CN102110302A - Method for compensating missing data in CT (Computed Tomography) scanning - Google Patents

Abstract

The invention relates to a method for compensating missing data in CT (Computed Tomography) scanning, comprising the following steps: according to incorrect or missing projection data information, correcting the incorrect or missing projection data successively with an opposite projection interpolation method, an adjacent projection interpolation method and an interpolation result weighted sum method so as to obtain correct projection data, wherein a weight function is calculated by the interpolation result weighted sum via the following constraint, and f(x) represents the continuous form of the weight: 1) f(x) is continuously differentiable on [0,pi/2]; 2) f(0)=1; 3) lim f(x) is equal to 0; and 4) f(x) is monotonic decreasing in a definitional domain, wherein x is the taper angle of each layer of a CT scanner. The method disclosed by the invention combines the advantages of the opposite projection interpolation and the adjacent projection interpolation, so that when scanning fails, an ideal correction effect can be obtained by using a big taper angle scanner or a small taper angle scanner, and a correct CT image can be reconstructed.

Description

The compensation method of missing data in the CT scan

Technical field

The present invention relates to medical image and rebuild pretreatment technology, the compensation method of missing data in a kind of specifically CT scan.

Background technology

In the CT scan process for some reason, make a mistake when the generation of for example little spark phenomenon or data transmission etc., can cause the data under some projection view (being called View) incorrect, at this moment, can not abandon whole scanning because of the mistake of low volume data and build the picture process, so need the data of mistake be revised by the mode of interpolation.But the method for revising directly influences final picture quality.

In the prior art,, usually utilize the two or more data for projection that are adjacent to carry out interpolation, thereby obtain the correction of this data for projection for the incorrect data of projection.Difference is little though adjacent data for projection is because angle differs less, but because projection angle difference between them, thereby ray is in the path of space process difference, change more violent position in some tissue, still the situation that correction result can not correctly reflect true projection can occur, thereby in image, cause pseudo-shadow.The method utilization that also has " (angle differs 180 degree) relatively " projection view carries out the interpolation correction to misdata, obtains the better pictures effect.

The Chinese patent application that the patent No. is 200510098005.3, name is called CT image rebuilding method, CT equipment and program, a kind of CT image rebuilding method that can reflect replacement data attribute (value and positional information) in the process that produces the image reconstruction data is provided, CT equipment and program, wherein said replacement data is used for the compensating defective data.Described replacement data is used for the compensating defective data.

But, when the cone angle of CT projection cone-beam is big, projection view and wait to revise between the view and can not pass through identical path relatively in the space, it also is inappropriate compensating with relative projection at this moment.

Summary of the invention

Can not be applied to weak point on the big cone angle CT scan device at the adjacent and relative view modification method that exists in the prior art, the technical problem to be solved in the present invention provides the compensation method of missing data in a kind of CT scan that can be applicable on the big cone angle CT scan device.

For solving the problems of the technologies described above, the technical solution used in the present invention is:

The compensation method of missing data may further comprise the steps in the CT scan of the present invention:

Incorrect or the drop-out according to data for projection adopts the method for relative projection interpolation method, adjacent projections interpolation method and interpolation result weighted sum that data for projection incorrect or that lose is revised successively, obtains correct data for projection.

Described interpolation result weighted sum is calculated the weights function by following constraint, represents the conitnuous forms of weights with f (x):

1) f (x) exists Last continuously differentiable;

2)f(0)＝1；

3) $\underset{x\→\mathrm{\π}/2}{\lim }f\left(x\right)=0;$

4) f (x) monotone decreasing in field of definition;

Wherein x is the cone angle of each layer of CT scan device.

The described weights function that satisfies above-mentioned constraint simultaneously is:

f(x)＝A ₃x ³+A ₂x ²+A ₁x+A ₀

Wherein, A ₀～A ₃Computing method as follows:

$\left\{\begin{array}{c}f\left(0\right)=1\\ f\left(\frac{\mathrm{\π}}{2}\right)=0\\ f^{/}\left(0\right)=C\\ f^{/}\left(\frac{\mathrm{\π}}{2}\right)=D\end{array}\right.$

Try to achieve four coefficients by the above-mentioned system of equations of simultaneous, wherein C, D be respectively function 0 and

The derivative of point can be specified arbitrarily, is used to control the contribution of the final interpolation result of adjacent view and relative view.

The present invention has following beneficial effect and advantage:

1. the advantage of comprehensive projection interpolation relatively of the inventive method and adjacent projections interpolation, provided a kind of defective data modification method of CT scan device, made when scanning makes a mistake, no matter small-angle still is an auger angle sweep device, desirable correction effect can both be reached, correct CT image can be rebuild.

Description of drawings

Fig. 1 is the inventive method process flow diagram;

Fig. 2 is an adjacent and relative perspective view in the CT scan device;

Fig. 3 is a relative perspective geometry graph of a relation in the CT scan device;

Fig. 4 is for satisfying a class function curve of weights constraint in the inventive method.

Embodiment

As shown in Figure 1, the compensation method of missing data is in the CT scan of the present invention: the incorrect or drop-out according to data for projection, adopt the method for relative projection interpolation method, adjacent projections interpolation method and interpolation result weighted sum that data for projection incorrect or that lose is revised successively, obtain correct data for projection.

Described interpolation result weighted sum is calculated the weights function by following constraint, represents the conitnuous forms of weights with f (x):

1) f (x) exists

Last continuously differentiable;

2)f(0)＝1；

3) $\underset{x\→\mathrm{\π}/2}{\lim }f\left(x\right)=0;$

4) f (x) monotone decreasing in field of definition;

Wherein x is the cone angle of each layer of CT scan device.

The inventive method may further comprise the steps:

(1) relative projection interpolation

As shown in Figure 2, radiographic source S ^ErrorThere is defective in place's projection view (view), and projection view shown in dotted line is lost, and need utilize other data to remedy by interpolation, at first utilizes its relative projection S ^c(this projection and defective projection angle differ 180 degree) comes interpolation to obtain.

As Fig. 3, projection view is under the fan-beam situation, establishes the radiographic source that S is interpolation view (data for projection that this radiographic source projection angle obtains down is incorrect), and θ and γ are respectively projected angle and the fan angle under this view; S ^cBe the radiographic source of its " relatively " view, θ ^cAnd γ ^cBe respectively projected angle and fan angle under this view.As can be seen from the figure, two view projected angles close and are:

θ ^c＝θ+Δ， (1)

The pass at two fan angles is:

γ ^c＝-γ； (2)

Wherein (direction and the sense of rotation of supposing the arrangement of fan-beam ray are opposite, and promptly γ is negative among Fig. 3, γ for Δ=π-2 γ ^cFor just).As can be seen from the figure, projection view P (θ ^c, γ ^c) and P (θ, γ) in the same path of space process (being that direction is opposite), so can use P (θ ^c, γ ^c) replace the defective projection P (θ, γ).

In actual CT scan, " relatively " view (S of interpolation view (S) ^c) and passage not necessarily just at the integer ray position, promptly two rays can not overlap fully, so need obtain by interpolation, comprise between two adjacent view interpolation two parts between interpolation and ray.Suppose that (being designated as P (i, j)) is defective data, and its projection angle is θ for the j bar ray of i view _i=i Δ θ, the fan angle is γ _j=(j-MidChannel) * Δ γ, Δ θ and Δ γ are respectively projected angle increment and fan angle increment, and MidChannel is the ray by the frame rotation center, then an interpolation process following (P represents data for projection) in the CT scan device:

A) seek " relatively " view

According to (1) formula, the projected angle of view is θ relatively ^c=θ _i+ π-2 γ _i, θ ^cNot necessarily at integer view ray position, projected angle θ ^cThe sequence number of two view on both sides is respectively:

With $i_b^c=i_f^c+1,$ Linear weight value is respectively $w_f^{\mathrm{View}}=1-w_b^{\mathrm{View}},$ $w_b^{\mathrm{View}}=\frac{{\mathrm{\θ}}^c}{\mathrm{\Δ\θ}}-i_f^c.$

B) certain bar ray of the relative view of searching makes it and the same path of defective ray process, and according to (2) formula, the fan angle of ray is γ relatively ^c=-γ _j, γ ^cAlso, fan angle γ not necessarily at the integer ray position ^cThe sequence number of two rays on both sides is respectively

With $j_b^c=j_f^c+1,$ Linear weight value is respectively $w_f^{\mathrm{channel}}=1-w_b^{\mathrm{channel}},$ $w_b^{\mathrm{channel}}=\frac{{\mathrm{\γ}}^c}{\mathrm{\Δ\γ}}+\mathrm{MidChannel}-j_f^c$

C) weighting obtains real relative projection view P _C(i, j)

Bilinear interpolation with former and later two relative view and former and later two projection ray obtains final relative projection view:

$P_C(i,j)=P(i_f^c,j_f^c)*w_f^{\mathrm{View}}*w_f^{\mathrm{channel}}+P(i_f^c,j_b^c)*w_f^{\mathrm{View}}*w_b^{\mathrm{channel}}$ (3)

$+P(i_b^c,j_f^c)*w_b^{\mathrm{View}}*w_f^{\mathrm{channel}}+P(i_b^c,j_b^c)*w_b^{\mathrm{View}}*w_b^{\mathrm{channel}}$

(2) adjacent projections interpolation

Present embodiment adopts the mean value of simple adjacent projections, owing to do not have the relative difference on the locus between two adjacent view, so weights can be made as w _-=w ₊=0.5.

Thereby the result of interpolation can be expressed as:

P _N(i，j)＝P _-(i，j)*w _-+P ₊(i，j)*w ₊ (4)

When projection of interpolation, its contiguous projection view needs to exist with relative projection view.

(3) final interpolation

The purpose of this step is that the interpolation result with the interpolation result of relative projection view and adjacent projections view carries out comprehensive interpolation processing, thereby obtains final correction result.Different detector layer can be used different weights, usefulness P (i, j, the m) projection of expression m layer, this projection view can be expressed as:

P(i，j，m)＝P _N(i，j，m)*(1-w _c(m))+P _C(i，j，m)*w _c(m) (5)

The function that satisfies 4 constraint conditions of weights function in the inventive method exists, and a simple example is exactly a linear function $f\left(x\right)=-\frac{2}{\mathrm{\π}}x+1.$ An other class function can be controlled adjacent projections and the shared ratio (for example hermite polynomial function) of opposite projection by the value and the derivative at A, B two-end-point place as shown in Figure 4, thereby reaches the compromise of weights.

A described class weight of a polynomial value function that satisfies above-mentioned constraint simultaneously is:

f(x)＝A ₃x ³+A ₂x ²+A ₁x+A ₀

Wherein, A ₀～A ₃Computing method as follows:

$\left\{\begin{array}{c}f\left(0\right)=1\\ f\left(\frac{\mathrm{\π}}{2}\right)=0\\ f^{/}\left(0\right)=C\\ f^{/}\left(\frac{\mathrm{\π}}{2}\right)=D\end{array}\right.$

Try to achieve four coefficients by the above-mentioned system of equations of simultaneous, wherein C, D be respectively function 0 and

The derivative of point can be specified arbitrarily, is used to control the contribution of the final interpolation result of adjacent view and relative view.(i j) is revised data to the data P that obtains through (5) formula interpolation, can be used for reconstructed image.

The inventive method is utilized the interpolation data for projection, certain bar ray in " relatively " projection in the CT scan device perpendicular in the scanning bed xy plane through same path, and in the CT scan device, be parallel on the scanning bed yz plane through these characteristics of similar path at " adjacent " data for projection, defective data is revised, the weight function of revising is relevant with the projection cone angle, make the different layers of detecting device of CT scan device add different weights, the advantage of relative projection interpolation when both keeping small-angle, reduce cone angle again when big, utilized the inconsistency of relative projection separately.The present invention has provided a constraint condition that satisfies the weights function of These characteristics simultaneously, makes all functions that satisfy this condition to obtain best weights function by experiment in these a series of functions as the weights function.

Claims (3)

1. the compensation method of missing data in the CT scan is characterized in that may further comprise the steps:

Incorrect or the drop-out according to data for projection adopts the method for relative projection interpolation method, adjacent projections interpolation method and interpolation result weighted sum that data for projection incorrect or that lose is revised successively, obtains correct data for projection.

2. by the compensation method of missing data in the described CT scan of claim 1, it is characterized in that: described interpolation result weighted sum is calculated the weights function by following constraint, represents the conitnuous forms of weights with f (x):

1) f (x) exists

Last continuously differentiable;

2)f(0)＝1；

$3),\underset{x\→\mathrm{\π}/2}{\lim }f\left(x\right)=0;$

4) f (x) monotone decreasing in field of definition;

Wherein x is the cone angle of each layer of CT scan device.

3. by the compensation method of missing data in the described CT scan of claim 2, it is characterized in that: the described weights function that satisfies above-mentioned constraint simultaneously is:

f(x)＝A ₃x ³+A ₂x ²+A ₁x+A ₀

Wherein, A ₀～A ₃Computing method as follows:

$\left\{\begin{array}{c}f\left(0\right)=1\\ f\left(\frac{\mathrm{\π}}{2}\right)=0\\ f^{/}\left(0\right)=C\\ f^{/}\left(\frac{\mathrm{\π}}{2}\right)=D\end{array}\right.$

Try to achieve four coefficients by the above-mentioned system of equations of simultaneous, wherein C, D be respectively function 0 and

The derivative of point can be specified arbitrarily, is used to control the contribution of the final interpolation result of adjacent view and relative view.

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