CN116630154A - Deconvolution super-resolution reconstruction method and device for optical coherence tomography - Google Patents
Deconvolution super-resolution reconstruction method and device for optical coherence tomography Download PDFInfo
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Abstract
The deconvolution super-resolution reconstruction method and device for the optical coherence tomography image can avoid artifacts generated by deconvolution iteration reconstruction and effectively improve the resolution of the reconstructed image. The method comprises the following steps: (1) Obtaining an OCT image with low resolution through Fourier transformation, and taking the OCT image as input original data; (2) Constructing an optimization function of sparse continuous prior deconvolution calculation; (3) performing initial setup of reconstruction optimization, including: original data mode, iteration round, sparsity prior weight and continuity prior weight; (4) Performing iterative training, and introducing intermediate variables to perform iterative calculation; (5) And after the optimization iteration is completed, outputting a final deconvolution super-resolution reconstructed OCT image.
Description
Technical Field
The invention relates to the technical field of optical imaging, in particular to a deconvolution super-resolution reconstruction method of an optical coherence tomography image and a deconvolution super-resolution reconstruction device of the optical coherence tomography image.
Background
Optical coherence tomography (Optical coherence tomography, OCT) is an emerging optical imaging technique that can provide non-contact, non-invasive cross-sectional imaging of biological tissue with spatial resolution on the order of microns. While OCT image micron-scale resolution has played an important role in the fields of fundus imaging, cardiovascular imaging, and endoscopic imaging, there is a continuing need for higher resolution OCT images. Further increasing the resolution of OCT images may reveal invisible microstructures, which will help the physician to achieve accurate diagnosis.
The axial resolution of OCT images is inversely proportional to the spectral bandwidth of the light source, so researchers often choose ultra-wideband system light sources to increase the resolution of OCT images. However, ultra wideband OCT light sources complicate the optical design of the entire OCT image acquisition system. In addition, there is a limit to push the improvement of the axial resolution by further expanding the bandwidth, which requires not only the technical progress of the laser light source but also the correct handling of chromatic aberration and chromatic dispersion of the OCT system. Therefore, the technique of improving the resolution of OCT images by only computational reconstruction is critical without hardware improvement. The existing reconstruction methods include a spectrum estimation method, a deconvolution method and a deep learning method.
Autoregressive spectrum estimation is a reconstruction technique which is commonly used at present and improves the axial resolution of OCT, but has two main limitations. First, the spectral estimation method can only improve the axial resolution. Second, mismatch of the spectral estimation model of the spectral estimation method and the spectral data can lead to inaccurate intensity of image reconstruction. Reconstruction artifacts may be generated in the image when an inappropriate model is selected.
In recent years, the deep learning method has shown a strong capability in terms of resolution improvement of OCT images. The generation of the antagonism network is used to enhance the optical axial and lateral resolution of OCT images while preserving and improving the details of the speckle content. Digital focusing based on deep learning has also been reported to extend OCT depth of focus and improve image lateral resolution. The deep learning method provides a plurality of new ideas for improving the OCT resolution. However, a dataset with the correct low resolution and high resolution mapping is critical to training neural network models, and generation of a true super resolution OCT image still requires acquisition by conventional methods.
The deconvolution method achieves an improvement in the axial and lateral resolutions at a lower computational cost, with Wiener filtering and Lucy-Richardson (LR) deconvolution being most pronounced. These methods achieve resolution enhancement by obtaining the Point Spread Function (PSF) of the OCT system. In the absence of noise, performing deconvolution operations a sufficient number of times can fully recover the high frequency information of the image. However, the image tends to degrade under the influence of noise, which will result in convergence to the noise dominant solution after a certain iteration. It is therefore often recommended to stop the reconstruction after a small number of iterations to avoid excessive image artifacts.
Compared with the OCT image calculation reconstruction super-resolution technology, the deconvolution iterative reconstruction has the optimal reconstruction result and is widely applied. However, the original data of OCT contains a large amount of speckle noise that is difficult to remove, and when deconvolution reconstruction is directly performed on the original data of such noise, serious artifacts are generated as a result of the reconstruction, which is unacceptable for super-resolution reconstruction of medical images.
Disclosure of Invention
In order to overcome the defects of the prior art, the technical problem to be solved by the invention is to provide a deconvolution super-resolution reconstruction method of an optical coherence tomography image, which can avoid artifacts generated by deconvolution iteration reconstruction and effectively improve the resolution of the reconstructed image.
The technical scheme of the invention is as follows: the deconvolution super-resolution reconstruction method of the optical coherence tomography image comprises the following steps of:
(1) Obtaining an OCT image with low resolution through Fourier transformation, and taking the OCT image as input original data;
(2) Constructing an optimization function of sparse continuous prior deconvolution calculation:
the first term of the optimization function is the computational fidelity term, representing the distance between the reconstructed image x and the original OCT image f, a being the point-spread function of the OCT systemThe numbers, second term and third term are continuity prior and sparsity prior, wherein I 1 and || ||2 Respectively represent l 1 and l2 Norms, lambda and lambda s For describing weights between balanced image fidelity terms and successive and sparse priors, in successive priors R (x), in order to distinguish reconstructed image x from subscript n representing different directions x，y，z The continuity prior is described by R (n) instead of R (x), where ε is y For regularization parameters, representing continuity along the y-axis, if the original OCT data input is a two-dimensional image only, will ε y Set to 0;
(3) The initial setting of reconstruction optimization is carried out, which comprises the following steps: original data mode, iteration round, sparsity prior weight and continuity prior weight;
(4) Performing iterative training, and introducing intermediate variables to perform iterative calculation;
(5) And after the optimization iteration is completed, outputting a final deconvolution super-resolution reconstructed OCT image.
According to the invention, a deconvolution reconstruction method is converted into an optimization calculation problem through a constraint iterative deconvolution algorithm taking sample sparsity and continuity as priori knowledge, the priori knowledge aiming at sample reconstruction is introduced, the sparsity of the image is utilized to ensure high-frequency information of the image, meanwhile, the continuity based on gray value correlation is utilized to relieve excessive sparsity and noise reduction of the image, then, initial setting of reconstruction optimization is carried out, iterative training is carried out, and intermediate variables are introduced to carry out iterative calculation, so that artifacts generated by deconvolution iterative reconstruction can be avoided, and the resolution of the reconstructed image is effectively improved.
Also provided is a deconvolution super-resolution reconstruction device of an optical coherence tomographic image, comprising:
an input module configured to obtain a low resolution OCT image by fourier transform as input raw data;
an optimization function construction module configured to construct an optimization function of a sparse continuous a priori deconvolution calculation:
the first term of the optimization function is a computational fidelity term, representing the distance between the reconstructed image x and the original OCT image f, A is the point spread function of the OCT system, and the second term and the third term are a continuity priori and a sparse priori, wherein I 1 and ||||2 Respectively represent l 1 and l2 Norms, lambda and lambda s For describing weights between balanced image fidelity terms and successive and sparse priors, in successive priors R (x), in order to distinguish reconstructed image x from subscript n representing different directions x，y，z The continuity prior is described by R (n) instead of R (x), where ε is y For regularization parameters, representing continuity along the y-axis, if the original OCT data input is a two-dimensional image only, will ε y Set to 0;
an initialization module configured to perform an initial setup of a reconstruction optimization, comprising: original data mode, iteration round, sparsity prior weight and continuity prior weight;
the iterative training module is configured to perform iterative training, and introduces intermediate variables to perform iterative calculation;
and the output module is configured to output a final deconvolution super-resolution reconstructed OCT image after the optimization iteration is completed.
Drawings
Fig. 1 is a conceptual of sparsity and continuity and a continuous representation of three-dimensional OCT volume data. (a) (b) specific examples of absolute sparsity and relative continuity are shown. (c) A visual representation of continuity in 3 x 3 pixels in OCT three-dimensional volume data is shown, along with spatial coordinates in the world coordinate system corresponding to the volume data.
Fig. 2 is a flow chart of a deconvolution super-resolution reconstruction method of an optical coherence tomographic image according to the present invention.
FIG. 3 is a biological sample reconstructionLambda and lambda in s Different choices of ratios. The images in the middle box give a better scale reconstruction of the test case.
FIG. 4 is a graph of exploring the best lambda and lambda for image reconstruction at different noise levels s And (5) selecting a ratio. (a) Four different scale reconstruction results at 5% and 25% noise levels, with the same column images representing the same ratio. The positions of the four different ratios in the graph (b) are also noted. (b) Reconstructed image signal-to-noise heat maps at different noise levels.
Detailed Description
As shown in fig. 2, the deconvolution super-resolution reconstruction method of the optical coherence tomography image comprises the following steps:
(1) Obtaining an OCT image with low resolution through Fourier transformation, and taking the OCT image as input original data;
(2) Constructing an optimization function of sparse continuous prior deconvolution calculation:
the first term of the optimization function is a computational fidelity term, representing the distance between the reconstructed image x and the original OCT image f, A is the point spread function of the OCT system, and the second term and the third term are a continuity priori and a sparse priori, wherein I 1 and ||||2 Respectively represent l 1 and l2 Norms, lambda and lambda s For describing weights between balanced image fidelity terms and successive and sparse priors, in successive priors R (x), in order to distinguish reconstructed image x from subscript n representing different directions x，y，z The continuity prior is described by R (n) instead of R (x), where ε is y For regularization parameters, representing continuity along the y-axis, if the original OCT data input is a two-dimensional image only, will ε y Set to 0;
(3) The initial setting of reconstruction optimization is carried out, which comprises the following steps: original data mode, iteration round, sparsity prior weight and continuity prior weight;
(4) Performing iterative training, and introducing intermediate variables to perform iterative calculation;
(5) And after the optimization iteration is completed, outputting a final deconvolution super-resolution reconstructed OCT image.
According to the invention, a deconvolution reconstruction method is converted into an optimization calculation problem through a constraint iterative deconvolution algorithm taking sample sparsity and continuity as priori knowledge, the priori knowledge aiming at sample reconstruction is introduced, the sparsity of the image is utilized to ensure high-frequency information of the image, meanwhile, the continuity based on gray value correlation is utilized to relieve excessive sparsity and noise reduction of the image, then, initial setting of reconstruction optimization is carried out, iterative training is carried out, and intermediate variables are introduced to carry out iterative calculation, so that artifacts generated by deconvolution iterative reconstruction can be avoided, and the resolution of the reconstructed image is effectively improved.
Preferably, in the step (2), λ is greater than λ s 。
Preferably, in the step (2), the original image with high signal-to-noise ratio is selected to have larger lambda/lambda s The ratio is low, and the original image with low signal-to-noise ratio is smaller lambda/lambda s Proportion. Wherein, the original image with high signal-to-noise ratio can select larger lambda/lambda s The ratio is generally in the range of (1, 5]The selection range of the original image with low signal-to-noise ratio is set as (1, 2)]。
Preferably, in the step (2), smaller parameter values are used to ensure a better signal-to-noise ratio of the image reconstruction. The smaller lambda parameter value range recommended for use is (1, 30).
Preferably, in the step (3), when the input OCT image is a two-dimensional image, a continuity prior regularization parameter epsilon is set y =0; setting a continuity priori regularization parameter epsilon when the input OCT image is three-dimensional volume data y ＝1。
Preferably, in the step (3), λ s And lambda setting is roughly evaluated according to the noise level of the original data, and the SNR of the original image is used as the noise level of the original dataAnd (5) evaluating indexes.
Preferably, in the step (4), the optimization is performed by the following formula:
the solution problem of the formula (8) is converted into a convex optimization problem, and the formula (9) is realized through deconvolution calculation.
Preferably, in the step (4), for the convex optimization problem of the formula (8), the solving process is as follows:
(4.1) replacing the variables with intermediate variables, converting equation (8) to a constraint minimization problem:
wherein ,u＝λs g，u zz ＝g zz ，u xx ＝g xx ，u yy ＝ε y g yy ，u zx ＝2g zx ，
(4.2) the following unconstrained problem will be obtained by the Lagrangian multiplier method:
wherein μ is the Lagrangian multiplier;
(4.3) the strict constraint iteration minimization procedure using the simplified Bregman iteration method is as follows:
wherein ,uij And v ij Respectively representing the calculation factors of three directions of different xyz;
and integrating the three formulas to obtain a final optimization result:
wherein ,
is a second derivative operator in the z-direction, which can be written +.>
Defined as the second derivative operator in the other direction.
Preferably, in the step (4), the solving process of the formula (9) uses the Lucy Richardson deconvolution algorithm to calculate, and in each iteration, the input of the Lucy Richardson deconvolution algorithm is the result of the calculation of the formula (8), and the output is the input of the formula (8) in the next iteration until the end of the loop, and the final high-resolution reconstruction result is output.
It will be understood by those skilled in the art that all or part of the steps in implementing the above embodiment method may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, where the program when executed includes the steps of the above embodiment method, and the storage medium may be: ROM/RAM, magnetic disks, optical disks, memory cards, etc. Accordingly, the invention also includes, corresponding to the method of the invention, a deconvolution super-resolution reconstruction device of an optical coherence tomographic image, which device is generally represented in the form of functional blocks corresponding to the steps of the method. The device comprises:
an input module configured to obtain a low resolution OCT image by fourier transform as input raw data;
an optimization function construction module configured to construct an optimization function of a sparse continuous a priori deconvolution calculation:
the first term of the optimization function is a computational fidelity term, representing the distance between the reconstructed image x and the original OCT image f, A is the point spread function of the OCT system, and the second term and the third term are a continuity priori and a sparse priori, wherein I 1 and ||||2 Respectively represent l 1 and l2 Norms, lambda and lambda s For describing weights between balanced image fidelity terms and successive and sparse priors, in successive priors R (x), in order to distinguish reconstructed image x from subscript n representing different directions x，y，z The continuity prior is described by R (n) instead of R (x), where ε is y For regularization parameters, representing continuity along the y-axis, if the original OCT data input is a two-dimensional image only, will ε y Set to 0;
an initialization module configured to perform an initial setup of a reconstruction optimization, comprising: original data mode, iteration round, sparsity prior weight and continuity prior weight;
the iterative training module is configured to perform iterative training, and introduces intermediate variables to perform iterative calculation;
and the output module is configured to output a final deconvolution super-resolution reconstructed OCT image after the optimization iteration is completed.
Specific embodiments of the present invention are described in detail below. The deconvolution super-resolution reconstruction method of the optical coherence tomography image is realized in the following manner:
fig. 1 is a schematic diagram of sparsity priors and continuity priors involved in an embodiment of the present invention.
The detailed descriptions of sparsity priors and continuity priors are as follows:
the sparsity concept in an image is shown in fig. 1 (a), where a clear boundary exists between a sparse center point and its neighborhood. The more sparse points exist in the image, the more clear boundaries are wrapped in the image, and the higher the resolution of the image. Therefore, increasing the resolution of the OCT image results in an increase in the sparsity of the OCT image. For better acquisition of sparse prior of OCT images, optionally, the invention adopts l1 norm of the image to represent image sparsity. And compared with the l0 norm, the l1 norm can simplify the calculation and improve the efficiency of the algorithm.
However, if only the sparsity priors of the image are considered, excessive sharpening may occur for noise corrupted image areas. The biological samples are typically continuously changing, which corresponds to a correlation of the gray values of the image in the 8 neighborhood of each point in the OCT image, as shown in fig. 1 (b). And selecting the correlation of gray values in a 3×3 region of each point neighborhood from the OCT two-dimensional image to represent the continuity of the image. Meanwhile, for three-dimensional OCT images, the method adopts the information of adjacent frames of OCT volume data to optimize three-dimensional continuity. Three-dimensional OCT of 3 x 3 region the continuity is shown in FIG. 1 (c). The invention selects the second partial derivative penalty to represent the continuity priori of the image, and realizes the continuity transition of the finally reconstructed super-resolution OCT image.
The embodiment of the invention provides a sparse continuous prior deconvolution super-resolution reconstruction method, as shown in fig. 2, in the embodiment, the sparse continuous prior deconvolution super-resolution reconstruction algorithm comprises the following steps:
step 1, obtaining an original low-resolution OCT image.
Specifically, the resolution of OCT images obtained by conventional fourier transform is limited by the bandwidth of the light source, and cannot be increased without upgrading the system bandwidth. Meanwhile, because the OCT spectrum calculation process contains interference of an autocorrelation term, the image contains a large amount of speckle noise which is difficult to remove. The low-resolution image data containing noise is used as the original data input by an algorithm, and OCT image super-resolution is realized through sparse continuous prior deconvolution.
And 2, constructing an optimization function of sparse continuous prior deconvolution calculation.
Specifically, a conventional Lucy-Richardson deconvolution reconstruction restores a low resolution image blurred by the system's known PSF to a high resolution image by statistical estimation. The basic algorithm is as follows:
wherein ,gn The optimization process is to perform interactive iteration based on the point spread function h (x, y) of the imaging system and the original image f (x, y) of the estimation value of the non-high-resolution image in the (x, y) iteration. Although increasing the mathematical resolution is theoretically possibleThe Lucy-Richardson deconvolution method is often unstable due to the presence of noise, and deconvolution from noise corrupted images to obtain final high resolution images is often an uncomfortable inverse problem. Noise in OCT images always creates excessive artifacts in the reconstruction, so we apply prior knowledge of the sample, sparsity, and continuity, creating a constraint model for OCT image deconvolution reconstruction. Specifically, the optimization function is as follows:
wherein the first term of the optimization function is a computational fidelity term, representing the distance between the reconstructed image x and the original OCT image f. A is the point spread function of the OCT system. The second and third terms are continuity priors and sparsity priors, wherein I 1 and ||||2 Respectively represent l 1 and l2 Norms. Lambda and lambda s To describe the weights between the balanced image fidelity terms and the continuous and sparse priors. In the continuity prior R (x), in order to distinguish the reconstructed image x from the subscript n representing a different direction x，y，z We describe the continuity prior with R (n) instead of R (x). In the continuity priors, ε y For regularization parameters, continuity along the y-axis is represented. If the original OCT data is input as a two-dimensional image, ε will be y Set to 0.
And step 3, performing initial setting of reconstruction optimization, wherein the initial setting comprises an original data mode, iteration rounds, sparsity priori weights and continuity priori weights.
Specifically, when the input original OCT data is a two-dimensional image, setting a continuity priori regularization parameter epsilon y =0. When the input original data is three-dimensional volume data, setting a continuity priori regularization parameter epsilon y =1. In this embodiment, the iteration round is set to 50, and the deconvolution solution is fully taken upAnd (5) astringing. For sparsity a priori weights lambda s And the setting of the continuity a priori weights lambda requires a rough assessment based on the noise level of the raw data. Alternatively, in this embodiment, the signal-to-noise ratio SNR of the original image is selected as an index for noise level evaluation of the original data. The specific parameter selection method will be given later on in the selection guidance for the optimization parameters in the sparse continuous deconvolution process included in the present invention.
Step 4: and performing iterative training. Because the calculation amount of directly performing optimization iteration is overlarge, intermediate variables are introduced for performing iterative calculation in order to improve the training speed and simplify the calculation complexity. Alternatively, the equation (1) is converted into a two-step optimization:
the solution problem of the formula (8) can be converted into a convex optimization problem, and the formula (9) is realized through deconvolution calculation. Optionally, the split Bregman algorithm is adopted to solve the convex optimization problem of the solution formula (8). The detailed solving process is as follows:
first, replacing the variables with intermediate variables, converting the loss function (8) into a constraint minimization problem:
wherein ,u＝λs g，u zz ＝g zz ，u xx ＝g xx ，u yy ＝ε y g yy ，u zx ＝2g zz ，
Secondly, the following unconstrained problem is obtained by the Lagrangian multiplier method optionally:
where μ is the Lagrangian multiplier.
Finally, the strict constraint iteration minimization process using the simplified Bregman iteration method is as follows:
wherein ,uij And v ij Respectively representing the calculation factors of three directions of different xyz. And integrating the three formulas to obtain a final optimized result:
wherein ,
is a second derivative operator in the z-direction, which can be written +.>Likewise-> Similarly defined as second derivative operators in other directions.
Preferably, the solution process of formula (4) is calculated using the Lucy Richardson deconvolution algorithm. Specifically, in each iteration, the input of the Lucy Richardson deconvolution algorithm is the result of the calculation of the formula (3), and the output is the input of the formula (3) in the next iteration until the cycle is finished, and the final high-resolution reconstruction result is output.
Step 5: and according to the input data type, the corresponding two-dimensional data or three-dimensional volume data is output and displayed.
All the steps of the sparse continuous prior deconvolution super-resolution reconstruction algorithm are as above.
In this embodiment, for the conventional deconvolution algorithm, a large amount of reconstruction artifacts caused by OCT speckle noise are generated during OCT image reconstruction, a sparse continuous constraint deconvolution algorithm based on sample sparse continuous priori knowledge is provided, artifacts generated by deconvolution iterative reconstruction are avoided, and the resolution of the reconstructed image is effectively improved.
In addition, the embodiment of the invention also provides a proposal for a sparse continuous prior deconvolution super-resolution optimization parameter selection method so as to cope with the challenges of noise robustness and complex signal intensity of OCT original images.
Sparse continuous deconvolution is used as a method for calculating super-resolution, and similar to other super-resolution calculation algorithms, some limitations are faced in parameter optimization, and as shown in fig. 3, wrong optimization parameters can cause differences in reconstruction results. Deconvolution of super-division for better use of the OCT images described aboveReconstruction method, referring to fig. 4, the embodiment synthesizes a ring structure corrupted by 5% and 25% amplitude and variance noise as a low resolution image corrupted by different levels of noise. Alternatively, four different sets of λ and λ are selected s The sparse continuous deconvolution reconstruction proposed by the present invention is performed on the values of (a). Optionally, different lambda and lambda are also systematically detected by the signal-to-noise ratio heatmap shown in FIG. 4 (b) s The signal-to-noise ratio of the reconstructed image under the set of values. The parameter selection suggestions proposed by the embodiment of the invention can be summarized from the figures:
(1) The value of the continuity a priori weight parameter λ must be greater than the sparsity a priori weight parameter λ s Values. When lambda/lambda s At ratios less than 1, the signal-to-noise ratio of the reconstructed image drops rapidly to zero.
(2) The original image with high signal-to-noise ratio can be selected to have larger lambda/lambda s The scale, while the original image at low signal-to-noise ratio requires a smaller scale.
(3) Smaller parameter values are used to ensure a better image reconstruction signal-to-noise ratio.
It is worth noting that the signal-to-noise ratio alone is not a good parameter to evaluate the improvement in image resolution. Therefore, the above factors are only used as general guidance and cannot be used as standard. However, the guidance and suggestion can better help those of ordinary skill in the art to achieve high resolution reconstruction implementations for their low resolution OCT images without undue creative effort.
In addition, the embodiment of the invention can realize the simultaneous processing of large-data-volume three-dimensional OCT volume data, which is beneficial to the rapid and large-volume generation of high-resolution and low-resolution OCT image pairs and provides a sufficient training set for an OCT image super-resolution method based on deep learning. The improvement of performance of the deep learning data set training network generated by the invention and the training network of the traditional training set is not an important point of the invention. However, the high-resolution and low-resolution OCT images generated by the methods of the present invention have a general effect on the general population, and can provide more data support for researchers in the field.
Those skilled in the art will appreciate from the foregoing description of the embodiments that all or part of the processes for implementing the methods of the embodiments described above may be implemented by a computer program for instructing relevant software, where the program may be programmed as Matlab code, c++ or Python code, and the program may include the processes of the embodiments of the methods described above when executed. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
The present invention is not limited to the preferred embodiments, but can be modified in any way according to the technical principles of the present invention, and all such modifications, equivalent variations and modifications are included in the scope of the present invention.
Claims (10)
1. The deconvolution super-resolution reconstruction method of the optical coherence tomography image is characterized by comprising the following steps of: which comprises the following steps:
(1) Obtaining an OCT image with low resolution through Fourier transformation, and taking the OCT image as input original data;
(2) Constructing an optimization function of sparse continuous prior deconvolution calculation:
the first term of the optimization function is a computational fidelity term, representing the distance between the reconstructed image x and the original OCT image f, A is the point spread function of the OCT system, and the second term and the third term are a continuity priori and a sparse priori, wherein I 1 and ||||2 Respectively represent l 1 and l2 Norms, lambda and lambda s For describing weights between balanced image fidelity terms and successive and sparse priors, in successive priors R (x), in order to distinguish reconstructed image x from subscript n representing different directions x，y，z R (n) is used to replace R (x)Describing a continuity prior in which ε y For regularization parameters, representing continuity along the y-axis, if the original OCT data input is a two-dimensional image only, will ε y Set to 0;
(3) The initial setting of reconstruction optimization is carried out, which comprises the following steps: original data mode, iteration round, sparsity prior weight and continuity prior weight;
(4) Performing iterative training, and introducing intermediate variables to perform iterative calculation;
(5) And after the optimization iteration is completed, outputting a final deconvolution super-resolution reconstructed OCT image.
2. The deconvolution super-resolution reconstruction method of an optical coherence tomographic image according to claim 1, characterized in that: in the step (2), lambda is greater than lambda s 。
3. The deconvolution super-resolution reconstruction method of an optical coherence tomographic image according to claim 2, characterized in that: in the step (2), lambda/lambda of the original image with high signal-to-noise ratio s The ratio is in the range of (1, 5)]λ/λ of the original image with low signal-to-noise ratio s The ratio is in the range of (1, 2)]。
4. The deconvolution super-resolution reconstruction method of an optical coherence tomographic image according to claim 3, wherein: in the step (2), the lambda parameter value range is (1, 30), so as to ensure better signal-to-noise ratio of image reconstruction.
5. The deconvolution super-resolution reconstruction method of an optical coherence tomographic image according to claim 4, wherein: in the step (3), when the input OCT image is a two-dimensional image, setting a continuity prior regularization parameter epsilon y =0; setting a continuity priori regularization parameter epsilon when the input OCT image is three-dimensional volume data y ＝1。
6. The method for deconvolution super-resolution reconstruction of an optical coherence tomographic image as recited in claim 5,the method is characterized in that: in the step (3), lambda s And setting lambda, roughly evaluating according to the noise level of the original data, and taking the signal-to-noise ratio SNR of the original image as an index of the noise level evaluation of the original data.
7. The deconvolution super-resolution reconstruction method of an optical coherence tomographic image according to claim 6, wherein: in the step (4), optimization is performed by the following formula:
the solution problem of the formula (8) is converted into a convex optimization problem, and the formula (9) is realized through deconvolution calculation.
8. The deconvolution super-resolution reconstruction method of an optical coherence tomographic image according to claim 7, wherein: in the step (4), aiming at the convex optimization problem of the formula (8), the solving process is as follows:
(4.1) replacing the variables with intermediate variables, converting equation (8) to a constraint minimization problem:
wherein ,u＝λs g，u zz ＝g zz ，u xx ＝g xx ，u yy ＝ε y g yy ，u zx ＝2g zx ，
(4.2) the following unconstrained problem will be obtained by the Lagrangian multiplier method:
wherein μ is the Lagrangian multiplier;
(4.3) the strict constraint iteration minimization procedure using the simplified Bregman iteration method is as follows:
wherein ,uij And v ij Calculation factors respectively representing three directions of different xyz
And integrating the three formulas to obtain a final optimization result:
wherein ,
is a second derivative operator in the z-direction, which can be written +.>
Defined as the second derivative operator in the other direction.
9. The deconvolution super-resolution reconstruction method of an optical coherence tomographic image according to claim 8, wherein: in the step (4), the solving process of the formula (9) adopts the Lucy Richardson deconvolution algorithm to calculate, and in each iteration, lucy
The input of the Richardson deconvolution algorithm is the result of the calculation of the formula (8), the output of the Richardson deconvolution algorithm is the input of the formula (8) in the next iteration until the cycle is finished, and the final high-resolution reconstruction result is output.
10. The apparatus of the deconvolution super-resolution reconstruction method of an optical coherence tomographic image according to claim 1, wherein: it comprises the following steps:
an input module configured to obtain a low resolution OCT image by fourier transform as input raw data;
an optimization function construction module configured to construct an optimization function of a sparse continuous a priori deconvolution calculation:
the first term of the optimization function is a computational fidelity term, representing the distance between the reconstructed image x and the original OCT image f, A is the point spread function of the OCT system, and the second term and the third term are a continuity priori and a sparse priori, wherein I 1 and ||||2 Respectively represent l 1 and l2 Norms, lambda and lambda s For describing weights between balanced image fidelity terms and successive and sparse priors, in successive priors R (x), in order to distinguish reconstructed image x from subscript n representing different directions x，y，z The continuity prior is described by R (n) instead of R (x), where ε is y For regularization parameters, representing continuity along the y-axis, if the original OCT data input is a two-dimensional image only, will ε y Set to 0;
an initialization module configured to perform an initial setup of a reconstruction optimization, comprising: original data mode, iteration round, sparsity prior weight and continuity prior weight;
the iterative training module is configured to perform iterative training, and introduces intermediate variables to perform iterative calculation;
and the output module is configured to output a final deconvolution super-resolution reconstructed OCT image after the optimization iteration is completed.
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