CN114022583A - OCT image reconstruction method based on non-uniform discrete Fourier transform - Google Patents
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Abstract
According to the OCT image reconstruction method based on the non-uniform discrete Fourier transform, the discrete Fourier transform method of non-uniform time sampling points and non-uniform frequency sampling points is used, loss of high-frequency signals in the discrete Fourier transform process is reduced, and the sensitivity reduction phenomenon at a larger depth position is improved; the conversion and interpolation of lambda space and k space in the traditional reconstruction method are not needed, and the operation process and the calculated amount of the reconstructed depth information are simplified; the frequency domain expansion can be realized by resampling the frequency domain, so that huge calculation amount caused by zero filling of front and back data is avoided; the method of selecting non-uniform time sampling points eliminates the influence of nonlinear sampling of the linear array CCD on the original signal on the quality of the reconstructed image; half of the frequency domain space is selected, similar to Hilbert transform, to eliminate the interference of complex conjugate image to the imaging quality.
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 (OCT) is a non-invasive, non-contact imaging method that uses the michelson interferometer Optical path to obtain high resolution images of the cross-section of a tissue microstructure. OCT has revolutionized ophthalmic diagnostics due to its non-invasive and ability to produce cross-sectional and volumetric imaging with micron resolution. OCT is a shallow imaging method, and is suitable for optical diagnosis technology of imaging of 2-3mm shallow biological tissues. In contrast to conventional time-domain OCT based on scanning optical delay lines, fourier-domain OCT enables fourier transformation to reconstruct depth profiles of biological tissue from acquired raw spectral data. There are two main types of frequency domain OCT, one is spectral domain OCT with a spectrometer and a line CCD (SD-OCT), and the other is swept source OCT with a swept source and point detection (SS-OCT). Compared with SS-OCT, SD-OCT has the advantages of high resolution and good phase stability. At present, the depth information reconstruction method mainly applied to SD-OCT is mainly discrete Fourier transform. However, there is no relevant patent for the OCT image reconstruction method based on the non-uniform discrete fourier transform mentioned herein.
The SD-OCT system adopts a broadband light source, a Michelson interferometer and a rapid multi-channel spectrometer to obtain interference information. The reflected light of the reference arm has a time delay, and the backscattered light of the sample arm contains structural information inside the sample, so that the interference spectrum signal is modulated. The interference spectrum is received by the fast linear array camera after being subjected to grating light splitting, and signals are collected by an image acquisition card. The acquired interference signal 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 system
The broadband light source comprises a broadband light source, a linear array CCD and delta lambda, wherein delta lambda is delta lambda/N, the delta lambda represents the spectral bandwidth of the broadband light source, N represents the number of pixels of the linear array CCD, and the delta lambda represents the spectral sampling interval of the CCD. Resolution of theoretical maximum imaging depth by spectrometer
And (6) determining. As the imaging depth increases, the depth-dependent sensitivity attenuation (fall-off) also limits the actual imaging depth. Another factor that affects axial resolution and depth-dependent sensitivity attenuation is the image reconstruction method. The current main image reconstruction method is to correct the original spectrum, subtract the direct current term, convert the lambda space into the k space, then interpolate the original data, compensate the dispersion, finally do the Fourier transform and get the sample chromatography signal by taking the modulus of the exponential term. While the application of Discrete Fourier Transform (DFT) to reconstruct a tomographic signal requires the wavenumber k linear sampling of the spectral data. Since the optical signal received by the spectrometer is in λ -space and the actually processed interference signal is in k-space, it is necessary to convert the λ -space signal into the k-space interference signal. Also, because λ is inversely related to k, the short wavelength portion of the spectrum is sampled more sparsely than the long wavelength portion. This means that if the resampled spectrum is interpolated to be uniformly sampled by k, the high frequency signal of the spectral fringe is lost, resulting in a reduction in sensitivity. That is, the spectral data is sampled at equal intervals when the DFT reconstructed image is performed, so that the data of the short wavelength part (high frequency signal) cannot be sampled more completely, thereby causing the loss of the high frequency signal. Resampling and interpolation need to be used, otherwise resolution degradation will result. Or, the spectral data is sampled irregularly, and the NDFT is directly performed on the spectral data without resampling and interpolation, so that the depth information can be reconstructed without causing a decrease in resolution.
Moreover, a large amount of calculation is required for the interpolation of the original spectrum converted from the λ space to the k space, and in order to meet the requirement of high-speed calculation, the interpolation of the whole image which is repeatedly scanned is required when OCTA blood flow imaging is performed, so that GPU acceleration is often used, and the complexity of an algorithm program is increased.
The existing method for reconstructing an image by using non-uniform Fourier transform mainly performs NDFT on spectral data in k space, which means that a swept-frequency OCT system can be directly used, and in SD-OCT, λ and k space conversion is required. In fact, in the SD-OCT system, the signal received by the linear CCD in the spectrometer is not ideally uniformly distributed in the λ space, but the original spectrum is non-uniformly distributed in the λ space due to the grating splitting, i.e. the original spectrum signal of the SD-OCT is non-linearly sampled, and therefore should be non-uniformly sampled in the time domain of the non-uniform fourier transform. In addition, the existing non-uniform fourier transform algorithm reconstructs data of all k-spaces, which may interfere with complex conjugate images.
Disclosure of Invention
The invention overcomes the defects in the prior art, and provides an OCT image reconstruction method based on non-uniform discrete Fourier transform, in order to realize OCT image reconstruction of non-uniform discrete Fourier transform, reduce the loss of high-frequency signals in the discrete Fourier transform process, improve the sensitivity reduction phenomenon at a larger depth, simplify the operation process and the calculation amount of reconstruction depth information, eliminate the influence of nonlinear sampling of a linear array CCD on original signals on the quality of reconstructed images, and eliminate the interference of complex conjugate images on the 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 to adjust interference signals in an OCT system, enabling a light source to reach the reference arm and the sample arm after light splitting through a coupler, and enabling return light of the reference arm to be ARexp (ik.2r), where k is the wave number, 2r is the optical path of the reference arm, ARIs the reflection coefficient of the reference light;
in the sample arm, the sample light can be backscattered or refracted in different depth layers after entering the sample, and the superposed sample light sigma of the backscattered light of the scattering tissues in different layers in the depth directionZAS(z) exp (ik · 2z), wherein AS(z) is the backscattering coefficient of the scattering tissue of different layers in the depth direction, and the interfered spectral signals are
Where S (k) is the power spectrum of the light source, r is set to 0, A for ease of calculationRSet to 1, then (1-1) can be written as:
in the above formula, two terms are respectively a first term, a second term and a third term, the first term is an autocorrelation spectrum of the reference light, is a direct current term and belongs to background information; the interference signals of the second item of reference light and the backward scattering light of different layers contain sample depth information and are the superposition of cosine signals of different frequencies; the third term is the autocorrelation signal of the backscattered light of different layers of the sample arm, and the signal is weak and can be ignored;
the DFT is performed on the raw data, requiring that the signal is discrete, discontinuous, and that the fourier transform is also defined in the frequency domain only at regular points as a function of time-frequency, resulting in the formula:
XF(m) represents the result of a discrete Fourier transform of the original signal x (N), where F represents Fourier, N represents the number of sample points in the frequency domain, and N represents the index;
step 2, subtracting a background direct current term from the acquired interference spectrum signal, and eliminating the interference of the original spectrum and the 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 spectral signals;
step 5, resampling a frequency domain interval of the spectrum signal after dispersion compensation, performing band-pass filtering on a depth z space of the spectrum signal, thinning the interval, selecting a depth range of the sample, selecting half of the image to perform Fourier transform, namely performing Hilbert transform, and avoiding the influence of complex conjugate image on image reconstruction;
step 6, constructing an exponential term of the non-uniform Fourier transform
And m, N is 0,1, … and N-1, and Fourier transform results are calculated.
Further, the light source is a broadband light source, using an optical fiber type OCT optical path system.
Further, in step 1), the DFT is performed on the original data, the signal is discrete and discontinuous, and the fourier transform is only defined at regular points in the frequency domain as a function of time and frequency, i.e. the intervals of X (ω) after the discrete fourier transform are regular, so that all samples ω are sampled ωmAre all dominant frequencies
Multiple of (i.e.
Wherein m is 0,1, …, N-1; t is the finite time of the duration of the signal x (T), during which the DFT of x (T) is defined, assuming the number of sample points in the frequency domainThe number of sampling points in the time domain is equal to N, and the discrete Fourier transform formula is
Considering omegamDefined at discrete values only
tn is also defined only at discrete values nTs(ii) a The above formula is rewritten as
Since m represents and ωmCorrelation, denoted by n with tnCorrelation; the above formula is simplified into
XF(m) represents the result of a discrete Fourier transform of the original signal x (N), where F represents Fourier, N represents the number of sample points in the frequency domain, and N represents the index;
extending the definition and calculation of DFT from regular sampling to irregular sampling domain; in general, NDFT is defined as a formula for discrete Fourier transform, taking into account the time domain tnAnd the frequency domain omegamThe sampling above may be non-uniform; assume a time-sampled coordinate of tnN is 0,1, …, N-1 e [0, N), and the frequency sampling coordinate is { ω { (ω) } NmM is 0,1, …, N-1 }. epsilon [0, N), if it is an equidistant sample, t is samplednAnd ωmReplaced 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, 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) the conversion and interpolation of lambda space and k space in the traditional reconstruction method are not needed, and the operation process and the calculated amount of the reconstructed depth information are simplified; (3) the frequency domain expansion can be realized by resampling the frequency domain, so that huge calculation amount caused by zero filling of front and back data is avoided; (4) the method of selecting non-uniform time sampling points eliminates the influence of nonlinear sampling of the linear array CCD on the original signal on the quality of the reconstructed image; (5) half of the frequency domain space is selected, similar to Hilbert transform, to eliminate the interference of complex conjugate image to the imaging quality.
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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, with the understanding that the present disclosure is to be considered as an exemplification of the invention and is not intended to limit the invention to the embodiments illustrated in the drawings, in which:
FIG. 1 is a flow chart of the non-uniform discrete Fourier transform OCT image reconstruction algorithm of the present invention.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.
As shown in fig. 1, the OCT image reconstruction method based on non-uniform discrete fourier transform proposed by the present invention includes the following steps:
step 1, placing reflectors on a reference arm and a sample arm, and adjusting interference signals in the OCT system. The light source is a broadband light source, and an optical fiber type OCT optical path system is used. The broadband light source reaches a reference arm and a sample arm after being split by a coupler, and the return light of the reference arm is ARexp (ik.2r), where k is the wave number, 2r is the optical path of the reference arm, ARIs the reflection coefficient of the reference light. In the sample arm, the sample light can be backscattered or refracted in different depth layers after entering the sample, and the superposed sample light sigma of the backscattered light of the scattering tissues in different layers in the depth directionZAS(z) exp (ik · 2z), wherein AS(z) is the backscattering coefficient in the depth direction of the scattering tissue of the different layers. The spectral signal of the interference is
Where S (k) is the power spectrum of the light source, r is set to 0, A for ease of calculationRSet to 1, then (1-1) can be written as:
the first term between "═ in the above equation" is an autocorrelation spectrum of the reference light, is a direct current term, and belongs to background information. The second term interference signal of the reference light and the backscattered light of different layers, which contains the sample depth information, is the superposition of cosine signals of different frequencies. The third term is the autocorrelation signal of the backscattered light of different layers of the sample arm, with a negligible signal weakness.
The DFT of the raw data requires that the signal be discrete, discontinuous, and it is also desirable that the fourier transform is defined only at regular points in the frequency domain as a function of time frequency. I.e. we want the intervals of X (ω) after the discrete fourier transform to be regular, so that all samples ω are sampledmAre all dominant frequencies
Multiple of (i.e.
Wherein m is 0,1, …, N-1. T is the finite time that the signal x (T) lasts, and we want to define the DFT of x (T) during this time. The number of samples in the frequency domain is assumed to be equal to the number of samples in the time domain, and is N. The discrete Fourier transform is formulated as
Considering omegamDefined at discrete values only
tn is also defined only at discrete values nTs. The above formula is rewritten as
Since m represents and ωmCorrelation, denoted by n with tnAnd (4) correlating. The above formula is simplified into
The definition and calculation of the DFT is extended from regular sampling to the irregular sampling domain. In general, NDFT is defined as a formula for discrete Fourier transform, taking into account the time domain tnAnd the frequency domain omegamThe sampling in may not be uniform. Assume a time-sampled coordinate of tnN is 0,1, …, N-1 e [0, N), and the frequency sampling coordinate is { ω { (ω) } NmAnd m is 0,1, …, N-1 }. epsilon [0, N). If the sampling is equal-interval sampling, t is addednAnd ωmReplaced with n and m, respectively.
Step 2, subtracting a background direct current term from the acquired interference spectrum signal, and eliminating the interference of the original spectrum and the 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 spectral signals;
and 5, resampling a frequency domain interval of the spectrum signal after dispersion compensation, performing band-pass filtering on a depth z space of the spectrum signal, and refining the interval. Selecting the depth range of the sample, and selecting half of the image to perform Fourier transform, which is equivalent to performing Hilbert transform, so that the influence of complex conjugate image on image reconstruction is avoided;
step 6, constructing an exponential term of the non-uniform Fourier transform
And m, N is 0,1, … and N-1, and Fourier transform results are calculated.
This patent uses non-uniform time sampling point and non-uniform frequency sampling point. Frequency resampling is equivalent to performing band-pass filtering on an original signal in a period, thinning an interval, selecting a depth range of Fourier transform sampling, selecting a half range, performing Fourier transform without conjugate image, and equivalent to Hilbert transform. The fourier transform is also defined in the frequency domain only to consist of regular points as a function of time and frequency. I.e. not for every frequency omega but only for some specific omegamIt makes sense. Post-simultaneous Fourier transform X (ω)m) Are also regular, so that all samples ω are takenmAre all dominant frequencies
Multiple of (i.e.
Wherein m is 0,1, …, N-1. The core of the non-uniform sampling is that more sampling points are allocated to a more concentrated part of the frequency spectrum in the frequency domain according to the frequency spectrum characteristics of the original signal, and the rough analysis can not cause serious errors for components with smaller amplitudes. Because the sampling time of the signal is not infinite long, the original signal is not infinite short in the frequency domain, the DFT has no proper frequency analysis, and no proper frequency range is selected, the signal after the DFT has a very wide frequency spectrum range, i.e. the frequency spectrum is widened. The NDFT method is introduced to densely distribute over a particular frequency range while reducing the number of sample points in 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 will be apparent to those skilled in the art that modifications may be made to the embodiments or portions thereof without departing from the spirit and scope 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 to adjust interference signals in an OCT system, enabling a light source to reach the reference arm and the sample arm after light splitting through a coupler, and enabling return light of the reference arm to be ARexp (ik.2r), where k is the wave number, 2r is the optical path of the reference arm, ARIs the reflection coefficient of the reference light;
in the sample arm, the sample light can be backscattered or refracted in different depth layers after entering the sample, and the superposed sample light sigma of the backscattered light of the scattering tissues in different layers in the depth directionZAS(z) exp (ik · 2z), wherein AS(z) is the backscattering coefficient of the scattering tissue of different layers in the depth direction, and the interfered spectral signals are
Where S (k) is the power spectrum of the light source, r is set to 0, A for ease of calculationRSet to 1, then (1-1) can be written as:
in the above formula, two terms are respectively a first term, a second term and a third term, the first term is an autocorrelation spectrum of the reference light, is a direct current term and belongs to background information; the interference signals of the second item of reference light and the backward scattering light of different layers contain sample depth information and are the superposition of cosine signals of different frequencies; the third term is the autocorrelation signal of the backscattered light of different layers of the sample arm, and the signal is weak and can be ignored;
the DFT is performed on the raw data, requiring that the signal is discrete, discontinuous, and that the fourier transform is also defined in the frequency domain only at regular points as a function of time-frequency, resulting in the formula:
XF(m) represents the result of a discrete fourier transform of the original signal x (N), N representing the number of sample points in the frequency domain, N representing the index;
step 2, subtracting a background direct current term from the acquired interference spectrum signal, and eliminating the interference of the original spectrum and the 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 spectral signals;
step 5, resampling a frequency domain interval of the spectrum signal after dispersion compensation, performing band-pass filtering on a depth z space of the spectrum signal, thinning the interval, selecting a depth range of the sample, selecting half of the image to perform Fourier transform, namely performing Hilbert transform, and avoiding the influence of complex conjugate image on image reconstruction;
step 6, constructing an exponential 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 according to claim 1, characterized in that said light source is a broadband light source, using an optical fiber-type OCT optical path system.
3. OCT image reconstruction method based on non-uniform discrete Fourier transform as claimed in claim 1Method, characterized in that in said step 1) the raw data is subjected to a DFT, requiring that the signal is discrete, discontinuous and that the fourier transform is defined in the frequency domain only at regular points, i.e. the X (ω) intervals after the discrete fourier transform are regular, as a function of time and frequency, so that all samples ω are sampled ωmAre all dominant frequencies
Multiple of (i.e.
Wherein m is 0,1, …, N-1; t is the finite time of the signal x (T) duration, the DFT of x (T) is defined in the time, the number of sampling points in the frequency domain is equal to the number of sampling points in the time domain, N is provided, and the formula of discrete Fourier transform is as follows
Considering omegamDefined at discrete values only
tnAlso defined only at discrete values nTs(ii) a The above formula is rewritten as
Since m represents and ωmCorrelation, denoted by n with tnCorrelation; the above formula is simplified into
XF(m) represents the result of a discrete fourier transform of the original signal x (N), N representing the number of sample points in the frequency domain, N representing the index;
extending the definition and calculation of DFT from regular sampling to irregular sampling domain; in general, NDFT is defined as a formula for discrete Fourier transform, taking into account the time domain tnAnd the frequency domain omegamThe sampling above may be non-uniform; assume a time-sampled coordinate of tnN is 0,1, …, N-1 e [0, N), and the frequency sampling coordinate is { ω { (ω) } NmM is 0,1, …, N-1 }. epsilon [0, N), if it is an equidistant sample, t is samplednAnd ωmReplaced with n and m, respectively.
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