CN103393410A - Fluorescence molecular tomography reconstruction method based on alternative iterative operation - Google Patents

Abstract

The invention discloses a fluorescence molecular tomography reconstruction algorithm based on an alternative iterative operation, which is characterized in that a weighted algebraic reconstruction technique and a steepest descent method are used alternately for solving. The fluorescence molecular tomography reconstruction algorithm comprises the following steps that (1), measurement data is acquired; (2), a linear relationship between the measurement data and target distribution is established; (3), a 2 norm minimization problem with a constraint condition is constructed; and (4), the weighted algebraic reconstruction technique and the steepest descent method are used alternately for solving the minimization problem, and a target distribution diagram is obtained. According to the fluorescence molecular tomography reconstruction algorithm, based on a light transmission theory and a finite element method, prior information such as an optical characteristic parameter and an anatomical structure is used, multipoint excitation and multipoint measurement are adopted, and the measurement data is obtained as far as possible, so that the pathosis of the problem is reduced; the weighted algebraic reconstruction technique and the steepest descent method are used alternately for solving the problem, so that a reconstruction result of fluorescence molecular tomography is improved effectively; and the fluorescence molecular tomography reconstruction algorithm has an important application value in the fields of molecular imaging, reconstruction algorithms and the like.

Description

A kind of fluorescent molecule tomography rebuilding method based on replacing interative computation

Technical field

The invention belongs to the molecular image field, further relate to a kind of fluorescent molecule tomography rebuilding algorithm based on replacing interative computation, the inverse problem that is used in the body fluorescent molecular tomography is rebuild.

Background technology

Fluorescent molecular tomography (hereinafter to be referred as FMT) is a kind of emerging optical molecular image technology in recent years, it utilizes some molecule (general main is polycyclic aromatic hydrocarbons or heterocyclic compound etc.) as labelling reconstructed object such as fluorogen, fluorescent probe, fluorescent dyes, externally under the irradiation of excitation source, molecule can absorb external excitation light, then launch photon, produce light intensity and be directly proportional to the quantity of target-marking.Outside the reconstructed object zone, utilize highly sensitive optical detecting instrument, can direct detection to the photon that transmits the reconstructed object zone, utilize effective fluorescent molecule tomography rebuilding algorithm, just can obtain position and the concentration of the fluorescent target of reconstructed object intra-zone.

Fluorescent molecular tomography belongs to Reverse Problem, has serious pathosis, and its essential reason is the strong scattering characteristic of light in the reconstructed object zone.The photon transmission of section within it is no longer along straightline propagation, but through a large amount of random governed scattering processes.Simultaneously, the signal that utilizes optical detecting instrument to detect at place, reconstructed object zone boundary is the value of boundary point, limited amount, and the quantity of Domain internal point is very huge.Solve a large amount of unknown numbers by a small amount of measurement data, this is an ill-posed problem, has serious pathosis, and its solution is not unique and be subject to measurement error and effect of noise.How building the fluorescent target in a kind of accurate reconstruction target area, is the key problem of fluorescent molecular tomography research.

Summary of the invention

The pathosis reconciliation nonuniqueness that exists in order to solve fluorescent molecular tomography, the present invention proposes a kind of fluorescent molecule tomography rebuilding method based on replacing interative computation.In order to reduce the pathosis of problem, the present invention adopts multi-point shooting and multiangular measurement, obtains measurement data as much as possible.In conjunction with light mode and finite element theory, with the optical property parameter of reconstructed object and anatomical information as prior information, set up the measurement data on surface and the linear relationship that the inner fluorescent target of reconstructed object distributes, this linear relationship is converted into the minimization problem of Prescribed Properties, algebraic reconstruction technique and the steepest descent method of alternately carrying out weighting solve, thereby obtain distributed in three dimensions and the concentration of the fluorescent target of reconstructed object inside.

For achieving the above object, concrete steps of the present invention are as follows:

A kind of fluorescent molecule tomography rebuilding method based on replacing interative computation, it is characterized in that: based on light mode and finite element theory, with the optical property parameter of reconstructed object and anatomical information as prior information, set up the measurement data on surface and the linear relationship that the inner fluorescent target of reconstructed object distributes, this linear relationship is converted into the minimization problem of Prescribed Properties, algebraic reconstruction technique and the steepest descent method of alternately carrying out weighting solve, thereby obtain distributed in three dimensions and the concentration of the fluorescent target of reconstructed object inside.

As a kind of improvement, step is as follows:

(1) obtain measurement data

A, excitation source carry out the transmission-type tomoscan of multi-angle to being fixed on reconstructed object on automatically controlled turntable;

B, use optical detecting instrument obtain measurement data, obtain pharosage Φ _m

(2) obtain anatomical information and the optical property parameter of reconstructed object.

(3) based on light mode and finite element theory, the anatomical information of reconstructed object and optical property parameter, as prior information, are set up the measurement data on surface and the linear relationship of the inner fluorescent target distribution of reconstructed object.

(4) above-mentioned linear relationship is converted into the minimization problem of Prescribed Properties:

min||X|| ₂，s.t.|AX-Φ _m|≤ε，X≥0

ε is a non-negative error coefficient, and this is the least norm of the 2-with a Prescribed Properties problem;

(5), to the minimization problem of belt restraining in step (4), adopt the algebraic reconstruction technique of weighting to solve constraints: | AX-Φ _m|≤ε, X 〉=0,2-least norm problem solves with steepest descent method.The algebraic reconstruction technique of weighting is following form:

$X=X+\mathrm{\β}{\stackrel{\→}{A}}_i\frac{{\mathrm{\Φ}}_m-{\stackrel{\→}{A}}_{i}X}{{\stackrel{\→}{A}}_i{\stackrel{\→}{A}}_i}$

Wherein The i that is matrix A is capable, and β is positive weights;

(6) utilize fluorescent target distribution results in step (5) to calculate pharosage

With pharosage value Φ on the border of measuring _mWith value of calculation

Poor

Stopping criterion as reconstruction algorithm.If

Finish reconstruction algorithm, obtain target distribution X; Otherwise, execution step (7);

(7) with the initial solution of the solution of step (5) as steepest descent method, iterative 2-least norm problem, and make solution meet nonnegativity:

$X=X-\mathrm{grad}\_\mathrm{dx}*\frac{{\▿}_X{\left|\right|X\left|\right|}_2}{\left|{\▿}_X{\left|\right|X\left|\right|}_2\right|};$

Wherein grad_dx is the iteration step length size,

The gradient of 2-least norm problem, It is the mould value of gradient;

(8) utilize fluorescent target distribution results in step (7) to calculate pharosage

With pharosage value Φ on the border of measuring _mWith value of calculation

Poor Stopping criterion as program.If

Finish reconstruction algorithm, obtain target distribution X; Otherwise, execution step (9);

(9) the solution X that step (7) is obtained, conversely again as the initial solution of carrying out algebraic reconstruction technique, goes to step (5);

(10) show result, the anatomical structure of last reconstructed results and imageable target is carried out image co-registration, with Tecplot software, show;

Owing to having adopted technique scheme, advantage of the present invention is:

The first, what the present invention adopted is multi-point shooting, multiangular measurement, thus the measurement data that obtains is more, is conducive to reduce the pathosis of problem.

The second, the present invention utilizes optical property parameter and anatomical information as priori, has improved the quality of accuracy and the reconstructed image of reconstructed results.

The 3rd, the present invention is converted into Problems of Reconstruction the 2-least norm problem of Prescribed Properties, and algebraic reconstruction technique and the steepest descent method of alternately used weighting solve, and it is minimum making data continuity and satisfied 2 norms of separating that solution has had.

Description of drawings

Fig. 1 is the flow chart based on fluorescence tomography rebuilding method of the present invention.

Fig. 2 is for being used for the digital mouse model of emulation experiment.

The surperficial surface of intensity distribution of Fig. 3 for obtaining under certain excitation source.

The fluorogen scattergram of Fig. 4 for algorithm for reconstructing of the present invention, obtaining.

The specific embodiment

The present invention is described in further detail below in conjunction with accompanying drawing, is to be noted that described embodiment only is intended to be convenient to the understanding of the present invention, and it is not played any restriction effect.

1 pair of step of the present invention is further described by reference to the accompanying drawings.

(1) obtain measurement data

A, excitation source carry out the transmission-type fault imaging of multi-angle to being fixed on reconstructed object on automatically controlled turntable;

The transmission-type fault imaging, be placed on laser instrument and optical detecting instrument the both sides of imageable target, and laser irradiation reconstructed object fluorescence excitation group sends fluorescence, and fluorescence penetrates imageable target and detected by the optical detecting instrument on laser instrument opposite.

Multi-angle transmission-type tomoscan, controlling automatically controlled turntable with computer uniformly-spaced rotates to an angle, generally be not more than 90 ° (selecting 40 ° in this example), laser instrument emission point laser irradiation imageable target, generally turning an angle excites once, turn like this what angles and just carried out how many times and excite, thereby realized the transmission-type imaging of multi-angle.

B, use optical detecting instrument obtain measurement data, obtain pharosage Φ _m

In step a, the Polaroid target of laser illumination, optical detecting instrument just gathers one group of fluorescence signal, the one group of measurement data that obtains, multi-angle excites corresponding many group measurement data that produce, and the organism surface three-dimensional energy reconstruction technique of describing in the market demand non-contact type optical sectioning imaging method is obtained the three-dimensional fluorescence DATA DISTRIBUTION of imageable target surface.

(2) obtain anatomical information and the optical property parameter of reconstructed object

The anatomical information of a, reconstructed object, carry out three-dimensional reconstruction to the computer tomography data for projection, and obtain the three-dimensional data of imageable target with the pretreatment of 3DMED software; Adopt the semi-automatic dividing method of man-machine interactive in 3DMED software to carry out tissue segmentation to volume data, obtain the anatomical structure of imageable target;

B, obtain optical property parameter, utilize anatomical information and application to obtain the optical property parameter of each tissue in imageable target based on the algorithm of the diffuse optical tomography based on zone of describing in the specific optical 3-dimensional method for reconstructing of biological tissue.

(3) based on light mode and finite element theory, the anatomical information of reconstructed object and optical property parameter, as prior information, are set up the measurement data on surface and the linear relationship of the inner fluorescent target distribution of reconstructed object.

A, light mode, adopt the diffusion approximation equation to describe the transmitting procedure of light in imageable target;

It is discrete that b, application Amira software carry out grid to imageable target, obtains the discrete grid block data of imageable target;

C, according to finite element theory, and anatomical information and the optical property parameter of the reconstructed object that obtains of fusion steps (2), the diffusion approximation equation is discrete, build the measurement data on surface and the linear relationship of the inner fluorescent target distribution of reconstructed object:

Φ _m=AX

Wherein A is sytem matrix, and X is fluorescent target distributed in three dimensions and the concentration that will solve, and is non-negative.

(4) above-mentioned linear relationship is converted into the minimization problem of Prescribed Properties:

min||X|| ₂，s.t.|AX-Φ _m|≤ε，X≥0

ε is a non-negative error coefficient, and this is the least norm of the 2-with a Prescribed Properties problem.

(5), to the minimization problem of belt restraining in step (4), adopt the algebraic reconstruction technique of weighting to solve constraints: | AX-Φ _m|≤ε, X 〉=0,2-least norm problem solves with steepest descent method.The algebraic reconstruction technique of weighting is following form:

$X=X+\mathrm{\β}{\stackrel{\→}{A}}_i\frac{{\mathrm{\Φ}}_m-{\stackrel{\→}{A}}_{i}X}{{\stackrel{\→}{A}}_i{\stackrel{\→}{A}}_i}$

Wherein

The i that is matrix A is capable, and β is positive weights.

(6) utilize fluorescent target distribution results in step (5) to calculate pharosage With pharosage value Φ on the border of measuring _mWith value of calculation

Poor

Stopping criterion as reconstruction algorithm.If

Finish reconstruction algorithm, obtain target distribution X; Otherwise, execution step (7).

(7) with the initial solution of the solution of step (5) as steepest descent method, iterative 2-least norm problem, and make solution meet nonnegativity:

$X=X-\mathrm{grad}\_d{x}^{*}\frac{{\▿}_X\left|\right|X|{|}_2}{\left|{\▿}_X\right|\left|X\right|{|}_2|};$

Wherein grad_dx is the iteration step length size, The gradient of 2-least norm problem, It is the mould value of gradient.

(8) utilize fluorescent target distribution results in step (7) to calculate pharosage

With pharosage value Φ on the border of measuring _mWith value of calculation Poor

Stopping criterion as program.If

Finish reconstruction algorithm, obtain target distribution X; Otherwise, execution step (9).

(9) the solution X that step (7) is obtained, conversely again as the initial solution of carrying out algebraic reconstruction technique, goes to step (5).

(10) show result, the anatomical structure of last reconstructed results and imageable target is carried out image co-registration, with Tecplot software, show.

Below give a kind of specific embodiment, by reference to the accompanying drawings 2, accompanying drawing 3,4 pairs of reconstructed results of the present invention of accompanying drawing be further described.

Accompanying drawing 2 is used for the digital mouse model of emulation experiment.Wherein figure (a) expression, with the nonuniformity numeral mouse model of light source, has comprised main several organs, as heart (large red part), lung (blue portion), liver (yl moiety), stomach (rose part), kidney (green portion), muscular tissue (lavender part).Torso portion and the fluorescent target (large red spherula) to be rebuild of figure (b) representative digit Mus.

Accompanying drawing 3 is the location drawing and the digital Mus surface surface of intensity distribution of excitation source on cross section.Figure (a) is the locations drawing of 9 exciting light source points on cross section.Figure (b) is the radiative surperficial surface of intensity distribution under certain excitation source.

Accompanying drawing 4 is based on reconstructed results of the present invention.It is shown as fluorescent target scattergram and the concentration in z=16.4mm cross section.The real center position of reconstructed object is (21.910.4,16.4) mm, and the target's center position that algorithm obtains is (22.0,10.7,16.9) mm.Site error is $\mathrm{LE}=\sqrt{{(x-x_0)}^2+{(y-y_0)}^2+{(z-z_0)}^2}\≈0.42\mathrm{mm}.$ The target Cmax of rebuilding is 5183.6nM/L, and its relative error is RE=|C _c-C _Real|/C _Real≈ 13.3%.Based on reconstruction of the present invention, its site error is little, and the relative concentration error is little, is a kind of effective fluorescent molecule tomography rebuilding algorithm.

Claims (2)

1. one kind based on the fluorescent molecule tomography rebuilding method of interative computation alternately, it is characterized in that: based on light mode and finite element theory, with the optical property parameter of reconstructed object and anatomical information as prior information, set up the measurement data on surface and the linear relationship that the inner fluorescent target of reconstructed object distributes, this linear relationship is converted into the minimization problem of Prescribed Properties, algebraic reconstruction technique and the steepest descent method of alternately carrying out weighting solve, thereby obtain distributed in three dimensions and the concentration of the fluorescent target of reconstructed object inside.

2. according to claim 1 based on the fluorescent molecule tomography rebuilding method of interative computation alternately, it is characterized in that:

Comprise the following steps:

(1) obtain measurement data

A, excitation source carry out the transmission-type tomoscan of multi-angle to being fixed on reconstructed object on automatically controlled turntable;

B, use optical detecting instrument obtain measurement data, obtain pharosage Φ _m

(2) obtain anatomical information and the optical property parameter of reconstructed object;

(3) based on light mode and finite element theory, the anatomical information of reconstructed object and optical property parameter, as prior information, are set up the measurement data on surface and the linear relationship of the inner fluorescent target distribution of reconstructed object;

(4) above-mentioned linear relationship is converted into the minimization problem of Prescribed Properties:

min||X|| ₂，s.t.|AX-Φ _m|≤ε，X≥0

ε is a non-negative error coefficient, and this is the least norm of the 2-with a Prescribed Properties problem;

(5), to the minimization problem of belt restraining in step (4), adopt the algebraic reconstruction technique of weighting to solve constraints: | AX-Φ _m|≤ε, X 〉=0,2-least norm problem solves with steepest descent method; The algebraic reconstruction technique of weighting is following form:

$X=X+\mathrm{\β}{\stackrel{\→}{A}}_i\frac{{\mathrm{\Φ}}_m-{\stackrel{\→}{A}}_{i}X}{{\stackrel{\→}{A}}_i{\stackrel{\→}{A}}_i}$

Wherein

The i that is matrix A is capable, and β is positive weights;

(6) utilize fluorescent target distribution results in step (5) to calculate pharosage With pharosage value Φ on the border of measuring _mWith value of calculation

Poor

Stopping criterion as reconstruction algorithm; If Finish reconstruction algorithm, obtain target distribution X; Otherwise, carry out next step;

(7) with the initial solution of the solution of step (5) as steepest descent method, iterative 2-least norm problem, and make solution meet nonnegativity:

$X=X-\mathrm{grad}\_d{x}^{*}\frac{{\▿}_X\left|\right|X|{|}_2}{\left|{\▿}_X\right|\left|X\right|{|}_2|};$

Wherein grad_dx is the iteration step length size,

The gradient of 2-least norm problem,

It is the mould value of gradient;

(8) utilize fluorescent target distribution results in step (7) to calculate pharosage

With pharosage value Φ on the border of measuring _mWith value of calculation Poor Stopping criterion as program; If Finish reconstruction algorithm, obtain target distribution X; Otherwise, execution step (9);

(9) the solution X that step (7) is obtained, conversely again as the initial solution of carrying out algebraic reconstruction technique, goes to step (5);

(10) show result, the anatomical structure of last reconstructed results and imageable target is carried out image co-registration, with Tecplot software, show.

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