CN108309340B - Excitation fluorescence fault reconstruction method based on correlation entropy matching pursuit - Google Patents
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Abstract
The invention provides an excitation fluorescence fault reconstruction method based on correlation entropy matching tracking, which utilizes sparsity prior information and realizes robust reconstruction of different types of noise data based on a correlation entropy matching tracking method. The correlation entropy matching pursuit-based excitation fluorescence fault reconstruction method provided by the disclosure is irrelevant to the noise distribution of the measured data, compared with the traditional matching pursuit method, the method does not assume that the noise distribution of the measured data accords with Gaussian distribution, and the property ensures that the method has better robustness to various types of noise, can better deal with the complex noise situation in the actual environment in the biomedical research, and is suitable for the noninvasive in-vivo stem cell tracing problem.
Description
Technical Field
The disclosure relates to the technical field of optical molecular imaging, in particular to an excitation fluorescence tomography reconstruction method based on correlated entropy matching pursuit.
Background
The fluorescence tomography is a new optical molecular imaging technology. The method is characterized in that a fluorescent probe is used for marking a certain target (stem cells, proteins, nucleic acids or small molecules and the like) in a living body, and under the irradiation of an excitation light source with specific wavelength in vitro, the fluorescent probe absorbs energy, generates photon transition, generates excitation light, penetrates through the surface of the living body, and is detected by a high-sensitivity optical detection instrument in vitro, such as a CCD camera. The in-vivo transmission process of photons is modeled, the forward and backward problems of the model are solved by using a mathematical method, the in-vivo fluorescent light source is subjected to three-dimensional reconstruction, and the three-dimensional position distribution and energy distribution in a molecular probe organism are obtained, so that the molecular probe has extremely high application value in the aspects of stem cell tracing, drug delivery, early tumor detection and the like.
The fluorescence tomography excitation reconstruction method can only utilize surface two-dimensional fluorescence data to carry out reverse deduction, the quantity of the fluorescence data is small compared with the solution space of the whole problem, so that the solution is not unique and is easy to be subjected to noisy images, and the fluorescence tomography excitation reconstruction method belongs to a serious ill-conditioned problem. In the stem cell tracing problem, the number of transplanted stem cells is very small compared with that of the whole animal body, signals are very weak, and the transplanted stem cells are easily interfered by various noises, so that the anti-noise performance requirement of a reconstruction algorithm is higher. Moreover, in the process of transmitting photons in vivo, biological tissues have strong scattering effect on the photons, so that the morbidity of the problem is further increased. Inspired by compressive sensing theory, many methods based on orthogonal matching pursuit are used to solve the inverse problem of tomographic reconstruction.
However, in the implementation of the present disclosure, the inventors of the present application find that the existing method based on orthogonal matching pursuit uses the mean square error as the objective function of the solution in the iterative process, provided that the noise conforms to the gaussian distribution. However, in the actual in vivo stem cell tracing problem, the noise introduced by the acquisition system is very complex in distribution, so that a gaussian error is used as an approximation, the effect is not accurate enough, and the algorithm robustness is not good enough.
BRIEF SUMMARY OF THE PRESENT DISCLOSURE
Technical problem to be solved
Based on the technical problems, the invention provides an excitation fluorescence fault reconstruction method based on correlation entropy matching pursuit, so as to solve the technical problems that the reconstruction method in the prior art uses Gaussian error as approximation, the non-Gaussian noise effect is not accurate enough, and the algorithm robustness is not good enough.
(II) technical scheme
The present disclosure provides an excitation fluorescence tomography reconstruction method based on correlated entropy matching pursuit, including: step A: acquiring CT imaging data and a surface excitation fluorescence image of an experimental animal; and B: segmenting and discretizing the CT imaging data, and endowing each discretized organ with corresponding optical parameters to obtain a discretized animal model; and C: mapping the surface-excited fluorescence image to the discretized animal model obtained in the step B to obtain the light intensity distribution of the body surface of the experimental animal, and accordingly establishing a photon transmission model in the experimental animal; step D: simplifying the photon transmission model into a diffusion equation, and converting the diffusion equation into a linear equation by adopting a finite element method; and step E: and (3) based on a strategy framework of orthogonal matching pursuit, using an evaluation criterion of the related entropy to solve the linear equation in an iterative manner to obtain the distribution condition of the stem cells in the experimental animal body.
In some embodiments of the present disclosure, in the step B, the optical absorption and scattering parameters of each organ are determined according to the excitation and emission wavelengths of the fluorescent probe for labeling the stem cells.
In some embodiments of the present disclosure, the surface-excited fluorescence image comprises N angles of surface-excited fluorescence image, N ≧ 1.
In some embodiments of the present disclosure, in the step D, the optical property of the biological tissue to photon scattering and/or absorption is used to simplify the transmission model of the photons into a diffusion equation.
In some embodiments of the present disclosure, in the step D, the linear equation is in the form of:
y＝Ax
where y is the measurement data of the surface-excited fluorescence image, a is the system matrix, and x is the distribution vector of the object to be solved.
In some embodiments of the present disclosure, the step E comprises: step E1: initial residual is set to r0The set of columns chosen is the null set Λ ═ y0Phi, the iteration number k is 0; step E2: updating the iteration number k to k +1, and selecting the column lambda with the maximum residual correlation degree in the system matrix AkWill be λkSet of added columns Λk＝Λk-1∪{λk}; wherein λ iskAn index for the selected column; step E3: the approximate solution in this iteration is calculated according to the criterion of minimum associated entropy using the following formula:
w(t+1)(i)＝gσ(y(i)-(AXt)(i))，i＝12...，m；
where t represents the number of iterations of the algorithm, gσ(X) represents the variance σ2I denotes the ith sample,
representing a vector X as an n-dimensional vector in a real number domain, wherein a support set of the X belongs to lambdk, diag (w) represents a matrix taking elements of the vector w as diagonal elements, and the w gives the weight of each measured data to the algorithm; step E4: and (3) residual error updating: r isk＝
And step E5: if K is not less than K or rkC, the calculation is finished, and output
Otherwise, returning to step E2, where K is the maximum number of iterations, determined by the number of solutions in the solution space, and c is the residual threshold.
In some embodiments of the present disclosure, in the step E2, the column with the largest degree of correlation with the residual error in the system matrix a is selected according to the following formula: lambada k equals arg max<rk-1,ai>1, |, i ═ 1,2, …, l; wherein, aiRepresenting the ith column of the system matrix a.
In some embodiments of the present disclosure, in the step a, the CT imaging data and the surface-excited fluorescence image are obtained by injecting stem cells labeled with an in vitro fluorescent probe into an experimental animal.
In some embodiments of the present disclosure, the reconstruction method is suitable for use in non-invasive in vivo stem cell tracking.
In some embodiments of the present disclosure, the reconstruction method is applied to non-gaussian noise.
(III) advantageous effects
According to the technical scheme, the excitation fluorescence tomography reconstruction method based on the correlated entropy matching pursuit has one or part of the following beneficial effects:
the reconstruction method is irrelevant to the noise distribution of the measured data, compared with the traditional matching tracking method, the reconstruction method does not assume that the noise distribution of the measured data conforms to Gaussian distribution, and the property ensures that the reconstruction method has better robustness to various types of noise, can better respond to the complex noise condition in the actual environment in the biomedical research, and is suitable for the problem of tracing the noninvasive in-vivo stem cells.
Drawings
Fig. 1 is a schematic diagram of reconstruction by using the correlation entropy matching pursuit-based excitation fluorescence tomography reconstruction method of the present disclosure.
Fig. 2 is a schematic diagram comparing the reconstruction results of the present disclosure with the conventional matching pursuit under the condition of non-gaussian noise.
Detailed Description
In the fluorescence tomography excitation reconstruction method based on the correlation entropy matching pursuit, the sparse prior information is utilized, the robust reconstruction of different types of noise data is realized based on the correlation entropy matching pursuit method, and the method has high practical value in the stem cell tracing problem.
For the purpose of promoting a better understanding of the objects, aspects and advantages of the present disclosure, reference is made to the following detailed description taken in conjunction with the accompanying drawings.
Fig. 1 is a schematic diagram of reconstruction by using the correlation entropy matching pursuit-based excitation fluorescence tomography reconstruction method of the present disclosure. Part a of fig. 1 is a three-dimensional schematic diagram of different organ tissues after segmentation and discretization of CT imaging data. Part b of fig. 1 is a schematic diagram of an animal model that gives corresponding optical parameters to each organ after dispersion. Section c in figure 1 is a slice of the reconstructed fluorescent object. Section d in figure 1 is a slice of the reconstructed fluorescent object at another angle.
The present disclosure provides an excitation fluorescence tomography reconstruction method based on correlated entropy matching pursuit, including: step A: acquiring CT imaging data and a surface excitation fluorescence image of an experimental animal; and B: segmenting and discretizing the CT imaging data (as shown in a part a in fig. 1), and endowing each discretized organ with corresponding optical parameters to obtain a discretized animal model (as shown in a part b in fig. 1); and C: mapping the surface-excited fluorescence image to the discretized animal model obtained in the step B to obtain the light intensity distribution of the body surface of the experimental animal, and accordingly establishing a photon transmission model in the experimental animal; step D: simplifying the photon transmission model into a diffusion equation, and converting the diffusion equation into a linear equation by adopting a finite element method; and step E: based on a strategy framework of orthogonal matching pursuit, the linear equation is solved iteratively by using an evaluation criterion of the correlation entropy to obtain the distribution condition of the stem cells in the experimental animal body (as shown in a part c in fig. 1 and a part d in fig. 1, source1 and source2 in the diagram are positions of the stem cells).
In some embodiments of the present disclosure, in step B, the major organs of the mouse are segmented by using the CT image, and the optical absorption and scattering parameters of each organ are determined according to the excitation and emission wavelengths of the fluorescent probe for labeling the stem cells.
In some embodiments of the present disclosure, the surface-excited fluorescence image comprises N angles of the surface-excited fluorescence image, N ≧ 1.
In some embodiments of the present disclosure, in step D, the anatomical structure information and the optical parameters in the animal model are used as prior information, and according to the radiation transmission equation, a transmission model of photons in the living body is established, and the transmission model of photons is simplified into a diffusion equation by using the optical characteristics of the living tissue on the scattering and/or absorption of photons.
The photon transmission model and the boundary conditions thereof are as follows:
in some embodiments of the present disclosure, in step D, the linear equation is of the form:
v＝Ax
wherein y is the measurement data of the surface-excited fluorescence image, a is the system matrix, x is the distribution vector of the object to be solved, and the linear equation establishes the relationship between the two-dimensional measurement data of the body surface and the three-dimensional fluorescence distribution in the body.
In some embodiments of the present disclosure, the step E comprises:
step E1: initial residual is set to r0The set of columns chosen is the null set Λ ═ y0Phi, the iteration number k is 0;
step E2: updating the iteration number k to k +1, and selecting the column lambda with the maximum residual correlation degree in the system matrix Ak＝arg max|<rk-1,ai>1,2, …, l, will be λkSet of added columns Λk＝Λk-1∪{λk}; wherein λ iskFor the index of the selected column, aiRepresents the ith column of the system matrix A;
step E3: the approximate solution in this iteration is calculated using the following equation:
w(t+1)(i)＝gσ(y(i)-(AXt)(i)),1＝1,2,,m；
where t represents the number of iterations of the algorithm, gσ(X) represents the variance σ2I denotes the ith sample,
the expression vector X is an n-dimensional vector in a real number domain, and the support set of X belongs to LambdakDiag (w) denotes a matrix with diagonal elements as elements of a vector w, which assigns each test to the algorithmThe weight of the data is small, the weight given by the data with serious noise pollution is large, and the influence of noise on a reconstruction result can be effectively inhibited;
step E4: and (3) residual error updating:
step E5: if K is not less than K or rkC, the calculation is finished, and output
Otherwise, returning to step E2, where K is the maximum number of iterations, determined by the number of solutions in the solution space, and c is the residual threshold.
In some embodiments of the present disclosure, in step a, the CT imaging data and the surface-excited fluorescence image are obtained by injecting stem cells labeled with an in vitro fluorescent probe into the experimental animal.
In some embodiments of the present disclosure, the reconstruction method is suitable for use in non-invasive in vivo stem cell tracking.
Fig. 2 is a schematic diagram comparing the reconstruction results of the present disclosure with the conventional matching pursuit under the condition of non-gaussian noise.
In some embodiments of the present disclosure, as shown in fig. 2, the reconstruction method is applied to non-gaussian noise, and the first two rows are traditional matching pursuit reconstruction results, and it can be clearly seen from the figure that the embodiments of the present disclosure have a better suppression effect on non-gaussian noise, and the reconstruction accuracy is higher than that of the other two methods, which proves the effectiveness of the reconstruction method provided by the embodiments of the present disclosure.
In addition, the algorithm result of the reconstruction method provided by the embodiment of the disclosure is independent of the distribution of noise, and therefore, the method can be applied to noise satisfying gaussian distribution as well.
So far, the embodiments of the present disclosure have been described in detail with reference to the accompanying drawings. It is to be noted that, in the attached drawings or in the description, the implementation modes not shown or described are all the modes known by the ordinary skilled person in the field of technology, and are not described in detail. Further, the above definitions of the various elements and methods are not limited to the various specific structures, shapes or arrangements of parts mentioned in the examples, which may be easily modified or substituted by those of ordinary skill in the art.
From the above description, those skilled in the art should have clear understanding of the excitation fluorescence tomographic reconstruction method based on correlated entropy matching pursuit provided by the present disclosure.
In conclusion, the correlation entropy matching pursuit-based fluorescence excitation fault reconstruction method provided by the disclosure utilizes sparse prior information, realizes robust reconstruction of different types of noise data based on the correlation entropy matching pursuit method, and has a high practical value in a stem cell tracing problem.
It should also be noted that directional terms, such as "upper", "lower", "front", "rear", "left", "right", and the like, used in the embodiments are only directions referring to the drawings, and are not intended to limit the scope of the present disclosure. Throughout the drawings, like elements are represented by like or similar reference numerals. Conventional structures or constructions will be omitted when they may obscure the understanding of the present disclosure.
And the shapes and sizes of the respective components in the drawings do not reflect actual sizes and proportions, but merely illustrate the contents of the embodiments of the present disclosure. Furthermore, in the claims, any reference signs placed between parentheses shall not be construed as limiting the claim.
Similarly, it should be appreciated that in the foregoing description of exemplary embodiments of the disclosure, various features of the disclosure are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various disclosed aspects. However, the disclosed method should not be interpreted as reflecting an intention that: that is, the claimed disclosure requires more features than are expressly recited in each claim. Rather, as the following claims reflect, disclosed aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this disclosure.
The above-mentioned embodiments are intended to illustrate the objects, aspects and advantages of the present disclosure in further detail, and it should be understood that the above-mentioned embodiments are only illustrative of the present disclosure and are not intended to limit the present disclosure, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present disclosure should be included in the scope of the present disclosure.
Claims (9)
1. An excitation fluorescence tomography reconstruction method based on correlation entropy matching pursuit, which is suitable for noninvasive in-vivo stem cell tracing and comprises the following steps:
step A: acquiring CT imaging data and a surface excitation fluorescence image of an experimental animal;
and B: segmenting and discretizing the CT imaging data, and endowing each discretized organ with corresponding optical parameters to obtain a discretized animal model;
and C: mapping the surface-excited fluorescence image to the discretized animal model obtained in the step B to obtain the light intensity distribution of the body surface of the experimental animal, and accordingly establishing a photon transmission model in the experimental animal;
step D: simplifying the photon transmission model into a diffusion equation, and converting the diffusion equation into a linear equation by adopting a finite element method; and
step E: and (3) based on a strategy framework of orthogonal matching pursuit, using an evaluation criterion of the related entropy to solve the linear equation in an iterative manner to obtain the distribution condition of the stem cells in the experimental animal body.
2. The excitation fluorescence tomography reconstruction method based on correlated entropy matching pursuit as claimed in claim 1, wherein in the step B, optical absorption and scattering parameters of each organ are determined according to excitation and emission wavelengths of fluorescent probes for labeling the stem cells.
3. The correlation entropy matching pursuit-based excited fluorescence tomography reconstruction method of claim 1, wherein the surface-excited fluorescence image comprises surface-excited fluorescence images at N angles, wherein N is greater than or equal to 1.
4. The excitation fluorescence tomography reconstruction method based on correlated entropy matching pursuit as claimed in claim 1, wherein in the step D, the optical characteristics of biological tissues on photon scattering and/or absorption are utilized to simplify the photon transmission model into a diffusion equation.
5. The correlated entropy matching pursuit-based excitation fluorescence tomography reconstruction method according to claim 1, wherein in the step D, the linear equation is in the form of:
y＝Ax
where y is the measurement data of the surface-excited fluorescence image, a is the system matrix, and x is the distribution vector of the object to be solved.
6. The correlated entropy matching pursuit-based excited fluorescence tomography reconstruction method of claim 5, the step E comprising:
step E1: initial residual is set to r0The set of columns chosen is the null set Λ ═ y0Phi, the iteration number k is 0;
step E2: updating the iteration number k to k +1, and selecting the column lambda with the maximum residual correlation degree in the system matrix AkWill be λkSet of added columns Λk＝Λk-1∪{λk}；
Wherein λ iskAn index for the selected column;
step E3: the approximate solution in this iteration is calculated according to the criterion of minimum associated entropy using the following formula:
w(t+1)(i)＝gσ(y(i)-(AXt)(i))，i＝1,2,…,m；
wherein t represents an algorithmNumber of iterations, gσ(X) represents the variance σ2I denotes the ith sample,
the expression vector X is an n-dimensional vector in a real number domain, and the support set of X belongs to LambdakDiag (w) represents a matrix with the elements of the vector w as diagonal elements, w giving the algorithm a weight for each measurement datum;
step E4: and (3) residual error updating:
step E5: if K is not less than K or rkC, the calculation is finished, and output
Otherwise, returning to step E2, where K is the maximum number of iterations, determined by the number of solutions in the solution space, and c is the residual threshold.
7. The excitation fluorescence tomography reconstruction method based on correlated entropy matching pursuit as claimed in claim 6, wherein in the step E2, the column in the system matrix A with the largest degree of correlation with the residual error is selected according to the following formula:
λk＝arg max|<rk-1,ai>|，i＝1,2,…,l；
wherein, aiRepresenting the ith column of the system matrix a.
8. The correlated entropy matching pursuit-based excited fluorescence tomography reconstruction method of claim 1, wherein in the step a, the CT imaging data and the surface-excited fluorescence image are obtained by injecting stem cells labeled with an in vitro fluorescence probe into an experimental animal.
9. The excitation fluorescence tomography reconstruction method based on correlation entropy matching pursuit according to any one of claims 1 to 8, applied in non-Gaussian noise.
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