, both are N, the discrete Fourier transform formula is
Consider that omega m is defined only at discrete valuesTn is also defined only at the discrete value nT s; the above is rewritten as
Since m is related to ω m, n is related to t n; the above is simplified into
X F (m) represents the discrete Fourier transform result of the original signal X (N), wherein F represents Fourier, N represents the number of sampling points in the frequency domain, and N represents the index;
Expanding the definition and computation of the DFT from regular sampling to irregular sampling domain; in general, NDFT is defined as a discrete fourier transform equation, considering that the samples in the time domain t n and frequency domain ω m may be non-uniform; assuming that the time sample coordinates are { t n, n=0, 1, …, N-1} ∈ [0, N), the frequency sample coordinates are { ω m, m=0, 1, …, N-1} ∈ [0, N), and if equally spaced samples, t n and ω m are replaced with N and m, respectively.
Compared with the prior art, the invention has the beneficial effects that:
(1) The discrete Fourier transform method of non-uniform time sampling points and non-uniform frequency sampling points is used, so that loss of high-frequency signals in the discrete Fourier transform process is reduced, and the phenomenon of sensitivity reduction at a larger depth is improved;
(2) Conversion and interpolation of lambda space and k space of the traditional reconstruction method are not needed, and the operation process and the calculated amount of the reconstruction depth information are simplified; (3) The frequency domain expansion can be realized by resampling the frequency domain, so that huge calculated amount caused by zero padding of front and rear data is avoided; (4) The method for selecting the non-uniform time sampling points eliminates the influence of linear array CCD on the original signal non-linear sampling on the reconstructed image quality; (5) Half of the frequency domain space is selected, and the interference of complex conjugate pair imaging quality is eliminated, like Hilbert transformation.
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The accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, in which:
fig. 1 is a flowchart of an OCT image reconstruction algorithm for non-uniform discrete fourier transform according to the present invention.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, it being understood that the preferred embodiments described herein are for illustration and explanation of the present invention only, and are not intended to limit the present invention.
As shown in fig. 1, the OCT image reconstruction method based on non-uniform discrete fourier transform according to the present invention includes the following steps:
And step 1, placing a reflecting mirror on the reference arm and the sample arm, and adjusting out interference signals in the OCT system. The light source is a broadband light source and a fiber-optic OCT light path system is used. The broadband light source reaches the reference arm and the sample arm after being split by the coupler, the reference arm return light is A R exp (ik.2r), wherein k is the wave number, 2r is the optical path of the reference arm, and A R is the reflection coefficient of the reference light. In the sample arm, backward scattering or refraction occurs in different depth layers after the sample light enters the sample, and the superimposed sample light Σ ZAS (z) exp (ik.2z) of the backward scattering light of the scattering tissue of different layers in the depth direction, where a S (z) is the backward scattering coefficient of the scattering tissue of different layers in the depth direction. The spectrum signal of the interference is
Where S (k) is the power spectrum of the light source, where r is set to 0 and A R is set to 1 for ease of calculation, then the formula (1-1) can be written as:
The first term between "=" in the above formula is the autocorrelation spectrum of the reference light, is a direct current term, and belongs to the background information. The interference signal of the second item of reference light and the backscattered light of the different layers, containing the sample depth information, is a superposition of cosine signals of different frequencies. The third term is the autocorrelation signal of the backscattered light of the different layers of the sample arm, with negligible signal weakness.
Performing a DFT on the raw data requires that the signal be discrete, discontinuous, and also that the fourier transform be defined only at regular points in the frequency domain as a function of time frequency. I.e. we want the interval of X (omega) after discrete Fourier transform to be regular, so that all samples omega m are the dominant frequencyMultiples of/>Wherein m=0, 1, …, N-1.T is the finite time that signal x (T) lasts, during which time we wish to define the DFT of x (T). Let N be the number of samples in the frequency domain equal to the number of samples in the time domain. The discrete Fourier transform formula is
Consider that omega m is defined only at discrete valuesTn is also defined only at the discrete value nT s. The above is rewritten as
Since m is related to ω m, n is related to t n. The above is simplified into
The definition and computation of DFT is extended from regular sampling to irregular sampling domain. In general, NDFT is defined as a discrete fourier transform equation, considering that the samples in the time domain t n and frequency domain ω m may be non-uniform. Let the time sampling coordinates be { t n, n=0, 1, …, N-1} ∈ [0, N), the frequency sampling coordinates be { ω m, m=0, 1, …, N-1} ∈ [0, N). If equally spaced samples, t n and ω m are replaced with n and m, respectively.
Step 2, subtracting a background direct current term from the acquired interference spectrum signal to eliminate interference of an original spectrum and a detector on the interference signal;
step 3, multiplying the interference signal after background removal by a window function, and shaping and correcting the spectrum;
step 4, performing dispersion compensation on the shaped spectrum signal;
and 5, resampling the frequency domain interval of the spectrum signal after dispersion compensation, and carrying out band-pass filtering on the depth z space of the spectrum signal to refine the interval. Selecting a depth range of a sample, selecting a half of images to carry out Fourier transform, which is equivalent to Hilbert transform, so that the influence of complex conjugate on image reconstruction is avoided;
Step6, constructing an index term of the non-uniform Fourier transform M, n=0, 1, …, N-1, and calculating the fourier transform result.
This patent uses non-uniform time sampling points and non-uniform frequency sampling points. The frequency resampling is equivalent to the band-pass filtering of the original signal of one period, the interval is thinned, the depth range of the Fourier transform sampling can be selected, and no conjugate image exists after half of the range is selected, which is equivalent to the Hilbert transform. The fourier transform is also defined only in the frequency domain as a function of time frequency, on regular points. I.e. not for every frequency ω, but only for some specific ω m. At the same time, the intervals of X (omega m) after Fourier transform are also regular, so that all samples omega m are the dominant frequencyMultiples of/>Where m=0, 1, …, N-1. The core of non-uniform sampling is that, according to the spectral characteristics of the original signal, more sampling points are allocated to the part of the frequency domain where the spectrum is more concentrated, and coarse analysis does not cause serious errors for the components with smaller amplitudes. Because the sampling time of the signal is not infinitely long, the original signal cannot be infinitely short in the frequency domain, the DFT does not have proper frequency analysis, and proper frequency range is not selected, so that the signal after the DFT has a very wide frequency spectrum range, namely frequency spectrum broadening. The approach of NDFT is introduced to densely distribute over a specific frequency range while reducing the number of sampling points over less important frequency ranges.
Finally, it should be noted that: although the present invention has been described in detail with reference to the embodiments, it should be understood that the invention is not limited to the preferred embodiments, but is capable of modification and equivalents to some of the features described in the foregoing embodiments, but is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (3)
1. The OCT image reconstruction method based on the non-uniform discrete Fourier transform is characterized by comprising the following steps of:
Step 1, placing reflectors on a reference arm and a sample arm, adjusting interference signals in an OCT system, enabling a light source to reach the reference arm and the sample arm after being split by a coupler, wherein the return light of the reference arm is A R exp (ik.2r), k is wave number, 2r is the optical path of the reference arm, and A R is the reflection coefficient of the reference light;
In the sample arm, backward scattering or refraction can occur on different depth layers after sample light enters the sample, the superimposed sample light sigma ZAS (z) exp (ik.2z) of backward scattering light of scattering tissues of different layers in the depth direction, wherein A S (z) is backward scattering coefficient of scattering tissues of different layers in the depth direction, and the interference spectrum signal is
Where S (k) is the power spectrum of the light source, where r is set to 0 and A R is set to 1 for ease of calculation, then the above formula can be written as:
In the above description, the two "=" are a first term, a second term and a third term respectively, wherein the first term is the autocorrelation spectrum of the reference light, is a direct current term, and belongs to background information; the interference signals of the second reference light and the backward scattered light of different layers, including the depth information of the sample, are the superposition of cosine signals of different frequencies; the third term is the autocorrelation signal of the backward scattered light of different layers of the sample arm, and the signal weakness is negligible;
Performing a DFT on the raw data requires that the signal be discrete, discontinuous, and that the fourier transform is also defined only at regular points in the frequency domain as a function of time frequency, yielding the formula:
X F (m) represents the discrete Fourier transform result of the original signal X (N), N represents the number of sampling points in the frequency domain, and N represents the index;
Step 2, subtracting a background direct current term from the acquired interference spectrum signal to eliminate interference of an original spectrum and a detector on the interference signal;
step 3, multiplying the interference signal after background removal by a window function, and shaping and correcting the spectrum;
step 4, performing dispersion compensation on the shaped spectrum signal;
Step 5, resampling a frequency domain interval of the spectrum signal after dispersion compensation, carrying out band-pass filtering on a depth z space of the spectrum signal, thinning the interval, selecting a depth range of a sample, selecting a half of images to carry out Fourier transform, which is equivalent to Hilbert transform, so that the influence of complex conjugate on image reconstruction is avoided;
Step6, constructing an index term of the non-uniform Fourier transform And calculating a Fourier transform result.
2. The non-uniform discrete fourier transform-based OCT image reconstruction method of claim 1, wherein the light source is a broadband light source using a fiber-optic OCT optical path system.
3. The OCT image reconstruction method according to claim 1, wherein in the step 1), the original data is DFT, the desired signal is discrete and discontinuous, and the fourier transform is defined only at regular points in the frequency domain as a function of time frequency, i.e., the intervals of X (ω) after the discrete fourier transform are regular, so that all the samples ω m are dominantMultiples of/>Wherein m=0, 1, …, N-1; t is the finite time for which the signal x (T) continues, during which time the DFT of x (T) is defined, assuming that the number of samples in the frequency domain is equal to the number of samples in the time domain, both are N, the discrete Fourier transform formula is
Consider that omega m is defined only at discrete valuesT n is also defined only at the discrete value nT s; the above is rewritten as
Since m is related to ω m, n is related to t n; the above is simplified into
X F (m) represents the discrete Fourier transform result of the original signal X (N), N represents the number of sampling points in the frequency domain, and N represents the index;
Expanding the definition and computation of the DFT from regular sampling to irregular sampling domain; in general, NDFT is defined as a discrete fourier transform equation, considering that the samples in the time domain t n and frequency domain ω m may be non-uniform; assuming that the time sample coordinates are { t n, n=0, 1, …, N-1} ∈ [0, N), the frequency sample coordinates are { ω m, m=0, 1, …, N-1} ∈ [0, N), and if equally spaced samples, t n and ω m are replaced with N and m, respectively.
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| 基于综合孔径辐射计稀疏阵列非均匀采样图像的快速重建;孙逢林;张升伟;;电子与信息学报;20130415(04);全文 * |
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