CN106650700B - Die body, method and device for measuring system matrix - Google Patents
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Abstract
The invention relates to a die body, which comprises a base body; and a marker disposed in the substrate, wherein a size of the marker is sufficiently small in at least one dimension such that a size of a projection image of the marker in the at least one dimension is smaller than a detector pixel size. The invention also relates to a method and corresponding device for measuring the system matrix, wherein the method comprises the steps of obtaining the diffusion function of the voxel in the phantom; and obtaining a system matrix based on the initial system matrix and the diffusion function of the voxel.
Description
Technical Field
The invention relates to the technical field of medicine, in particular to a die body, and a method and a device for measuring a system matrix by using the die body.
Background
The system matrix establishes the relation between the known projection image and the unknown reconstruction volume element, and can be used for iterative reconstruction algorithm, geometric modeling in system simulation, artifact correction and the like. Therefore, the iteratively reconstructed image quality, the system simulation and the artifact correction result all depend on the accuracy of the system matrix.
The most common system matrix, considering the source focus and detector pixels as ideal points, usually uses a line integral model based on the intensity of the radiation beam passing through the voxel to perform the simulation calculation. The system matrix only considers the space geometric relationship among the focal point of the ray source, the volume element and the detector pixel, and does not consider the influence of various non-ideal geometric factors, such as:
1) the focal spot of the source of radiation generally has a non-zero finite size. The line integral model considers the focus of the ray source as an ideal point light source, and ignores image blurring possibly caused by the fact that the focus has certain size and distribution;
2) the detector pixels typically have a non-zero finite size. The line integral model discretizes the detector, the pixel response of the detector is regarded as 1, and image blurring caused by certain distribution of the detector response is ignored;
in order to introduce the above non-ideal geometric factors into the system matrix, the prior art generally adopts the following scheme:
1. the geometric dimensions of the focal spot, voxels and detector pixels of the radiation source are divided into smaller units, and the non-ideal geometric factors are simulated by a plurality of projection lines between the focal spot and the detector unit. An example of such a prior art solution is shown in fig. 1, for example.
2. The effect of the focus size and detector pixel size on the system matrix is simulated using the response function. An example of such a prior art solution is shown in fig. 2, for example.
All the above prior art schemes need to measure the characteristics of the radiation source, such as focal point, voxel, detector pixel size, detector response distribution, etc., and perform subsequent calculation based on the characteristics. Compared with the method 2, the method 1 is simple and direct, is used more in practical application, but has one to two orders of magnitude larger calculation amount than the method 2, low calculation efficiency and overlarge expense; while method 2 is computationally inexpensive, the response function is often difficult to model accurately.
Disclosure of Invention
According to an aspect of the disclosure, a mold body includes: a substrate; and a marker disposed in the substrate, wherein a size of the marker is sufficiently small in at least one dimension such that a size of a projection image of the marker in the at least one dimension is smaller than a detector pixel size.
According to an exemplary embodiment of this aspect, the phantom includes a plurality of markers disposed at different locations on the substrate.
According to another exemplary embodiment of this aspect, the markers are arranged such that their positions in the projection image at the same projection angle do not coincide.
According to a further exemplary embodiment of this aspect, the marker is a plurality of markers and the plurality of markers are arranged in the matrix as one or more of the following designs: helical, linear, curvilinear, and dog-leg.
According to yet another exemplary embodiment of this aspect, the shape of the marker is a pellet shape, a filament shape, or a combination of both.
According to a further exemplary embodiment of this aspect, the material of the marker differs from the material of the matrix in its absorption coefficient.
According to another aspect of the present disclosure, a method of measuring a system matrix includes: obtaining a diffusion function of voxels in a phantom as described in any of the above exemplary embodiments; and obtaining a system matrix based on the initial system matrix and the diffusion function of the voxel.
According to an exemplary embodiment of this aspect, the marker is a sphere and obtaining a diffusion function of voxels in the phantom comprises: collecting a projection image of the die body, and acquiring a projection central point of the small ball in the projection image; selecting a preset neighborhood by taking the projection central point of the small ball in the projection image as a center, and normalizing the gray value of the pixel point of the neighborhood by taking the gray value of the projection central point of the small ball as a reference; generating a diffusion function of the small ball based on the distance from the pixel point in the preset neighborhood to the projection center point of the small ball and the normalized gray value of the pixel point; and generating a diffusion function of the voxels in the phantom based on the diffusion function and the interpolation function of the sphere.
According to another exemplary embodiment of this aspect, generating a diffusion function for voxels in the phantom based on the diffusion function and the interpolation function of the globule comprises: establishing a basis function corresponding to the diffusion function of the small ball; interpolating the base function characteristic representation corresponding to the diffusion function of the small ball to obtain the base function characteristic representation of the voxel in the model body; and converting the base function characteristic representation of the voxel in the phantom into a diffusion function corresponding to the voxel.
According to a further exemplary embodiment of this aspect, the interpolation function is: one of a nearest neighbor interpolation function, a trilinear interpolation function, and a B-spline interpolation function.
According to a further exemplary embodiment of this aspect, the marker is a filament, and the obtaining a diffusion function of voxels in the phantom comprises: acquiring a projection image of the die body at a first projection angle, and acquiring a first diffusion function of each point on the filament in the projection image in a direction perpendicular to the direction of the filament; acquiring a projection image of the die body at a second projection angle, and acquiring a second diffusion function of each point on the filament in a direction perpendicular to the direction of the filament; the first projection angle is perpendicular to the second projection angle; multiplying the first diffusion function and the second diffusion function corresponding to each point on the filament to obtain a diffusion function of the filament; generating a diffusion function for voxels in the phantom based on the diffusion function and the interpolation function of the filament.
According to a further exemplary embodiment of this aspect, acquiring a spread function of a point on the filament in the projection image in a direction perpendicular to the direction in which the filament is located comprises: acquiring a projected central point of a point on the filament in the projected image; selecting a preset neighborhood by taking the projection central point of the point on the filament in the projection image as a center, and normalizing the gray value of the pixel point of the neighborhood by taking the gray value of the projection central point of the point on the filament as a reference; and generating a diffusion function of the point on the filament in the direction vertical to the direction of the filament based on the distance from the pixel point in the preset neighborhood to the projection center point of the point on the filament and the normalized gray value of the pixel point.
According to another exemplary embodiment of this aspect, generating a diffusion function for a voxel in the phantom based on the diffusion function and the interpolation function of the filament comprises: establishing a base function characteristic representation corresponding to a diffusion function of the filament; interpolating the basis function characteristic representation corresponding to the diffusion function of the filament to obtain the basis function characteristic representation of the voxel in the phantom; and converting the base function characteristic representation of the voxel in the phantom into a diffusion function corresponding to the voxel.
According to a further exemplary embodiment of this aspect, the interpolation function is: one of a nearest neighbor interpolation function, a trilinear interpolation function, and a B-spline interpolation function.
Yet another aspect of the disclosure also relates to a corresponding apparatus.
Drawings
FIG. 1 illustrates a prior art approach to introducing non-ideal geometric factors into a system matrix;
FIG. 2 illustrates another prior art approach to introducing non-ideal geometric factors into a system matrix;
FIG. 3 shows various motifs with markers according to an illustrative but non-limiting example of the present invention;
FIG. 4 shows a flow chart of a method of obtaining a diffusion function of voxels in a labeled phantom according to an illustrative, non-limiting example of the present invention;
FIG. 5 illustrates a flow chart of a method of measuring a system matrix for helical CT/industrial CT according to an exemplary but non-limiting embodiment of the present invention;
FIG. 6 shows a flow chart of a method of measuring a system matrix and for system simulation according to an exemplary but non-limiting embodiment of the present invention.
Detailed Description
Embodiments will be described in detail with reference to the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts. References made to particular examples and figures are for illustrative purposes and are not intended to limit the scope of the invention or the claims. The word "exemplary" is used herein to mean "serving as an example, instance, or illustration. Any implementation described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other implementations.
The die body generally refers to a voxel position object, and the matrix of the die body adopted by the invention is distributed with markers which are used for carrying out corresponding tests so as to obtain system matrixes of different systems.
According to an exemplary but non-limiting embodiment of the invention, the phantom is formed by placing markers at different locations in a matrix of homogeneous material, the markers having a different absorption coefficient than the matrix material of homogeneous material, thereby making it easier to distinguish the markers from the matrix in the projected image. The uniform markers can be different materials to examine the influence of different materials on the system matrix.
For example, various such motifs and applications thereof according to an illustrative, but non-limiting example of the invention are shown in FIGS. 3(a) - (d). These exemplary mold bodies may be cylindrical or hexahedral mold bodies of a uniform material. However, one of ordinary skill in the art will readily appreciate that the shape of the mold body is not so limited. The matrix of the mold body may be a low atomic number material such as PMMA, but the material suitable for the mold body is not limited thereto.
In the exemplary embodiment of fig. 3(a) - (d), each phantom further includes a number of markers disposed at different locations on the substrate. The labels may include labels having the same physical properties, such as, but not limited to, uniform labels having the same physical properties, such as atomic number, electron density, and the like.
The marker material may be a high atomic number material such as tungsten, aluminum, iron, etc., but the material suitable for making the marker is not limited thereto.
The size of the tag is sufficiently small in at least one dimension (e.g., diameter). For example, the size of the marker in the projection data in the at least one dimension is preferably smaller than the detector pixel size. In a non-limiting example, if the detector pixel size is 0.2mm, the source-detector distance is 1.5m, and the source-object distance is 1m, the diameter of the marker is preferably less than 0.13 mm.
To make the size of the marker sufficiently small in at least one dimension (e.g., diameter), the shape of the marker can take the form of, for example, a bead, a filament, or the like. For example, in practice, a marker in the shape of a small sphere may be used for measurement. To approximate the impulse response, a very small sphere must be used. For example, in order to make the size of the bead in the projection plane smaller than the detector size, the diameter of the bead must be less than a fraction of a millimeter. The diameter of the small ball is difficult to ensure under the influence of the processing technology.
A simpler method is to use a filamentous marker, such as a linear or thin strip marker. Such markers may be placed perpendicular to the scan plane. During scanning, lines or slivers are projected onto the detector plane. The processing of linear or thin-strip markers is simpler than bead/ball processing, e.g. tungsten wire can be processed to less than a tenth of a millimeter, so that its projection in the diameter dimension onto the detector plane can be seen as an ideal point.
The markers are preferably arranged such that their respective positions at the same projection angle do not coincide. The markers are arranged in the phantom to form a design as a whole, such as may include, but are not limited to, a helical design, a linear design, a curved/polyline type design, a combination, and the like, or any combination thereof.
In another exemplary embodiment, the distribution density of the markers (or, respectively, the spacing between the markers in each dimension) may be configured according to accuracy requirements, design needs, and the like. The greater the distribution density of the markers (or, correspondingly, the smaller the spacing between the markers in each dimension), the better the correction for the non-ideal set of factors, but with a corresponding increase in the amount of computation and storage.
In a further embodiment, the absorption coefficients of the marker and matrix material are different, clearly distinguishing the marker from the phantom material in the projected image.
For example, according to an exemplary embodiment, a matrix of a measurement system is provided, in which a plurality of air holes parallel to a scanning plane are drilled at different positions in a uniform material matrix for placing extremely fine linear markers; the linear marker has different absorption coefficients from the base material and is easy to distinguish in a projection image; the surface of the mould body can also be provided with cross hairs, and the material of the cross hairs is the same as that of the mould body.
The present invention incorporates the effects of non-ideal geometric factors into the measurement of the system matrix by using such labeled motifs.
According to an aspect of the invention, such a method of measuring a system matrix comprises obtaining a diffusion function of voxels in a phantom with a marker. Such a method of measuring a system matrix further includes obtaining a system matrix based on the initial system matrix and the diffusion function of the voxel. The initial system matrix may be obtained, for example, by a classical method, or may be obtained in other ways.
For example, with reference to fig. 4, according to an exemplary but nonlimiting embodiment of the invention, a method 400 of obtaining a diffusion function of voxels in a labeled phantom is provided, which may include, for example, at least one or more of the following steps:
1) acquiring a precise geometric position (401) at which a marker is or will be placed in the phantom;
2) acquiring a projection image (402) of a phantom in which a marker is placed;
3) obtaining a diffusion function (403) for each marker based on the projection image and based on the precise geometric position of the marker; and
4) a diffusion function for voxels in the phantom is derived based on the diffusion function and the interpolation function of the marker (404).
In order to obtain the diffusion function of the markers, a predetermined neighborhood in the projection image may be selected, for example, with a projection center point of each marker in the projection image as a center, and the gray values of the pixel points in the neighborhood may be normalized with the gray value of the projection center point as a reference. The neighborhood may be, for example, a square with a side length of 2n +1, where n > is 0, for example, the neighborhood may be a 5x5 square region. As one of ordinary skill in the art will appreciate, the neighborhood may take any suitable shape and size.
After the gray value of the pixel point in the neighborhood is normalized, the diffusion function of the marker can be generated based on the distance from the pixel point in the predetermined neighborhood to the projection center point and the normalized gray value of the pixel point. It is understood, however, that the diffusion function of the label may be used directly without normalization and is within the scope of the present invention.
The diffusion function of voxels in the phantom may be generated based on the diffusion function of the marker and by using an interpolation function. The interpolation function may use various interpolation functions commonly used in the art, such as a nearest neighbor interpolation function, a trilinear interpolation function, a B-spline interpolation function, and the like.
To generate a diffusion function for a voxel in the phantom, a basis function corresponding to the diffusion function of the marker may be established and the characteristic representation of the basis function interpolated to obtain a characteristic representation of the basis function for the voxel in the phantom. The basis function feature representation of a voxel in the phantom may then be converted to a diffusion function corresponding to the voxel.
Based on the initial matrix and on the diffusion function corresponding to the voxel obtained as above, a systematic function is obtained. Because the die body is utilized to actually measure the markers at the isolated points and with the determinable precise geometric positions, the system matrix generated by the method is more direct and accurate than a system matrix generated by a simple analytic mode. And during the calculation process, the geometric correction is introduced into the system matrix calculation, so that the additional geometric correction flow is reduced.
In a further embodiment of the method, the marker may be a bead. In this exemplary but non-limiting embodiment, the method may include one or more of the following steps:
1) the geometric position of the embedded pellet is obtained (e.g., corresponding to step 401 in fig. 4). For example, the geometric location may include spatial three-dimensional coordinates. The geometric position of the embedded pellets can be obtained by, for example, industrial CT.
2) Projection images of a phantom in which a bead is embedded are acquired (e.g., corresponding to step 402 in FIG. 4).
3) Based on the projection images and on the exact geometric positions of the beads, a diffusion function for each bead is obtained (e.g., corresponding to step 403 in fig. 4). For example, the precise geometric position of the pellet can be obtained according to step 1). Because the position coordinates of the X-ray system are known, the coordinate position of the small ball marker on the detector can be calculated according to the geometric coordinates of the small ball, the distance from the ray source to the detector and the like, and the coordinate position is the projection central point of the small ball marker. A neighborhood (e.g., without limitation, a 5x5 square neighborhood) is chosen from this center point to obtain the spreading function of the bead marker according to the methods described above. The diffusion function of the bead marker may be a point diffusion function, and the matrix size may be the same as the neighborhood size described above. The point spread function of all the markers can be obtained by taking the same operation for each marker. According to different embodiments, the point spread function may be normalized according to the gray value of the central point, or may be used directly without normalization.
4) The diffusion function of the voxels in the phantom is derived based on the diffusion function and the interpolation function of the bead markers (e.g., corresponding to step 404 in fig. 4). This may be done, for example, by establishing a basis function corresponding to the diffusion function of the bead marker as described previously, interpolating the feature representation of the basis function to obtain a basis function feature representation of a voxel in the phantom, and then converting the basis function feature representation of the voxel in the phantom to the diffusion function corresponding to the voxel. The basis function model established may be, for example, a gaussian function (e.g., one-dimensional, two-dimensional … …), a cubic spline function, a B-spline function, etc., which may depend on the particular needs. The line integral model of the prior art only considers the contribution of the voxel to the projection central point, and the invention introduces non-ideal factors through a measurement method and also considers the contribution of the voxel to the peripheral region of the projection central point.
In another further embodiment of the method, the marker may be a filament. In this exemplary but non-limiting embodiment, the method may comprise:
1) without placing the linear marker, the exact geometric location of the groove in the phantom is obtained (e.g., corresponding to step 401 in fig. 4).
2) Placing the die body at a target scanning position, and accurately placing the die body by using wall laser and cross hairs on the surface of the die body; inserting a linear marker into an air bore of the phantom acquires projection images of the phantom at least two projection angles (e.g., corresponding to step 402 in figure 4). For example, the two projection angles may be perpendicular to each other, in order to obtain a line spread function at a plurality of angles in a direction perpendicular to the direction of the line-like marker, i.e. the filament.
3) From the projection images acquired at the at least two projection angles, two spread functions of each point on the filament marker in respective directions perpendicular to the direction in which the filament is located are obtained, respectively, and the two spread functions corresponding to each point on the filament marker are multiplied to obtain a spread function of each point on the filament, and thus a line spread function of the filament marker is obtained (for example, corresponding to step 403 in fig. 4). For example, the diffusion function for each point on the filament marker at one projection angle may be calculated in a similar manner as described above for the bead marker.
4) The diffusion function of the voxels in the phantom is derived based on the diffusion function and the interpolation function of the filament marker (e.g., corresponding to step 404 in fig. 4). For example, this may include establishing a representation of a basis function characteristic corresponding to a diffusion function of the filament; interpolating the base function characteristic representation corresponding to the diffusion function of the filament to obtain the base function characteristic representation of the voxel in the phantom; and converting the base function characteristic representation of the voxel in the phantom into a diffusion function corresponding to the voxel.
In yet another exemplary embodiment according to the present invention, the system matrix measurement method of the present invention may be used for system simulation. The system simulation is used for spatial resolution analysis, algorithm verification and algorithm comparison (such as beam hardening correction algorithm verification, FDK (Feldkamp-Davis-Kress) algorithm and iterative algorithm comparison, and various filter kernel comparison of FDK algorithm). For example, with reference to FIG. 6, a method 600 of measuring a system matrix and for system simulation according to an exemplary but nonlimiting embodiment of the invention may include, for example, at least one or more of the following steps:
1) acquiring precise geometric positions and sizes of uniform markers (601);
2) placing the used die body at a required scanning position to obtain a projection image (602) of the die body;
3) calculating a system matrix from the projection image, and circularly calculating until all system matrixes are calculated and stored (603);
4) generating a digital phantom for system simulation (e.g., spatial resolution analysis may use thin lines at different locations, algorithm verification and comparison may typically use Shepp-logan, Forbild, etc. phantoms or actual CT images as the digital phantom) (604);
5) measuring to obtain a desired energy spectral distribution (605); and
6) using the system matrix, the energy spectral distribution, and the digital phantom, a projection image of the digital phantom used for simulation of the system is obtained as follows (606)
Where Φ (E) is the spectral distribution, μw(E) Is a linear attenuation coefficient, ItIs the traversal length.
The method of measuring a system matrix of the present invention may be adapted to include, but is not limited to, the various applications described above, and the like. The invention is applicable to various medical image processing, such as MRI, CT, PET, etc. According to the scheme of the invention, at least one or more of non-ideal geometric factors such as the focal point size, the detector pixel size and the continuous acquisition mode are introduced into the system matrix obtained by adopting the measurement method, so that the system matrix generated by a simple analytic mode is more direct and accurate.
Those of ordinary skill in the art appreciate that the benefits of the invention are not realized in full in any single embodiment. Various combinations, modifications, and alternatives will be apparent to those skilled in the art in light of this disclosure.
Furthermore, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or". That is, unless specified otherwise, or clear from context, the phrase "X employs A or B" is intended to mean any of the natural inclusive permutations. That is, the phrase "X employs a or B" is satisfied by any of the following examples: x is A; x is B; or X employs both A and B. In addition, the articles "a" and "an" as used in this application and the appended claims should generally be construed to mean "one or more" unless specified otherwise or clear from context to be directed to a singular form.
Various aspects or features will be presented in terms of systems that may include a number of devices, components, modules, and the like. It is to be understood and appreciated that the various systems may include additional devices, components, modules, etc. and/or may not include all of the devices, components, modules etc. discussed in connection with the figures. Combinations of these approaches may also be used.
The various illustrative logics, logical blocks, modules, and circuits described in connection with the embodiments disclosed herein may be implemented or performed with a general purpose processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. Further, at least one processor may comprise one or more modules operable to perform one or more of the steps and/or actions described above.
Further, the steps and/or actions of a method or algorithm described in connection with the aspects disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two.
All structural and functional equivalents to the elements of the various aspects described throughout this disclosure that are known or later come to be known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed by the claims. Moreover, nothing disclosed herein is intended to be dedicated to the public regardless of whether such disclosure is explicitly recited in the claims.
Claims (15)
1. A phantom for use in the measurement of a system matrix, comprising:
a substrate; and
a marker disposed in the substrate, wherein the marker has a size in at least one dimension sufficiently small that a projection image of the marker in the at least one dimension is smaller than a detector pixel size, and wherein the detector captures the projection image of a radiation beam from the radiation source after passing through the phantom.
2. The phantom according to claim 1, wherein said phantom comprises a plurality of said markers disposed at different locations on said substrate.
3. The phantom of claim 2, wherein said markers are arranged such that their positions in the projected image at the same projection angle do not coincide.
4. The phantom according to claim 3, wherein said marker is a plurality of markers and said plurality of markers are arranged in said matrix in one or more of the following designs: helical, linear, curvilinear, and dog-leg.
5. The phantom according to claim 1, wherein the shape of the marker is a pellet shape, a filament shape, or a combination thereof.
6. The phantom according to claim 1, wherein the material of said marker and the material of said substrate have different absorption coefficients.
7. A method of measuring a system matrix, comprising:
obtaining a diffusion function of a voxel in a phantom according to any one of claims 1 to 6; and
a system matrix is obtained based on the initial system matrix and the diffusion function of the voxels.
8. The method of measuring a system matrix according to claim 7, wherein the marker is a bead and the obtaining a diffusion function of voxels in the phantom comprises:
collecting a projection image of the die body, and acquiring a projection central point of the small ball in the projection image;
selecting a preset neighborhood by taking the projection central point of the small ball in the projection image as a center, and normalizing the gray value of the pixel point of the neighborhood by taking the gray value of the projection central point of the small ball as a reference;
generating a diffusion function of the small ball based on the distance from the pixel point in the preset neighborhood to the projection center point of the small ball and the normalized gray value of the pixel point; and
and generating the diffusion function of the voxel in the model body based on the diffusion function and the interpolation function of the small ball.
9. The method of measuring a system matrix of claim 8, wherein generating a diffusion function for voxels in the phantom based on the diffusion function and interpolation function of the globule comprises:
establishing a basis function corresponding to the diffusion function of the small ball;
interpolating the base function characteristic representation corresponding to the diffusion function of the small ball to obtain the base function characteristic representation of the voxel in the model body;
and converting the base function characteristic representation of the voxel in the phantom into a diffusion function corresponding to the voxel.
10. A method of measuring a system matrix as claimed in claim 8, the interpolation function being: one of a nearest neighbor interpolation function, a trilinear interpolation function, and a B-spline interpolation function.
11. The method of measuring a system matrix of claim 7, wherein the marker is a filament and the obtaining a diffusion function of voxels in the phantom comprises:
acquiring a projection image of the die body at a first projection angle, and acquiring a first diffusion function of each point on the filament in the projection image in a direction perpendicular to the direction of the filament;
acquiring a projection image of the die body at a second projection angle, and acquiring a second diffusion function of each point on the filament in a direction perpendicular to the direction of the filament; the first projection angle is perpendicular to the second projection angle;
multiplying the first diffusion function and the second diffusion function corresponding to each point on the filament to obtain a diffusion function of the filament;
generating a diffusion function for voxels in the phantom based on the diffusion function and the interpolation function of the filament.
12. The method of measuring a system matrix of claim 11, wherein obtaining a spread function of points on the filament in the projection image in a direction perpendicular to the direction of the filament comprises:
acquiring a projected central point of a point on the filament in the projected image;
selecting a preset neighborhood by taking the projection central point of the point on the filament in the projection image as a center, and normalizing the gray value of the pixel point of the neighborhood by taking the gray value of the projection central point of the point on the filament as a reference;
and generating a diffusion function of the point on the filament in the direction vertical to the direction of the filament based on the distance from the pixel point in the preset neighborhood to the projection center point of the point on the filament and the normalized gray value of the pixel point.
13. The method of measuring a system matrix of claim 11, wherein generating a diffusion function for a voxel in the phantom based on a diffusion function and an interpolation function of the filament comprises:
establishing a base function characteristic representation corresponding to a diffusion function of the filament;
interpolating the basis function characteristic representation corresponding to the diffusion function of the filament to obtain the basis function characteristic representation of the voxel in the phantom;
and converting the base function characteristic representation of the voxel in the phantom into a diffusion function corresponding to the voxel.
14. The method of measuring a system matrix of claim 11, wherein the interpolation function is: one of a nearest neighbor interpolation function, a trilinear interpolation function, and a B-spline interpolation function.
15. An apparatus for measuring a system matrix, comprising:
means for obtaining a diffusion function of a voxel in a phantom according to any of claims 1 to 6; and
means for obtaining a system matrix based on the initial system matrix and the diffusion function of the voxel.
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