CN105004444B - A kind of non-iterative ultrasound computed tomography temperature rebuilding method - Google Patents

Abstract

The invention discloses a kind of non-iterative ultrasound computed tomography temperature rebuilding method, comprise the following steps：Problems of Reconstruction is abstracted into matrix equation, cost equation is constructed, cost equation is solved using non-minimumization optimal method, Temperature Distribution is rebuild according to the velocity of sound.Beneficial effect of the present invention：Innovative introduces non-minimumization optimization algorithm, is calculated using characteristic value and characteristic root and instead of traditional iterative algorithm, method is simple, and amount of calculation is small, practical.The long-range measurement of air themperature can be realized using this algorithm, temperature distribution image is reconstructed, the non-contact measurement that can be widely applied in terms of medical science, industry.

Description

A kind of non-iterative ultrasound computed tomography temperature rebuilding method

Technical field

The present invention relates to ultrasound computed tomography reconstruction technique field, more particularly to a kind of non-iterative ultrasound computed tomography temperature rebuilding method.

Background technology

CT technologies are a kind of by the energy wave launched, and tested region are scanned, so as to obtain the technology of information needed.Phase For traditional e measurement technology, CT technologies will not be interfered to tested region, be a kind of preferable non-destructive measuring method.

Ultrasound computed tomography, is a kind of CT technologies using ultrasonic wave as energy wave, and its general principle is that transmitting multi beam ultrasonic wave makes Pass through measured medium, due to the inhomogeneities that target signature is distributed in measured medium, the speed of ultrasonic wave will change therewith. So, by measuring the ultrasonic wave of outgoing, according to the propagation time of ultrasonic wave, you can counter point for pushing away target signature in measured medium Cloth, and then obtain reconstruction image.Due to ultrasonic wave, spread speed is affected by temperature in atmosphere, it is possible to use ultrasonic wave carries out remote Journey temperature survey.Because ultrasonic wave has the advantages that cost is low, penetration power is strong, harmless in itself, the technology medical science into Picture, Non-Destructive Testing, atmospheric monitoring etc. are multi-field to be with a wide range of applications.

Algorithm for reconstructing is the key link in ultrasonic temperature reconstructing system, and the algorithm for reconstructing of present main flow mainly has filter Ripple backprojection algorithm, iterative algorithm, and least square method based on solution matrix equation etc..The reconstruction of filter back-projection algorithm Error is larger by filters affect, is typically only capable to obtain more rough result, is not suitable for carrying out fine image reconstruction work. Iterative algorithm definition is higher, but calculates complicated, and speed is slightly slow, different iterative algorithm to the sensitiveness of measurement error not yet Together.The universal reduction degree of algorithm based on solution matrix equation is higher, speed, but least square method is unable to processing path number Less than the situation of pixel count, the resolution ratio of reconstruction image is restricted.In addition, when tested region pixel count and number of path all compare When many, sytem matrix is very huge, and matrix operation efficiency is substantially reduced.

It should be noted that the aerial propagation path of ultrasonic wave is more complicated, the phenomenon such as diffraction, refraction is tighter Weight.It has been generally acknowledged that in the ideal case, influence of the inhomogeneities to sound field of medium can be ignored, recognized in theory of algorithm research It is ultrasonic wave along straightline propagation.

The content of the invention

The purpose of the present invention is exactly to solve the above problems, it is proposed that a kind of non-iterative ultrasound computed tomography temperature rebuilding side Method, this method optimizes (Non-Minimization Optimization) algorithm using non-minimumization, is calculated using characteristic value Method solution matrix equation, calculating process can be simplified, with calculate it is simple, rebuild the features such as speed is fast, result is accurate.

To achieve these goals, the present invention is adopted the following technical scheme that：

A kind of non-iterative ultrasound computed tomography temperature rebuilding method, comprises the following steps：

The first step：Path is set as Γ_i, c (x, y) is velocity of the ultrasonic wave at point (x, y) place, builds ultrasonic wave edge The equation of time of path travel time；

Second step：Tested region is divided into m grid, using each grid as the base unit of measurement, according to path Each grid length and ultrasonic wave correspondence grid in spread speed, by equation of time discretization, obtain ultrasonic wave Along the propagation time of path discretization；m≥1；

3rd step：Propagation time of the ultrasonic wave along path discretization under all paths is calculated respectively, obtains propagation time square Battle array equation；

4th step：The unknown matrix U in propagation time matrix equation is determined, cost is constructed using propagation time matrix equation Equation, the cost equation is met：The solution for making cost equation minimum is the optimal of unknown matrix U in propagation time matrix equation Neutralizing；

5th step：Estimation equation is constructed, the method optimized using non-minimumization obtains the solution of cost equation, i.e., unknown square The optimum solution of battle array, rate matrices are obtained using the optimum solution of unknown matrix；

6th step：According to the relation between Temperature Distribution and ultrasonic velocity, using the optimum solution of time matrix equation, Try to achieve Temperature Distribution.

In the first step, the ultrasonic wave of structure is specially along the equation of time of path travel time：

Wherein, Γ_iThe path of expression ultrasonic propagation, i=1,2 ..., n, n is the total number of paths of setting.

In the second step, propagation time of the ultrasonic wave along path discretization is specially：

Wherein, p_ijRepresent path Γ_iLength in j-th of grid, c_jRepresent the speed of ultrasonic wave in j-th of grid, j =1,2 ..., m.

In 3rd step, propagation time matrix equation is specially：

Wherein, t_iRepresent in path Γ_iPropagation time of the lower ultrasonic wave along path discretization；p_ijRepresent path Γ_iIn jth Length in individual grid；c_jRepresent the speed of ultrasonic wave in j-th of grid；I=1,2 ..., n；J=1,2 ..., m.

In 4th step, the specific method that propagation time matrix equation is converted into cost equation is：

Make time matrixSytem matrixRate matrices

Wherein, t_iRepresent in path Γ_iPropagation time of the lower ultrasonic wave along path discretization；p_ijRepresent path Γ_iIn jth Length in individual grid；c_jRepresent the speed of ultrasonic wave in j-th of grid；I=1,2 ..., n；J=1,2 ..., m.

Propagation time matrix equation is converted into following form：

W=[P-T] is made, is known matrix, is madeFor unknown matrix；Construction optimizes cost equation：

Wherein w_iRepresent known matrix W the i-th row.

Solve cost equation specific method be：

Cost equation is written as form：

Wherein parameter matrixIn order that J → 0, uses estimation equation：

MU=λ U

Due to containing noise in W, M order is considered as generation always greater than m, the M corresponding smallest real eigenvalue U of minimal eigenvalue λ Valency equation J non-minimumization optimum solution；

After U is tried to achieve, the Matrix C of the velocity of sound can be solved.

In 6th step, the specific method for trying to achieve Temperature Distribution is：

The beneficial effects of the invention are as follows：

Compared with prior art, what Ultrasonic CT method for reconstructing of the invention was innovative introduces non-minimumization optimization calculation Method, is calculated using characteristic value and characteristic root and instead of traditional iterative algorithm, method is simple, and amount of calculation is small, practical.Utilize This algorithm can realize the long-range measurement of air themperature, reconstruct temperature distribution image, can be widely applied to medical science, industry etc. The non-contact measurement of aspect.

Brief description of the drawings

Fig. 1 is ultrasound computed tomography system schematic of the present invention；

Fig. 2 is the holistic approach flow chart of the present invention.

Embodiment：

The present invention will be further described with embodiment below in conjunction with the accompanying drawings：

In ultrasonic CT system as shown in Figure 1, black round dot represents to be fixed on the ultrasonic transmitter of same point and reception Device, each transmitter launches ultrasonic wave, through tested region, is received by other all receivers.From transmitter to reception The straight line of device is referred to as path, according to the launch time of record and reception time, when can calculate propagation of the ultrasonic wave along path Between.

As shown in Fig. 2 a kind of non-iterative ultrasound computed tomography temperature rebuilding method, comprises the following steps：

The first step, according to the principle of Ultrasonic CT, solution matrix equation is abstracted into by Problems of Reconstruction.

If c (x, y) is velocity of the ultrasonic wave at point (x, y) place, then the time used in ultrasonic wave along propagated It can be expressed as：

Wherein Γ_iThe path of expression ultrasonic propagation, i=1,2 ..., n, n is the total number of paths of setting.In algebraic manipulation In, measurement field is divided into m grid by us, and m sizes determine the resolution ratio of reconstruction image, and each grid is used as ultrasonic velocity The base unit of calculating.Thus the propagation time of discretization is obtained：

Wherein p_ijRepresent path Γ_iLength in j-th of grid, c_jRepresent the speed of ultrasonic wave in j-th of grid, j =1,2 ..., m.The situation in all paths is taken into account, matrix equation is obtained：

Second step, statement known matrix and unknown matrix, construct cost equation, and target is to make cost equation minimum to ask Solve the optimum solution of ill-posed matrix equation.

It is ill in view of the matrix equation obtained in the first step, makes time matrixSytem matrixRate matricesSo this equation can be converted into following form：

For convenience, W=[P-T], referred to as known matrix are made, is madeReferred to as unknown matrix.Then construct most Optimize cost equation：

Wherein w_iRepresent known matrix W the i-th row.

3rd step, according to cost equation, constructs estimation equation, using solving parameter matrix smallest real eigenvalue and characteristic vector Method solve velocity of sound matrix.

It is desirable that minimizing the U for obtaining an optimization by cost equation.For convenience of calculation, cost equation is write as Following form：

Wherein parameter matrixIn order that J → 0, can use estimation equation：

MU=λ U

Due to containing noise in W, M order is always greater than m, the M corresponding smallest real eigenvalue U of minimal eigenvalue λ, it is possible to It is considered as cost equation J non-minimumization optimum solution.After U is tried to achieve, the Matrix C of the velocity of sound can be solved.

4th step, according to temperature in air and the relation of the velocity of sound, seeks calculation Temperature Distribution.

Utilize the relation between Temperature Distribution T (x, y) and ultrasonic velocity c (x, y)

Can be in the hope of Temperature Distribution T (x, y).

Although above-mentioned the embodiment of the present invention is described with reference to accompanying drawing, not to present invention protection model The limitation enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not Need to pay various modifications or deform still within protection scope of the present invention that creative work can make.

Claims (6)

1. a kind of non-iterative ultrasound computed tomography temperature rebuilding method, it is characterized in that, comprise the following steps：

The first step：Path is set as Γ_i, c (x, y) is velocity of the ultrasonic wave at point (x, y) place, builds ultrasonic wave along path The equation of time in propagation time；

Second step：Tested region is divided into m grid, using each grid as the base unit of measurement, according to path every Spread speed of the length and ultrasonic wave of individual grid in correspondence grid, by equation of time discretization, obtains ultrasonic wave along road The propagation time of footpath discretization；m≥1；

3rd step：Propagation time of the ultrasonic wave along path discretization under all paths is calculated respectively, obtains propagation time matrix side Journey；

4th step：The unknown matrix U in propagation time matrix equation is determined, cost side is constructed using propagation time matrix equation Journey, the cost equation is met：The solution for making cost equation minimum is the optimization of unknown matrix U in propagation time matrix equation Solution；

5th step：Estimation equation is constructed, the method optimized using non-minimumization obtains the solution of cost equation, i.e. unknown matrix Optimum solution, rate matrices are obtained using the optimum solution of unknown matrix；

The method that non-minimumization is optimized is specially：Utilize the method for solving parameter matrix smallest real eigenvalue and characteristic vector Solve velocity of sound matrix；

Solve cost equation specific method be：

Cost equation is written as form：

$J=U^T\left(\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{w_i}^T{w}_i\right)U=U\·MU$

Wherein parameter matrixIn order that J → 0, uses estimation equation：

MU=λ U

Due to containing noise in W, M order is considered as cost side always greater than m, the M corresponding smallest real eigenvalue U of minimal eigenvalue λ Journey J non-minimumization optimum solution；

After U is tried to achieve, the Matrix C of the velocity of sound can be solved；

6th step：According to the relation between Temperature Distribution and ultrasonic velocity, using the optimum solution of time matrix equation, try to achieve Temperature Distribution.

2. a kind of non-iterative ultrasound computed tomography temperature rebuilding method as claimed in claim 1, it is characterized in that, in the first step, The ultrasonic wave of structure is specially along the equation of time of path travel time：

$t_i={\∫}_{{\mathrm{\Γ}}_i}\frac{ds}{c(x,y)}$

Wherein, Γ_iThe path of expression ultrasonic propagation, i=1,2 ..., n, n is the total number of paths of setting.

3. a kind of non-iterative ultrasound computed tomography temperature rebuilding method as claimed in claim 1, it is characterized in that, in the second step, Propagation time of the ultrasonic wave along path discretization be specially：

$t_i=\underset{j=1}{\overset{m}{\Σ}}\frac{p_{ij}}{c_j}$

Wherein, p_ijRepresent path Γ_iLength in j-th of grid, c_jRepresent the speed of ultrasonic wave in j-th of grid, j=1, 2 ..., m.

4. a kind of non-iterative ultrasound computed tomography temperature rebuilding method as claimed in claim 1, it is characterized in that, in the 3rd step, Propagation time matrix equation is specially：

Wherein, t_iRepresent in path Γ_iPropagation time of the lower ultrasonic wave along path discretization；p_ijRepresent path Γ_iIn j-th of side Length in lattice；c_jRepresent the speed of ultrasonic wave in j-th of grid；I=1,2 ..., n；J=1,2 ..., m.

5. a kind of non-iterative ultrasound computed tomography temperature rebuilding method as claimed in claim 1, it is characterized in that, in the 4th step, The specific method that propagation time matrix equation is converted into cost equation is：

Make time matrixSytem matrixRate matrices

Wherein, t_iRepresent in path Γ_iPropagation time of the lower ultrasonic wave along path discretization；p_ijRepresent path Γ_iIn j-th of side Length in lattice；c_jRepresent the speed of ultrasonic wave in j-th of grid；I=1,2 ..., n；J=1,2 ..., m；

Propagation time matrix equation is converted into following form：

$\[\begin{array}{cc}P& -T\end{array}\]\left[\begin{array}{c}C\\ 1\end{array}\right]=0_{n\×1}$

W=[P-T] is made, is known matrix, is madeFor unknown matrix；Construction optimizes cost equation：

$J=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}{\left(w_{i}U\right)}^2$

Wherein w_iRepresent known matrix W the i-th row.

6. a kind of non-iterative ultrasound computed tomography temperature rebuilding method as claimed in claim 1, it is characterized in that, in the 6th step, The specific method for trying to achieve Temperature Distribution is：

$c(x,y)=20.05\sqrt{T(x,y)}.$