CN106251383B - A kind of estimation method of power spectrum CT substratess matter sinogram - Google Patents
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- OMOVVBIIQSXZSZ-UHFFFAOYSA-N [6-(4-acetyloxy-5,9a-dimethyl-2,7-dioxo-4,5a,6,9-tetrahydro-3h-pyrano[3,4-b]oxepin-5-yl)-5-formyloxy-3-(furan-3-yl)-3a-methyl-7-methylidene-1a,2,3,4,5,6-hexahydroindeno[1,7a-b]oxiren-4-yl] 2-hydroxy-3-methylpentanoate Chemical compound CC12C(OC(=O)C(O)C(C)CC)C(OC=O)C(C3(C)C(CC(=O)OC4(C)COC(=O)CC43)OC(C)=O)C(=C)C32OC3CC1C=1C=COC=1 OMOVVBIIQSXZSZ-UHFFFAOYSA-N 0.000 claims description 5
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- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 2
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Abstract
The present invention provides a kind of estimation method of power spectrum CT substratess matter sinogram, is related to computed tomography reconstruction method and technology field.Utilize the recessed characteristic of the forward projection physical model function of power spectrum CT scan, by the corresponding high energy data for projection of every X-ray, low energy data for projection, high energy projects estimated value vector current value, low energy projects estimated value vector current value, the current value of sinogram matrix A and the current value of sinogram matrix B determine that this X-ray corresponds to the new value of sinogram matrix A and the new value of sinogram matrix B, according to by high energy data for projection, low energy projects number, the evaluated error size that forward direction high energy projection estimated value and forward direction low energy projection estimated value obtain judges whether sinogram matrix is newly worth qualified.Method provided by the invention, strong applicability, for different power spectrum CT scan systems, perhaps different substratess confrontations do not need regulation coefficient or re-establish look-up table；Calculating speed is improved while guaranteeing accuracy, is reduced and is calculated the time.
Description
The technical field is as follows:
the invention relates to the technical field of reconstruction methods of Computed Tomography (CT), in particular to an estimation method of a sinogram of a spectral CT-based substance.
Background art:
in Computed Tomography (CT), an object to be detected is scanned by X-rays at different viewing angles to obtain a set of projection sinograms, the sinograms are used for reconstructing the internal structure of the object to be detected, the contrast of each part in a reconstructed image is determined by the attenuation coefficient of each part to the X-rays, and the attenuation coefficients of different substances to the X-rays are changed along with the energy level of the X-rays for scanning. In the conventional CT reconstruction, the X-ray for scanning is assumed to be a single energy level, while the X-ray for actual scanning comprises a plurality of energy levels, the approximation of the X-ray energy level by the conventional CT easily causes a reconstructed image to generate metal artifacts, reduces the contrast between different substances, and may cause different substances to have the same reconstruction result in severe cases. In addition, the conventional CT can only provide shape information of the inside of the detected substance, and cannot provide composition information of the substance.
The energy spectrum CT cancels the approximation of the traditional CT to the energy level of X-rays, utilizes two X-rays with different energy spectrums to scan a detected object to obtain two groups of projection sinograms, and utilizes the two groups of projection sinograms to reconstruct a single energy attenuation image of the detected object under a plurality of energy levels according to the characteristic that the material attenuation coefficient changes along with the energy level of the X-rays. In addition, the energy spectrum CT can also obtain information such as electron density distribution and equivalent atomic number distribution of the object to be detected, thereby obtaining component information of the object to be detected. Therefore, compared with the traditional CT, the energy spectrum CT can effectively reduce metal artifacts, improve the contrast of images and provide object composition information. Therefore, the energy spectrum CT has great significance in the fields of clinical medical diagnosis, nondestructive testing, safety inspection and the like, and is increasingly widely applied. The energy spectrum CT reconstruction algorithm is a key point of the energy spectrum CT technology and is a current research hotspot.
At present, the energy spectrum CT reconstruction method is mainly divided into three categories: (1) the image domain method comprises the steps of obtaining two traditional CT images by two groups of projection sinograms respectively by utilizing a traditional CT reconstruction method, and then obtaining a single-energy-level image by utilizing the two traditional CT images in a linear combination mode; (2) firstly, estimating a base material sinogram from two groups of projection sinograms by adopting different methods, then reconstructing the base material sinogram from the base material sinogram, and further obtaining a single-energy-level CT image by utilizing linear combination of the base material sinograms; (3) and in the direct inversion method, a base material map is directly reconstructed from two groups of projection sinograms obtained by scanning through an iterative method, and then a single-energy-level CT image is obtained through linear combination of the base material maps. At present, the method is widely applied to the actual method of the base material sinogram, because the method of the base material sinogram is more accurate than the method of the image domain, and compared with the direct inversion method, the method is simpler and has less calculation amount.
The method for estimating the base material sinogram from two sets of projection sinograms obtained by scanning is a key point of the base material sinogram method, and the current commonly used method for estimating the base material sinogram comprises a polynomial fitting method and a lookup table method. The accuracy of the polynomial fitting method is changed along with the highest power of the polynomial, the higher the highest power is, the higher the accuracy is, and correspondingly, the longer the calculation time is; in addition, the polynomial fitting method needs to perform polynomial fitting again for different energy spectrum CT scanning systems. The lookup table method firstly establishes a lookup table about the base material sinogram value and the projection sinogram value, and then correspondingly looks up corresponding base material sinogram values according to the two groups of obtained projection sinograms, so as to obtain the base material sinogram. The accuracy of the base material sinogram obtained by the lookup table method is related to the accuracy of the established lookup table, the higher the accuracy of the lookup table is, the higher the accuracy of the obtained base material sinogram is, and meanwhile, the larger the volume of the lookup table is, and the longer the time for lookup is. In addition, although the lookup table method does not require the creation of different lookup tables for different spectral CT scanning systems, the lookup tables need to be re-created when the selected basis substance changes. In short, both the polynomial fitting method and the lookup table method are slow in speed and long in time consumption, and the applicability is not strong when correlation coefficients are recalculated or lookup tables are established for different energy spectrum CT scanning systems or different basic substances.
The invention content is as follows:
aiming at the defects of the prior art, the invention provides the method for estimating the sinogram of the energy spectrum CT base substance, which can deduce an iterative formula by utilizing the concave characteristic of a forward projection physical model function of energy spectrum CT scanning, thereby improving the applicability of the method for estimating the sinogram of the energy spectrum CT base substance and reducing the calculation time while ensuring the accuracy.
A method for estimating a spectral CT-based material sinogram comprises the following steps:
step 1, energy spectrum calibration is carried out;
step 2, acquiring high-energy projection data and low-energy projection data by using a detector of the energy spectrum CT imaging system, and storing the high-energy projection data and the low-energy projection data into vectors PH and PL respectively;
step 3, setting a projection diagram of a ratio coefficient diagram of two base substances a and B, namely setting the initial values of a base substance a sinogram matrix A and a base substance B sinogram matrix B to be 0, and setting an error threshold value V;
step 4, defining the current values of E-th elements in the concave combined coefficient vectors alpha and betaAndare defined by the formulae (6) and (7), respectively;
wherein E represents the energy level of X-rays, the value of the E-th element in α and beta represents a concave combination coefficient corresponding to the energy level E, SH (E) and SL (E) are respectively normalized high-energy spectrum distribution and low-energy spectrum distribution, HEU and HED respectively represent the highest energy level and the lowest energy level contained in the high-energy spectrum, LEU and LED respectively represent the highest energy level and the lowest energy level contained in the low-energy spectrum, and mua(E) And mub(E) Respectively represents the linear attenuation coefficients of the base substances a and b under X-rays with the energy level E, and the linear attenuation coefficients are known quantities;andthe ith element value A of the base material a sinogram matrix A and the base material B sinogram matrix B are respectively representediAnd BiCurrent value of, i-th element value AiAnd BiThe sine map amplitude corresponding to the ith X-ray is obtained;
defining the forward high-energy projection estimation value vector and the forward low-energy projection estimation value vector as the current values of the ith element in the PHE and the PLE respectivelyAndrespectively, formula (10) and formula (11);
step 5, the high-energy projection data PH corresponding to the ith X rayiLow energy projection data PLiCurrent value of forward high-energy projection estimated value vectorCurrent value of forward low energy projection estimated value vectorCurrent values of the sinogram matrix aAnd the current values of the sinogram matrix BObtaining a new value A of the base material a sinogram matrix A corresponding to the ith X-ray according to the formula (14) and the formula (15)iAnd new values B of the sinogram matrix B of the base material Bi；
Step 6, obtaining a new value A of the base material a sinogram matrix A corresponding to the ith X-ray obtained in the step 5iAnd new values B of the sinogram matrix B of the base material BiObtaining a forward high energy projection estimated value PHE corresponding to the ith X-ray according to the formula (16) and the formula (17)iAnd forward low energy projection estimate PLEi；
Step 7, the high-energy projection data PH corresponding to the ith X-rayiLow energy projection dataPLiForward high energy projection estimation PHEiAnd forward low energy projection estimate PLEiThe estimation error ERR is obtained from the equation (18)i；
ERRi＝|PHi-PHEi|+|PLi-PLEi| (18)
Step 8, judging the obtained estimated error ERRiWhether the difference is larger than the set error threshold value V or not, if so, the new value A of the base material a sinogram matrix A obtained in the step 5 is used foriAnd new values B of the sinogram matrix B of the base material BiRespectively as the current value of the base substance a sinogram matrix A and the current value of the base substance B sinogram matrix B, and returning to the step 4 to obtain A againiAnd BiOtherwise, executing step 9;
and 9, judging whether the ith X-ray is the last X-ray, if not, adding 1 to the ith X-ray, returning to the step 4, carrying out sinogram estimation on the (i + 1) th X-ray, if so, finishing the step, and outputting sinograms of the base substances a and b obtained through estimation.
According to the technical scheme, the invention has the beneficial effects that: according to the method for estimating the sinogram of the energy spectrum CT base substance, provided by the invention, an iterative formula can be deduced by utilizing the concave characteristic of a forward projection physical model function of energy spectrum CT scanning, so that the applicability of the method for estimating the sinogram of the energy spectrum CT base substance is improved, and for different energy spectrum CT scanning systems or different base substance pairs, coefficients do not need to be adjusted or a lookup table does not need to be reestablished; the accuracy is ensured, meanwhile, the calculation speed is improved, and the calculation time is reduced; the method is not limited to the scanning mode, and is suitable for different scanning modes such as a circular track, a spiral track, a cone beam, a fan beam and the like.
Description of the drawings:
FIG. 1 is a flowchart of a method for estimating a sinogram of a spectral CT-based material according to an embodiment of the present invention;
fig. 2 is a sinogram of a base material water obtained by an estimation method based on a sinogram of a base material of a spectral CT provided by an embodiment of the present invention;
fig. 3 is a sinogram of a base substance iodine obtained by the method for estimating a sinogram of a base substance based on energy spectrum CT according to the embodiment of the present invention.
The specific implementation mode is as follows:
the following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
A method for estimating sinograms of energy spectrum CT basic substances is shown in FIG. 1, two basic substances a and b in the embodiment are water and iodine respectively, and the method for estimating the sinograms is described as follows.
Step 1, energy spectrum calibration is carried out.
And 2, acquiring a high-energy projection data matrix and a low-energy projection data matrix by using a detector of the energy spectrum CT imaging system, wherein the high-energy projection data matrix and the low-energy projection data are respectively recorded as PH and PL. Wherein, the high-energy projection data value and the low-energy projection data value obtained by the ith X-ray scanning are respectively PHiAnd PLi，PHiAnd PLiRespectively satisfy the formula (1) and the formula (2),
wherein SH (E) and SL (E) are respectively normalized high-energy spectrum distribution and low-energy spectrum distribution; e represents the energy level of the X-ray, and μ (E) represents the linear attenuation coefficient of the object with respect to the X-ray having the energy level E; HEU and HED respectively represent the highest energy level and the lowest energy level contained in the high energy spectrum; the LEU and LED represent the highest and lowest energy levels, respectively, contained in the low energy spectrum.
In the spectral CT reconstruction, μ (E) is decomposed into a linear combination of the linear attenuation coefficients of the basis substances iodine and water, represented by formula (3),
μ(E)＝Aiμa(E)+Biμb(E) (3)
wherein, mua(E) And mub(E) Respectively representing the linear attenuation coefficients of the base substances, namely water and iodine under X-rays with the energy level of E, and being known quantities; a. theiAnd BiThe values of the ith element values of the water-based species sinogram matrix a and the iodine-based species sinogram matrix B are represented, respectively. The basis material sinogram matrices a and B are the two matrices that need to be estimated.
Substituting the formula (3) into the formula (1) and the formula (2), and taking natural logarithms at two sides of the formula to obtain relational expressions of sinogram matrixes A and B of two base materials and the high-energy and low-energy projection data PH and PL, wherein the relational expressions are shown as a formula (4) and a formula (5),
wherein the pH isiAnd PLiThe values of the ith element of the high-and low-energy projection data PH and PL, respectively, are represented.
According to the equations (4) and (5), it is difficult to directly estimate the sinogram matrices a and B of two base materials, the currently common methods are a polynomial fitting method and a table look-up method, both of which take a long time, and in order to increase the speed, the embodiment adopts an iterative estimation calculation method.
And 3, setting a projection diagram of a ratio coefficient diagram of two base substances a and B, namely setting the initial values of a base substance a sinogram matrix A and a base substance B sinogram matrix B to be 0, and setting an error threshold value V.
step 4, defining new concave combined coefficient vectors alpha and β, and defining current values of E-th elements in alpha and βAndare defined by the formulae (6) and (7), respectively;
wherein,andthe value of the E-th element in alpha and β are represented, namely the concave combination coefficient corresponding to the energy level E is represented;andthe ith element value A of the base material a sinogram matrix A and the base material B sinogram matrix B are respectively representediAnd BiCurrent value of, i-th element value AiAnd BiI.e. the sinogram amplitude corresponding to the ith X-ray.
The right sides of the above equations (4) and (5) are concave functions, and the equations (6) and (7) are a group of concave combination coefficients of the right concave functions of the equations (4) and (5), respectively. Equations (8) and (9) can be obtained by integrating equations (4) to (7) based on the characteristics of the concave function.
Wherein,andthe current values of the ith element, which represent the forward high-energy and low-energy projection estimates PHE and PLE, respectively, are shown in equations (10) and (11), respectively.
And (3) taking equal signs in the formulas (8) and (9) to obtain a binary linear equation set of the base substance sinograms A and B relative to the high-energy projection PH and the low-energy projection PL, wherein the equation set is shown in the formula (12) and the formula (13).
And 5, solving the linear equation sets of the two-dimensional equations shown in the formula (12) and the formula (13) to obtain iteration of the base substance sinograms A and BThe new value A of the base material a sinogram matrix A corresponding to the ith X-ray is obtained according to the formula shown in the formula (14) and the formula (15)iAnd new values B of the sinogram matrix B of the base material Bi。
After initial values of the base material sinograms a and B are given, estimated values of the base material sinograms a and B can be obtained through continuous iterative computation according to the above equations (14) and (15).
Step 6, obtaining a new value A of the base material a sinogram matrix A corresponding to the ith X-ray obtained in the step 5iAnd new values B of the sinogram matrix B of the base material BiObtaining a forward high energy projection estimated value PHE corresponding to the ith X-ray according to the formula (16) and the formula (17)iAnd forward low energy projection estimate PLEi。
And 7, introducing an error calculation method of the estimated values of the base substance sinograms A and B to judge whether the iterative calculation is ended, and using the high-energy projection data PH corresponding to the ith X-rayiLow energy projection data PLiForward high energy projection estimation PHEiAnd forward low energy projection estimate PLEiThe estimation error ERR is obtained from the equation (18)i。
ERRi＝|PHi-PHEi|+|PLi-PLEi| (18)
Wherein ERRiThe value of the i-th element representing the estimation error.
Step 8, judging the estimation error ERRiWhether the water-based substance is larger than a set error threshold value V or not, if so, the new value A of the sinogram matrix A of the water-based substance obtained in the step 5 is used foriAnd new values B of the sinogram matrix B of iodine-based speciesiRespectively used as the current value of the sinogram matrix A of the water-based substance and the current value of the sinogram matrix B of the iodine-based substance, and returning to the step 4 to obtain A againiAnd BiOtherwise, executing step 9;
and 9, judging whether the ith X-ray is the last X-ray, if not, adding 1 to the ith X-ray, returning to the step 4, carrying out sinogram estimation on the (i + 1) th X-ray, if so, finishing the step, and outputting the sinograms of the energy spectrum CT basic substance water and iodine obtained by estimation.
In the specific implementation, the method for estimating the sinogram of the energy spectrum CT basic substance by taking water and iodine as the basic substances is as follows.
1) Calibrating the high-energy and low-energy spectrums SH (E) and SL (E);
2) acquiring high-energy projection data PH and low-energy projection data PL by using a detector of an energy spectrum CT imaging system;
3) initializing a sinogram matrix, wherein A is 0, B is 0, and setting an error threshold value V to be 10-5In specific implementation, the setting of the error threshold value can select a suitable value according to actual requirements;
4) determining the current concave combination coefficient from equation (6) and equation (7)And
5) forward high energy is determined by equations (10), (11)Projection estimates and forward low energy projection estimates to the current value of the ith elementAnd
6) determining new value A of water-based substance sinogram matrix A corresponding to ith (i is 1, 2, …, N) X-ray according to formula (14) and formula (15)iAnd new values B of the iodine-based material sinogram matrix BiN represents the total number of X-rays;
7) determining forward high energy projection estimated value PHE from equation (16) and equation (17)iAnd forward low energy projection estimate PLEi；
8) The estimation error ERR is obtained from equation (18)i；
9) Determining an estimation error ERRiIf it is greater than the set error threshold V, if the error ERR is estimatediIf the error threshold value is larger than the error threshold value V, the new value A of the water-based substance sinogram matrix A obtained in the step 6) is usediAnd new values B of the iodine-based material sinogram matrix BiRespectively as the current value of the water-based substance sinogram matrix A and the current value of the iodine-based substance sinogram matrix B, i is unchanged, the step 4) is returned to, and the A is re-estimatediAnd BiOtherwise, executing step 10);
10) and judging whether i is equal to N, if not, adding 1 to i, namely i is i +1, returning to the step 4, estimating the sinogram of the next X-ray, if so, finishing the step, and outputting the sinograms of the water-based substance and the iodine-based substance obtained by estimation.
Fig. 2 is a sinogram of a water-based substance obtained by the above estimation method, and fig. 3 is a sinogram of an iodine-based substance obtained.
In the present embodiment, the method for estimating the sinogram of the CT-based material in the energy spectrum has been described using iodine and water as the base materials, but the method is not limited thereto, and any other base material set may be used.
In the embodiment, a new proper concave combination coefficient is introduced according to the concave characteristic of a forward projection physical model function of the energy spectrum CT, so that the energy spectrum CT base substance sinogram iteration estimation method which can ensure the accuracy of the energy spectrum CT base substance sinogram estimation value and greatly reduce the time consumption for calculation is obtained; the embodiment is not limited to the scanning mode, and is suitable for scanning modes such as a spiral track, a circular track, a fan-shaped beam, a cone beam and the like; compared with the existing estimation method of the sinogram of the main flow energy spectrum CT base substance in the field, the estimation method of the sinogram of the energy spectrum CT base substance has strong applicability and does not need to be adjusted due to the change of an energy spectrum CT scanning system or the change of a selected base substance; in addition, compared with the existing estimation method of the sinogram of the main flow energy spectrum CT-based substance in the field, the estimation method of the sinogram of the energy spectrum CT-based substance of the embodiment greatly improves the calculation speed under the condition of ensuring the same calculation accuracy.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (1)
1. A method for estimating a spectral CT-based material sinogram, comprising the steps of:
step 1, energy spectrum calibration is carried out;
step 2, acquiring high-energy projection data and low-energy projection data by using a detector of the energy spectrum CT imaging system, and storing the high-energy projection data and the low-energy projection data into vectors PH and PL respectively;
step 3, setting a projection diagram of a ratio coefficient diagram of two base substances a and B, namely setting the initial values of a base substance a sinogram matrix A and a base substance B sinogram matrix B to be 0, and setting an error threshold value V;
step 4, defining the current values of E-th elements in the concave combined coefficient vectors alpha and betaAndare defined by the formulae (6) and (7), respectively;
wherein E represents the energy level of X-rays, the value of the E-th element in α and beta represents a concave combination coefficient corresponding to the energy level E, SH (E) and SL (E) are respectively normalized high-energy spectrum distribution and low-energy spectrum distribution, HEU and HED respectively represent the highest energy level and the lowest energy level contained in the high-energy spectrum, LEU and LED respectively represent the highest energy level and the lowest energy level contained in the low-energy spectrum, and mua(E) And mub(E) Respectively represents the linear attenuation coefficients of the base substances a and b under X-rays with the energy level E, and the linear attenuation coefficients are known quantities;andthe ith element value A of the base material a sinogram matrix A and the base material B sinogram matrix B are respectively representediAnd BiCurrent value of, i-th element value AiAnd BiThe sine map amplitude corresponding to the ith X-ray is obtained;
defining the forward high-energy projection estimation value vector and the forward low-energy projection estimation value vector as the current values of the ith element in the PHE and the PLE respectivelyAndrespectively, formula (10) and formula (11);
step 5, the high-energy projection data PH corresponding to the ith X rayiLow energy projection data PLiCurrent value of forward high-energy projection estimated value vectorCurrent value of forward low energy projection estimated value vectorCurrent values of the sinogram matrix aAnd the current values of the sinogram matrix BObtaining a new value A of the base material a sinogram matrix A corresponding to the ith X-ray according to the formula (14) and the formula (15)iAnd new values B of the sinogram matrix B of the base material Bi；
Step 6, obtaining the base material corresponding to the ith X-ray obtained in the step 5a new value A of the sinogram matrix AiAnd new values B of the sinogram matrix B of the base material BiObtaining a forward high energy projection estimated value PHE corresponding to the ith X-ray according to the formula (16) and the formula (17)iAnd forward low energy projection estimate PLEi；
Step 7, the high-energy projection data PH corresponding to the ith X-rayiLow energy projection data PLiForward high energy projection estimation PHEiAnd forward low energy projection estimate PLEiThe estimation error ERR is obtained from the equation (18)i；
ERRi＝|PHi-PHEi|+|PLi-PLEi| (18)
Step 8, judging the obtained estimated error ERRiWhether the difference is larger than the set error threshold value V or not, if so, the new value A of the base material a sinogram matrix A obtained in the step 5 is used foriAnd new values B of the sinogram matrix B of the base material BiRespectively as the current value of the base substance a sinogram matrix A and the current value of the base substance B sinogram matrix B, keeping the value of i unchanged, returning to the step 4, and obtaining A againiAnd BiOtherwise, executing step 9;
and 9, judging whether the ith X-ray is the last X-ray, if not, adding 1 to the ith X-ray, returning to the step 4, carrying out sinogram estimation on the (i + 1) th X-ray, if so, finishing the step, and outputting sinograms of the base substances a and b obtained through estimation.
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