CN103767686B - Method for positioning bioluminescence imaging light sources in small animal - Google Patents

Abstract

The invention discloses a method for positioning bioluminescence imaging light sources in small animal. The method is characterized by comprising the following steps: building a relation between body surface measured data vectors and in-vivo unknown light source distribution of the small animal by utilizing a quantitative optical molecular tomography device and a finite element method; computing the in-vivo light source distribution of the small animal by adopting an algebraic iterative reconstruction method; determining a threshold value according to sparseness, and performing correction on the light source distribution, obtained by adopting the algebraic iterative reconstruction method, by utilizing the threshold value; circulating for multiple times to finally obtain the in-vivo light source distribution of the small animal to realize the positioning of the bioluminescence imaging light sources. The method disclosed by the invention has the beneficial effects that the L0 normalization item does not need to be added to a mathematic model of the reconstruction problem, and approximation analysis does not even to be performed on the L0 norm by adopting the L1 norm and the Lp (0&1t; p≪ 1) norm, but the correction is performed on the light source distribution, obtained by adopting the algebraic iterative reconstruction method, directly by utilizing the sparseness. As norm approximation in the prior art is not adopted, the in-vivo light source positioning precision of the small animal is improved by the method provided by the invention.

Description

A kind of toy biodiversity resources light source localization method

Technical field

The present invention relates to a kind of imaging source localization method, be specifically related to a kind of toy biodiversity resources light source localization method, belong to optical imaging field.

Background technology

Biodiversity resources technology luciferase gene labeled cell or DNA, utilize semiconductor refrigerating CCD camera to gather optical signalling, directly can monitor the cellular activity in living organisms and gene behavior.

Biodiversity resources technology can also observe the biological process such as expression of the growth of living animal in-vivo tumour and transfer, infectious disease evolution, specific gene.

Biodiversity resources technology has without ionizing radiation, the feature such as highly sensitive, cost is low, is widely used in biological study.

One of key problem of biodiversity resources technology is bioluminescence light source location in petty action object, and light source location can obtain according to the toy body surface fluorescence signal rebuilding body inner light source distribution of measuring.Because measurement data number is less than unknown number number, the solution of biodiversity resources Problems of Reconstruction is not unique.For obtaining truly distributing with light source close solution, regularization term can be added in the object function of Problems of Reconstruction.Consider that petty action object inner light source distributes sparse feature, researcher proposes to adopt l ₀norm retrains the regularization term added.And mathematically, l ₀norm regularization problem is difficult to solve, and usually adopts l in reality ₁norm or l _p(0<p<1) norm is to l ₀norm is similar to.

Chinese invention patent " a kind of Bioluminescence tomography reconstruction method ", application number 201310259527.1, the applying date 20160626, publication date 20130904, discloses a kind of bioluminescence cross sectional reconstruction method, adds l in the object function of Problems of Reconstruction _0.5regularization term, and adopt weighting interior point method by l _0.5regularization object function transforms to attach most importance to composes the l of power ₁regularization minimization problem, then utilizes interior point method to solve minimization problem, obtains the three-dimensional localization quantitative information of fluorescence light source in organism.Due to l ₀norm is similar to, and must introduce reconstruction error, causes location inaccurate.

Summary of the invention

For solving the deficiencies in the prior art, the object of the present invention is to provide a kind of toy biodiversity resources light source localization method, the method first adopts algebraically iterative approximation (ART) method to calculate distribution of light sources, recycling threshold value is revised above-mentioned distribution of light sources, the degree of rarefication of revised distribution of light sources is made to meet given condition, then using revised distribution of light sources as initial value, continue to adopt ART method to calculate new distribution of light sources, repeatedly repeat, until the toy body surface fluorescence signal calculated according to distribution of light sources and CCD detection to fluorescence signal between error be less than given error, calculate and terminate, finally calculate light source position according to distribution of light sources, realize the accurate location to the light source in petty action object.

In order to realize above-mentioned target, the present invention adopts following technical scheme:

A kind of toy biodiversity resources light source localization method, is characterized in that, comprise the following steps:

(1) toy body surface optical signalling and internal structural information is obtained

1.a utilizes quantitative optical molecular tomographic device to obtain the two-dimentional bioluminescence image of toy body surface and the three-dimensional computer faultage image of internal structure;

The bioluminescence graphical arrangement collected is become data vector by 1.b, and utilizes Finite Element Method to build the relation of unknown distribution of light sources in data vector and body, as shown in the formula:

y=Ax+n (1)

In formula, y is obtained by bioluminescence image, and size is that M capable 1 arranges,

A is the coefficient matrix obtained by computed tomography image, and size is the capable N row of M,

X is the unknown distribution of light sources in petty action object, and size is that N capable 1 arranges,

N is noise, and size is that M capable 1 arranges;

(2) initialization

The distribution of setting primary light source x, initial threshold β, initial sparse degree wherein, x>=0, β>=1,

(3) iteration upgrades distribution of light sources

3.a gets the 1st row of coefficient matrix, is designated as A ₁, the 1st element of the vectorial Y that fetches data, is designated as y ₁, calculate increment:

$\mathrm{\&Delta;}=\mathrm{\&gamma;}\frac{A_1(y_1-A_{1}x)}{{\left|\right|A_1\left|\right|}_2^2}---\left(2\right)$

In formula, for A ₁l ₂norm square,

γ is weights, γ <1;

3.b utilizes above-mentioned increment △ to upgrade x, and the x after renewal represents have with x':

x'=x+△ （3）

The x' that step 3.b obtains by 3.c substitutes into formula (2), gets the 2nd row A of coefficient matrices A ₂with the 2nd the element y of vectorial y ₂, calculate new increment △, continue to utilize formula (3) to upgrade x; Until the M of usage factor matrix A is capable and M element of vectorial y calculates increment and it is complete to upgrade x, the distribution of light sources after renewal is designated as x _new;

(4) threshold value correction distribution of light sources

4.a gets the x that step 3.c obtains _newgreatest member, be designated as x_max, calculate $\mathrm{\&alpha;}=\frac{x\_\max }{\mathrm{\&beta;}};$

4.b is by x _newthe 1st element compare with the α of step 4.a successively to N number of element, if aforementioned elements is less than α, then aforementioned elements is set to zero, obtain revise distribution of light sources, be designated as

4.c utilizes following formula to calculate the distribution of light sources of above-mentioned correction degree of rarefication:

$\mathrm{\&psi;}=\frac{\sqrt{N}-{\left|\right|{\stackrel{\&OverBar;}{x}}_{\mathrm{new}}\left|\right|}_1/{\left|\right|{\stackrel{\&OverBar;}{x}}_{\mathrm{new}}\left|\right|}_2}{\sqrt{N}-1}---\left(4\right)$

In formula, be respectively l ₁norm and l ₂norm;

The degree of rarefication ψ that step 4.c obtains by 4.d and initial sparse degree compare, if then change threshold value beta and return step 4.a, 4.b and 4.c and carry out again calculating and judging; If then the distribution of light sources of the threshold value obtained and correction is designated as respectively with perform step (5); ε is error;

(5) error of calculation and judge stop condition

According to the distribution of light sources revised in step 4.d calculate and will compare with the y in formula (1), if then obtain with step 4.d with as initial threshold and primary light source distribution, namely with return step (3) and step (4), iteration upgrades distribution of light sources and threshold value correction distribution of light sources again; If as final distribution of light sources, be designated as x _opt, perform step (6);

(6) light source location

According to the final distribution of light sources x that step (5) obtains _opt, find the greatest member position of aforementioned final distribution of light sources, complete light source location.

Aforesaid toy biodiversity resources light source localization method, is characterized in that, in step (2), during initialization, and x=0, β=2,

Aforesaid toy biodiversity resources light source localization method, is characterized in that, in step (3), when iteration upgrades distribution of light sources calculating increment, and γ=0.25.

Aforesaid toy biodiversity resources light source localization method, is characterized in that, in step (4) and step (5), and error ε=1e ^-6.

Aforesaid toy biodiversity resources light source localization method, is characterized in that, when utilizing quantitative optical molecular tomographic device to obtain the computed tomography image of the bioluminescence image of toy body surface and internal structure, toy attitude remains unchanged.

Usefulness of the present invention is: light source localization method of the present invention does not need to add l in the mathematical model of Problems of Reconstruction ₀regularization term, does not more need to adopt l ₁norm or l _p(0<p<1) norm is to l ₀norm carries out approximate solution, but directly utilize degree of rarefication to revise the distribution of light sources that ART method obtains, thus realize positioning the bioluminescence light source in petty action object, be similar to owing to not adopting the norm in prior art, method of the present invention improves the light source positioning precision in petty action object, can be used for tumor earlier detection and treats research fields such as following the tracks of.

Accompanying drawing explanation

Fig. 1 is the flow chart of toy biodiversity resources light source localization method of the present invention.

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, concrete introduction is done to the present invention.

With reference to Fig. 1, toy biodiversity resources light source localization method of the present invention, comprises the following steps:

1, anesthesia and fixing toy

To there being the toy of bioluminescence light source to anaesthetize in body, and the extremity of toy, head and afterbody are all fixed on sample holder.

2, toy body surface optical signalling and internal structural information is obtained

2.a, in darkroom, utilizes quantitative optical molecular tomographic device disclosed in Chinese invention patent ZL201010173473.3, first gathers the fluorescence signal of toy body surface, and gather once every 90 degree, toy rotates a circle and can collect 4 width fluoroscopic images; Under the prerequisite that toy attitude remains unchanged, then the data for projection of collecting computer fault imaging, gather once every 1 degree, toy rotates a circle collection 360 data for projection, utilizes backprojection algorithm to obtain the three-dimensional computer faultage image of toy.

The 4 width fluoroscopic images collected are arranged in data vector by 2.b, the three-dimensional computer faultage image of professional software Amira to toy is utilized to carry out subdivision, diffusion equation is adopted to carry out modeling to the transmitting procedure of light in petty action object, utilize Finite Element Method, the relation of unknown light source in the data vector of toy body surface fluorescence signal and petty action object can be built, as shown in the formula:

y=Ax+n (1)

In formula, y is obtained by bioluminescence image, and size is that M capable 1 arranges,

A is the coefficient matrix obtained by computed tomography image, and size is the capable N row of M,

X is the unknown distribution of light sources in petty action object, and size is that N capable 1 arranges,

N is noise, and size is that M capable 1 arranges.

3, initialization

The distribution of setting primary light source x, initial threshold β, initial sparse degree wherein, x>=0, β>=1, preferably, x=0, β=2,

4, iteration upgrades distribution of light sources

4.a gets the 1st row of coefficient matrix, is designated as A ₁, the 1st element of the vectorial Y that fetches data, is designated as y ₁, calculate increment:

$\mathrm{\&Delta;}=\mathrm{\&gamma;}\frac{A_1(y_1-y_{1}x)}{{\left|\right|A_1\left|\right|}_2^2}---\left(2\right)$

In formula, for A ₁l ₂norm square,

γ is weights, γ <1, preferably, and γ=0.25.

4.b utilizes above-mentioned increment △ to upgrade x, and the x after renewal represents have with x':

x'=x+△ （3）

The x' that step 4.b obtains by 4.c substitutes into formula (2), gets the 2nd row A of coefficient matrices A ₂with the 2nd the element y of vectorial y ₂, calculate new increment △, continue to utilize formula (3) to upgrade x; Until the M of usage factor matrix A is capable and M element of vectorial y calculates increment and it is complete to upgrade x, the distribution of light sources after renewal is designated as x _new.

5, threshold value correction distribution of light sources

5.a gets the x that step 4.c obtains _newgreatest member, be designated as x_max, calculate $\mathrm{\&alpha;}=\frac{x\_\max }{\mathrm{\&beta;}}.$

5.b is by x _newthe 1st element and the α of step 5.a compare, if described 1st element is less than α, then described 1st element is set to zero; If described 1st element is more than or equal to α, then described 1st element remains unchanged.

Compare successively, until x _newlast element, obtain revise distribution of light sources, be designated as

5.c utilizes following formula to calculate the distribution of light sources of above-mentioned correction degree of rarefication:

$\mathrm{\&psi;}=\frac{\sqrt{N}-{\left|\right|{\stackrel{\&OverBar;}{x}}_{\mathrm{new}}\left|\right|}_1/{\left|\right|{\stackrel{\&OverBar;}{x}}_{\mathrm{new}}\left|\right|}_2}{\sqrt{N}-1}---\left(4\right)$

In formula, be respectively l ₁norm and l ₂norm, in 1 fewer, degree of rarefication ψ more close to 1, when only having an element to be 1, ψ=1.

The degree of rarefication ψ that step 5.c obtains by 5.d and initial sparse degree compare, if then change threshold value beta and return step 5.a, 5.b and 5.c and carry out again calculating and judging; If then the distribution of light sources of the threshold value obtained and correction is designated as respectively with perform step 6.

ε is error, is an a small amount of, preferably, and ε=1e ^-6.

6, the error of calculation and judgement stop condition

According to the distribution of light sources revised in step 5.d calculate and will compare with the toy body surface fluorescent signal data vector y in formula (1), if then obtain with step 5.d with as initial threshold and primary light source distribution, namely with return step 4 and step 5, iteration upgrades distribution of light sources and threshold value correction distribution of light sources again; If as final distribution of light sources, be designated as x _opt, perform step 7.

7, light source location

According to the final distribution of light sources x that step 6 obtains _opt, find the greatest member position of described final distribution of light sources, complete light source location.

Light source localization method of the present invention does not need to add l in the mathematical model of Problems of Reconstruction ₀regularization term, does not more need to adopt l ₁norm or l _p(0<p<1) norm is to l ₀norm carries out approximate solution, but directly utilizes degree of rarefication to revise the distribution of light sources that ART method obtains, and owing to not adopting the norm in prior art to be similar to, improves the light source positioning precision in petty action object with the inventive method.

Light source localization method of the present invention, can be used for tumor earlier detection and treats research fields such as following the tracks of.

It should be noted that, above-described embodiment does not limit the present invention in any form, the technical scheme that the mode that all employings are equal to replacement or equivalent transformation obtains, and all drops in protection scope of the present invention.

Claims (5)

1. a toy biodiversity resources light source localization method, is characterized in that, comprise the following steps:

One, toy body surface optical signalling and internal structural information is obtained:

1.a utilizes quantitative optical molecular tomographic device to obtain the two-dimentional bioluminescence image of toy body surface and the three-dimensional computer faultage image of internal structure;

The bioluminescence graphical arrangement collected is become data vector by 1.b, and utilizes Finite Element Method to build the relation of unknown distribution of light sources in data vector and body, as shown in the formula:

y＝Ax+n (1)

In formula, y is obtained by bioluminescence image, and size is that M capable 1 arranges,

A is the coefficient matrix obtained by computed tomography image, and size is the capable N row of M,

X is the unknown distribution of light sources in petty action object, and size is that N capable 1 arranges,

N is noise, and size is that M capable 1 arranges;

Two, initialization:

The distribution of setting primary light source x, initial threshold β, initial sparse degree wherein, x>=0, β>=1,

Three, iteration upgrades distribution of light sources:

3.a gets the 1st row of coefficient matrix, is designated as A ₁, the 1st element of the vectorial Y that fetches data, is designated as y ₁, calculate increment:

$\mathrm{\&Delta;}=\mathrm{\&gamma;}\frac{A_1(y_1-A_{1}x)}{{\left|\right|A_1\left|\right|}_2^2}---\left(2\right)$

In formula, for A ₁l ₂norm square,

γ is weights, γ <1;

3.b utilizes above-mentioned increment △ to upgrade x, and the x after renewal represents have with x':

x'＝x+Δ (3)；

The x' that step 3.b obtains by 3.c substitutes into formula (2), gets the 2nd row A of coefficient matrices A ₂with the 2nd the element y of vectorial y ₂, calculate new increment Delta, continue to utilize formula (3) to upgrade x; Until the M of usage factor matrix A is capable and M element of vectorial y calculates increment and it is complete to upgrade x, the distribution of light sources after renewal is designated as x _new;

Four, threshold value correction distribution of light sources:

4.a gets the x that step 3.c obtains _newgreatest member, be designated as x_max, calculate $\mathrm{\&alpha;}=\frac{x\_\max }{\mathrm{\&beta;}};$

4.b is by x _newthe 1st element compare with the α of step 4.a successively to N number of element, if described element is less than α, then described element is set to zero, obtain revise distribution of light sources, be designated as

4.c utilizes following formula to calculate the distribution of light sources of above-mentioned correction degree of rarefication:

$\mathrm{\&psi;}=\frac{\sqrt{N}-{\left|\right|{\stackrel{\&OverBar;}{x}}_{\mathrm{new}}\left|\right|}_1/{\left|\right|{\stackrel{\&OverBar;}{x}}_{\mathrm{new}}\left|\right|}_2}{\sqrt{N}-1}---\left(4\right)$

In formula, be respectively l ₁norm and l ₂norm;

The degree of rarefication ψ that step 4.c obtains by 4.d and initial sparse degree compare, if then change threshold value beta and return step 4.a, 4.b and 4.c and carry out again calculating and judging; If then the distribution of light sources of the threshold value obtained and correction is designated as respectively with perform step 5; ε is error;

Five, the error of calculation and judgement stop condition:

According to the distribution of light sources revised in step 4.d calculate and will compare with the y in formula (1), if then obtain with step 4.d with as initial threshold and primary light source distribution, namely with return step 3 and step 4, iteration upgrades distribution of light sources and threshold value correction distribution of light sources again; If as final distribution of light sources, be designated as x _opt, perform step 6;

Six, light source location:

According to the final distribution of light sources x that step 5 obtains _opt, find the greatest member position of described final distribution of light sources, complete light source location.

2. toy biodiversity resources light source localization method according to claim 1, is characterized in that, in step 2, during initialization, and x=0, β=2,

3. toy biodiversity resources light source localization method according to claim 1, is characterized in that, in step 3, when iteration upgrades distribution of light sources calculating increment, and γ=0.25.

4. toy biodiversity resources light source localization method according to claim 1, is characterized in that, in step 4 and step 5, and error ε=1e ^-6.

5. toy biodiversity resources light source localization method according to claim 1, it is characterized in that, when utilizing quantitative optical molecular tomographic device to obtain the computed tomography image of the bioluminescence image of toy body surface and internal structure, toy attitude remains unchanged.