CN104700438A - Image reconstruction method and device - Google Patents

Image reconstruction method and device Download PDF

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CN104700438A
CN104700438A CN201410669318.9A CN201410669318A CN104700438A CN 104700438 A CN104700438 A CN 104700438A CN 201410669318 A CN201410669318 A CN 201410669318A CN 104700438 A CN104700438 A CN 104700438A
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image
attenuation
pet
mrow
msub
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CN104700438B (en
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朱闻韬
何任杰
李洪第
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Shanghai United Imaging Healthcare Co Ltd
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Shanghai United Imaging Healthcare Co Ltd
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/002D [Two Dimensional] image generation
    • G06T11/003Reconstruction from projections, e.g. tomography
    • G06T11/005Specific pre-processing for tomographic reconstruction, e.g. calibration, source positioning, rebinning, scatter correction, retrospective gating
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
    • G06T2207/10Image acquisition modality
    • G06T2207/10072Tomographic images
    • G06T2207/10081Computed x-ray tomography [CT]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
    • G06T2207/10Image acquisition modality
    • G06T2207/10072Tomographic images
    • G06T2207/10104Positron emission tomography [PET]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2211/00Image generation
    • G06T2211/40Computed tomography
    • G06T2211/416Exact reconstruction

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  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Apparatus For Radiation Diagnosis (AREA)
  • Nuclear Medicine (AREA)

Abstract

The invention discloses an image reconstruction method and an image reconstruction device. The image reconstruction method comprises the following steps: obtaining an MR (magnetic resonance) image of a scanned object through MR scanning; obtaining a CT (computed tomography) valuated image corresponding to the MR image; using the CT valuated image to generate a corresponding initial attenuation image used for reconstruction of a PET image; through the PET scanning, obtaining PET radiating data of the scanned object; using the PET radiating data and the initial attenuation image, iteratively reconstructing the PET radiating image and the attenuation image of the scanned object. The image reconstruction method and the image reconstruction device can improve the precision and speed of PET image reconstruction.

Description

Image reconstruction method and device
Technical Field
The invention relates to the technical field of image processing, in particular to a PET image reconstruction method and device.
Background
Positron Emission Tomography (PET) is a neuroimaging examination instrument that has been rapidly developed after relaying electron Computer Tomography (CT). At present, the method has prominent important value in diagnosis and treatment of three main diseases, namely tumor, coronary heart disease and brain disease, and is an advanced clinical examination imaging technology in the field of nuclear medicine. It can inject radioactive tracer into living organism to participate in the physiological metabolism of living organism without changing the physiological state. The tracer labels decay to produce positrons which undergo an annihilation effect producing pairs of oppositely emitted 511keV gamma photons. Detecting photon pairs which appear in pairs by using a coincidence detection technology, determining a coincidence response Line (LOR), acquiring a large number of LORs through acquisition, correcting, and then carrying out image fault reconstruction to observe the metabolic function of the living organism.
PET signal attenuation estimation in PET-MR can be largely divided into two categories, in addition to acquisition of penetration attenuation information with conventional CT scanning. One is based on MR image processing by taking an image segmentation or a priori map based approach, assigning predefined attenuation coefficients to different detector pairs, and possibly some specific MR sequences, to improve the contrast of the MR image. Another direction of study is images where emission and attenuation are co-estimated during iterative reconstruction of the images. However, for nonTOF PET data, studies have shown that the co-estimation method is not mathematically steady-state, and that optimization will result in it reaching an optimal solution locally but possibly deviating from a globally optimal solution. On the other hand, TOF information will help to achieve a stable co-estimation of emission and attenuation, but the computation time and the number of iterations of emission and attenuation estimation are long, and such multiple iterations will inevitably bring high-frequency noise on PET emission images, so that the co-estimation using only toffet data is time-consuming. In the method based on MR image processing, when a local image such as an arm appears outside the FOV and is truncated, a part of the MR image is missing, and the attenuation coefficient of PET in this part cannot be effectively estimated. In conclusion, the existing PET image reconstruction method cannot obtain a more accurate attenuation image for PET image reconstruction by using an MR image.
Disclosure of Invention
The problem to be solved by the invention is how to obtain a corresponding attenuation image for PET image reconstruction from an MR image and to use the obtained attenuation image for PET image reconstruction.
In order to solve the above problem, the present invention provides an image reconstruction method, including:
acquiring an MR image of a scanning object through MR scanning;
acquiring a CT estimated value image corresponding to the MR image;
generating a corresponding initial attenuation image by using the CT estimation image;
acquiring PET emission data of the scanning object through PET scanning;
iteratively reconstruct a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image.
Optionally, the acquiring a CT estimation image corresponding to the MR image includes:
establishing a joint dictionary of the MR image and the CT image;
inquiring the joint dictionary to obtain the sparse solution of the MR image of the scanning object;
and acquiring a CT estimated value image corresponding to the MR image of the scanning object based on the sparse solution and the joint dictionary.
Optionally, the acquiring a CT estimation image corresponding to the MR image includes:
establishing a joint dictionary of the MR image and the CT image;
extracting a plurality of MR image blocks from an MR image of the scanned object;
inquiring the joint dictionary to obtain sparse solutions of the MR image blocks;
acquiring CT image blocks corresponding to the MR image blocks based on the sparse solution and the joint dictionary;
and aggregating the obtained CT image blocks to obtain a CT estimated image, wherein the CT estimated image corresponds to the MR image of the scanning object.
Optionally, at least part of the MR image patches overlap.
Optionally, the establishing the joint dictionary of the MR image and the CT image includes: and acquiring a joint dictionary of the MR images and the CT images through learning of a training set, wherein the training set comprises a plurality of pairs of MR image blocks and CT image blocks which are registered in space.
Optionally, said iteratively reconstructing a PET radiation image and an attenuation image of said scanned object using said PET radiation data and said initial attenuation image comprises: iteratively reconstructing a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image using an ordered subset approach.
Optionally, said iteratively reconstructing a PET radiation image and an attenuation image of said scanned object using said PET radiation data and said initial attenuation image comprises: and iteratively reconstructing a PET radiation image and an attenuation image of the scanning object by using the PET radiation data and the initial attenuation image by establishing a penalty function positively correlated with the difference between the attenuation image obtained by iterative reconstruction and the initial attenuation image.
The present invention also provides an image reconstruction apparatus, comprising:
a first acquisition unit adapted to acquire an MR image of a scan object by MR scanning;
a second acquisition unit, adapted to acquire a CT estimation image corresponding to the MR image;
a generating unit adapted to generate a corresponding initial attenuation image using the CT estimate image;
a third acquisition unit adapted to acquire PET radiation data of the scan object by a PET scan;
a reconstruction unit adapted for iteratively reconstructing a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image.
Optionally, the second obtaining unit includes:
a first establishing subunit adapted to establish a joint dictionary of the MR image and the CT image;
a first query subunit, adapted to query the joint dictionary, to obtain a sparse solution of the MR image of the scanning object;
a first obtaining subunit, adapted to obtain a CT estimation image corresponding to the MR image of the scanned object based on the sparse solution and the joint dictionary.
Optionally, the second obtaining unit includes:
a second establishing subunit, adapted to establish a joint dictionary of the MR image and the CT image;
a molecular segmentation unit adapted to extract a plurality of MR image patches from an MR image of the scan object;
the second query subunit is suitable for querying the joint dictionary to obtain sparse solutions of the MR image blocks;
the second acquisition subunit is suitable for acquiring CT image blocks corresponding to the MR image blocks on the basis of the sparse solution and the joint dictionary;
and the aggregation subunit is suitable for aggregating the obtained CT image blocks to obtain a CT estimated image, and the CT estimated image corresponds to the MR image of the scanning object.
Optionally, at least part of the MR image patches overlap.
Optionally, the first and second establishing subunits are adapted to obtain the joint dictionary of MR images and CT images by learning of a training set comprising pairs of spatially registered MR image blocks and CT image blocks.
Optionally, the reconstruction unit is adapted for iteratively reconstructing a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image using an ordered subset approach.
Optionally, the reconstruction unit is adapted to iteratively reconstruct a PET radiation image and an attenuation image of the scan object using the PET radiation data and the initial attenuation image by establishing a penalty function positively correlated with a difference between the iteratively reconstructed attenuation image and the initial attenuation image.
Compared with the prior art, the technical scheme of the invention has the following advantages:
because the corresponding CT image is obtained through the MR image firstly, and the corresponding attenuation image used for PET image reconstruction is obtained by utilizing the obtained CT image, a more accurate attenuation image can be obtained.
Because the obtained attenuation image used for PET image reconstruction has smaller deviation with the real attenuation image, the PET radiation image and the attenuation image can be reconstructed by less iteration times, and therefore, the image reconstruction speed can be improved.
Furthermore, by establishing and acquiring a joint dictionary of the MR image and the CT image and inquiring the joint dictionary, the CT estimated image corresponding to the MR image can be acquired quickly, so that the acquisition speed of the CT estimated image can be improved, and the reconstruction speed of the PET image can be further improved.
Further, by establishing a penalty function positively correlated with the difference between the attenuation image obtained by iterative reconstruction and the initial attenuation image obtained by the CT estimation image and applying the penalty function to the iterative estimation process of the attenuation image, the iterative estimation can be rapidly converged to obtain the attenuation image, and the obtained attenuation image does not deviate from the attenuation image for PET image reconstruction, so that a more accurate attenuation image can be obtained.
Drawings
FIG. 1 is a flow chart of a method of image reconstruction in an embodiment of the present invention;
FIG. 2 is a flow chart of another image reconstruction method in an embodiment of the present invention;
FIG. 3A is a prior art attenuation image acquired by a CT scan;
FIG. 3B is a PET reconstructed image obtained using the attenuation image shown in FIG. 3A;
FIG. 4A is a prior art attenuation image acquired by MR image processing;
FIG. 4B is a PET reconstructed image obtained using the attenuation image shown in FIG. 4A;
FIG. 5A is an attenuation image obtained by an image reconstruction method in an embodiment of the present invention;
fig. 5B is a PET reconstructed image obtained by the image reconstruction method in the embodiment of the present invention;
FIG. 6 is a schematic structural diagram of an image reconstruction apparatus according to an embodiment of the present invention;
fig. 7 is a schematic structural diagram of a second obtaining unit in the embodiment of the present invention;
fig. 8 is a schematic structural diagram of another second obtaining unit in the embodiment of the present invention.
Detailed Description
In the prior art, a corresponding attenuation image can be obtained through a Magnetic Resonance (MR) image. However, because the field of view (FOV) of the MR image may be limited, it is truncated at the edges of the MR image, especially for larger patients. In addition, due to the metal implant or the port, the MR image is distorted, and therefore, the image reconstruction method in the prior art cannot obtain a more accurate attenuation image for PET image reconstruction by using the MR image.
In order to solve the above problems in the prior art, in the technical scheme adopted by the embodiment of the invention, the MR image is used to obtain the corresponding CT image, and the obtained CT image is used to obtain the corresponding attenuation image for PET image reconstruction, so that a more accurate attenuation image can be obtained.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
Fig. 1 shows a flowchart of an image reconstruction method in an embodiment of the present invention. The PET image reconstruction method as shown in fig. 1 may include:
step S101: an MR image of the scanned object is acquired by an MR scan.
Step S102: and acquiring a CT estimation image corresponding to the MR image.
Step S103: and generating a corresponding initial attenuation image by using the CT estimation image.
Step S104: PET radiation data of the scanned object is acquired by a PET scan.
Step S105: iteratively reconstruct a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image.
The image reconstruction method of the present invention will be described in further detail with reference to specific embodiments.
Fig. 2 shows a flow chart of another image reconstruction method in an embodiment of the invention. The image reconstruction method as shown in fig. 2 may include:
step S201: an MR image of the scanned object is acquired by an MR scan.
In a specific implementation, MR data is acquired by means of an MR scan, and an MR image of the scanned object is reconstructed using the acquired MR data.
Step S202: and establishing a joint dictionary between the MR image and the CT image, acquiring a sparse solution corresponding to the MR image through the joint dictionary, and inquiring the joint dictionary according to the acquired sparse solution to acquire a corresponding CT estimated value image.
In an embodiment of the present invention, the spatially (geometrically) registered MR image training set and CT image training set are first concatenated as an independent input, so that the finally obtained joint dictionary also includes two sub-matrices, i.e., MR sub-matrix and CT sub-matrix. When the dictionary training method is adopted for dictionary training, the MR submatrix and the CT submatrix are not distinguished, but are completed uniformly, and a combined dictionary of the MR image and the CT image is obtained.
In image reconstruction, the joint dictionary matrix of the MR image and the CT image may be divided into an MR sub-dictionary and a CT sub-dictionary (sub-matrix). Firstly, using the MR image to obtain a corresponding sparse solution by inquiring the MR sub-dictionary, and then obtaining a corresponding CT image through the CT sub-dictionary by using the obtained sparse solution, thereby obtaining a CT estimation image corresponding to the MR image.
Because the MR image training set and the CT image training set adopted during dictionary training are subjected to spatial registration, the CT estimated value image obtained by the joint dictionary does not need to be subjected to spatial registration with the corresponding MR image. Spatial registration is not only computationally intensive, but also has the potential for failure. In the prior art, even if the MR image and the CT image can be obtained simultaneously, the spatial registration between them is required. In the embodiment of the invention, when the CT estimated image is obtained through the MR image, no classification limitation is required to the image (actually, the method is equivalent to infinite classification), and no model assumption is required to be made by utilizing the statistical property and the spatial relationship of the image, so that the method is reliable and rapid.
In another embodiment of the invention, the MR and CT joint dictionary is built by step-by-step optimization learning of the MR sub-dictionary and the CT sub-dictionary. The combined dictionary obtained by performing step-by-step optimization learning on the MR sub-dictionary and the CT sub-dictionary can ensure that the optimized result is also optimal for the MR or CT alone.
It should be noted here that, in the process of acquiring the joint dictionary of the MR image and the CT image by the dictionary training method, a penalty function proportional to the first-order norm of the estimated parameter may be designed, and the number of non-zero values in the sparse solution is limited to 3, so as to reduce the calculation cost.
In an embodiment of the present invention, to further improve the accuracy of the acquired CT estimation image, a plurality of image blocks may be extracted from the acquired MR image of the scanning object, and the MR image is blocked by using a sliding window, so that there is an overlapping region between the acquired partial MR image blocks. Then, the CT image blocks corresponding to the MR image blocks obtained by the joint dictionary also have corresponding overlapping areas, each pixel in the CT estimated image has a plurality of values, and the obtained CT image blocks are aggregated, for example, averaged, so that a more accurate CT estimated image can be obtained.
Step S203: and generating a corresponding initial attenuation image by using the CT estimation image.
In a specific implementation, an initial attenuation image corresponding to the CT estimation image and used for PET image reconstruction may be acquired by a bilinear method.
According to the fact that the attenuation coefficient distribution of the ray in a new substance composed of two different substance components and the attenuation coefficients of the ray in the different substance components respectively have approximate linear relation, the substance with the CT density lower than that of water in the CT image is represented by a water-air model, and the substance with the CT density higher than that of water is represented by a water-bone model, so that the attenuation coefficients of the gamma ray penetrating through the different substances can be obtained, and the attenuation correction is completed.
Continuous practical studies show that the conversion relationship between the CT density of CT images and the attenuation coefficient of 511keV gamma rays can be approximated as a straight line of two segments. The bilinear method has high enough precision for biological tissues with lower atomic mass numbers.
Therefore, in an embodiment of the present invention, by using the density distribution of the CT estimation image and querying the two segmented straight lines, the attenuation coefficient distribution of the attenuation image for PET image reconstruction is obtained, and finally the attenuation image for PET image reconstruction is obtained, so that the accuracy of the obtained attenuation image for PET image reconstruction can be improved.
Step S204: PET radiation data of the scanned object is acquired by a PET scan.
In a specific implementation, the PET radiation data may be acquired by a PET scan, acquiring PET radiation data of the scan subject. MR data of the scanned object and toffet radiation data can also be acquired by PET-MR, and MR images can be reconstructed using the acquired MR data. The PET-MR is a large functional metabolism and molecular imaging diagnostic device which is formed by integrally combining a positron emission computed tomography (PET) and a Magnetic Resonance Imaging (MRI), and has the examination functions of PET and MR.
Step S205: a PET radiation image and an attenuation image of the scanned object are iteratively reconstructed using the PET radiation data and the initial attenuation image.
In an embodiment of the invention, an ordered subset method is used to iteratively reconstruct a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image. Wherein:
firstly, the initial attenuation image is used as a non-zero iteration initial value, and the attenuation image for PET image reconstruction is sequentially updated by adopting the following formula:
<math> <mrow> <msup> <msub> <mover> <mi>a</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>&Sigma;</mi> <mi>j</mi> </msub> <msub> <mi>l</mi> <mi>ij</mi> </msub> <msubsup> <mi>u</mi> <mi>j</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </msubsup> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>
wherein,is passing throughThe attenuation coefficient of the ith element in the sinusoidal attenuation map obtained by the mth sub-iteration in the n iterations, e is a natural logarithm,is the value of the jth voxel in the attenuation image obtained through the mth sub-iteration in the n iterations, lijIs a system matrix of a line integral model mapped to an attenuation coefficient from an attenuation image, n is the iteration number, m is the sequence number of the sub-iteration number in each iteration, and i is the sequence number of a response line;
<math> <mrow> <msup> <msub> <mi>f</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>=</mo> <mfrac> <msubsup> <mi>f</mi> <mi>j</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <msub> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <msub> <mi>S</mi> <mi>m</mi> </msub> </mrow> </msub> <msup> <msub> <mover> <mi>a</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </msup> <msub> <mi>H</mi> <mi>ijt</mi> </msub> </mrow> </mfrac> <msub> <mi>&Sigma;</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <msub> <mi>S</mi> <mi>m</mi> </msub> </mrow> </msub> <msub> <mi>H</mi> <mi>ijt</mi> </msub> <mfrac> <mrow> <mn>1</mn> <mo>/</mo> <msub> <mi>&epsiv;</mi> <mi>i</mi> </msub> </mrow> <mrow> <msub> <mi>&Sigma;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <msub> <mi>H</mi> <mi>ikt</mi> </msub> <msubsup> <mi>f</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <mfrac> <mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> </mrow> <msubsup> <mover> <mi>a</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </msubsup> </mfrac> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>
wherein f isj (n,m+1)Representing the PET radiological image, S, obtained through the mth sub-iteration of the n iterations in the reconstruction processmRepresenting the mth data subset, H, in the data spaceijtAnd HiktA transformation matrix representing the sinogram, k representing the kth voxel in the radiological image, t representing the number of temporal flight bins,irepresenting normalized coefficients for tabulated data, siAnd riRespectively represent the scattering coincidence on the ith response lineThe number of events and random coincident events;
<math> <mrow> <msup> <msub> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <msub> <mover> <mi>a</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </msup> <msub> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>,</mo> <mi>t</mi> </mrow> </msub> <msub> <mi>H</mi> <mi>ijt</mi> </msub> <msubsup> <mi>f</mi> <mi>j</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>
wherein,representing the expected value of the ith voxel in the PET radiological image obtained through the (m + 1) th sub-iteration in the n iterations;
<math> <mrow> <msup> <msub> <mi>&mu;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <msub> <mi>&mu;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>&Element;</mo> <msub> <mi>S</mi> <mi>m</mi> </msub> </mrow> </msub> <msub> <mi>l</mi> <mi>ij</mi> </msub> <mfrac> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mrow> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>&beta;</mi> <mo>&times;</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <mi>C</mi> </mrow> <mrow> <mo>&PartialD;</mo> <mi>&mu;</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mi>&mu;</mi> <mo>,</mo> <msub> <mi>&mu;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <msub> <mo>|</mo> <mrow> <mi>&mu;</mi> <mo>=</mo> <mi>&mu;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>&Element;</mo> <msub> <mi>S</mi> <mi>m</mi> </msub> </mrow> </msub> <msub> <mi>l</mi> <mi>ij</mi> </msub> <mfrac> <msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> </mrow> </mfrac> <msub> <mi>&Sigma;</mi> <mi>k</mi> </msub> <msub> <mi>l</mi> <mi>ik</mi> </msub> <mo>+</mo> <mi>&beta;</mi> <mo>&times;</mo> <mfrac> <mrow> <msup> <mo>&PartialD;</mo> <mn>2</mn> </msup> <mi>C</mi> </mrow> <msup> <mrow> <mo>&PartialD;</mo> <mi>&mu;</mi> </mrow> <mn>2</mn> </msup> </mfrac> <mrow> <mo>(</mo> <mi>&mu;</mi> <mo>,</mo> <msub> <mi>&mu;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <msub> <mo>|</mo> <mrow> <mi>&mu;</mi> <mo>=</mo> <mi>&mu;</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>
wherein, muj (n,m+1)Representing the sub-iterations from the m-th subset of n iterations followed byj (n,m)Updated attenuation image,/ikIs a line integral system matrix mapped from the attenuation image to the attenuation coefficient representing the length of the i-th response line in the sinogram across voxel k, yiDenotes the number of annihilation photon pairs acquired on the ith line of response, β C (μ, μ)0) In order to add a new penalty function to the system,respectively, the newly added penalty function beta C (mu, mu)0) At mu ═ mu(n,m)First and second derivatives of time, beta being an adjustable penalty weight, the greater beta, the deviation from mu0The smaller the probability of (A), and the larger the probability of (B), the larger the probability of (A)0A corresponding initial attenuation image is generated for the CT estimate image.
In the iterative reconstruction process, in each sub-iteration process, firstly keeping the attenuation image unchanged and updating the PET radiation image by using the formula (2), then keeping the PET radiation image unchanged and updating the attenuation image by using the formula (4), traversing all the ordered subsets in one iteration process, then performing the next iteration, repeating the iteration until a preset iteration stop condition is met, and stopping the iteration to obtain the PET radiation image and the attenuation image. Otherwise, the value obtained by the iteration is taken as an initial value, and the generation reaching process is continued.
In which formula (2) used in the embodiment of the present invention updates the PET radiation image using a reconstruction algorithm of the list data type. On the one hand, compared with the traditional sinogram approach, the computational complexity is only related to the list data size, but not to the sinogram size. Therefore, when the data volume is small, the calculation cost is low, and the speed of the algorithm can be effectively improved. On the other hand, the method of the ordered subsets is used in the iterative updating process of the PET radioactive image and the attenuation image, the calculation of the formulas (1) to (4) is carried out in turn in each alternation of the ordered subsets, and the convergence rate of the image is higher compared with the method without the ordered subsets.
In addition, in the image reconstruction process in the embodiment of the present invention, the following formula (5) is generally adopted in the prior art to update the attenuation image:
<math> <mrow> <msup> <msub> <mi>&mu;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msup> <mo>=</mo> <msup> <msub> <mi>&mu;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </msup> <mo>+</mo> <mfrac> <mrow> <msub> <mi>&Sigma;</mi> <mi>i</mi> </msub> <msub> <mi>l</mi> <mi>ij</mi> </msub> <mfrac> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mrow> <mo>(</mo> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo></mo> </mrow> </msub> <msub> <mi>l</mi> <mi>ij</mi> </msub> <mfrac> <msup> <mrow> <mo>(</mo> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <msubsup> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </msubsup> <mo>+</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> </mrow> </mfrac> <msub> <mi>&Sigma;</mi> <mi>k</mi> </msub> <msub> <mi>l</mi> <mi>ik</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>
the penalty function corresponding to equation (5) is:
<math> <mrow> <mi>cos</mi> <mi>t</mi> <mo>=</mo> <msub> <mi>&Sigma;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mi>ln</mi> <msub> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>
wherein cost represents a penalty function value,is the inverse of the data likelihood function of the data statistical characteristic. It can be seen that the update amount in the above formula (5) is the quotient of the first derivative and the second reciprocal of the formula (6).
The penalty function corresponding to equation (4) used in the above embodiment of the present invention is:
<math> <mrow> <mi>cos</mi> <mi>t</mi> <mo>=</mo> <msub> <mi>&Sigma;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mi>ln</mi> <msub> <mover> <mi>y</mi> <mo>&OverBar;</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>&beta;C</mi> <mrow> <mo>(</mo> <mi>&mu;</mi> <mo>,</mo> <msub> <mi>&mu;</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>
the inverse of the likelihood function can be seen from equation (7)And the newly added penalty function β C (μ, μ)0) The larger the value of (A), the larger the penalty function value added by the two values, otherwise, the smaller the penalty function value. Thus, the penalty function β C (μ, μ)0) Arranged to iteratively obtain an attenuation image mu and an initial attenuation image mu from the CT estimation image0The difference between them being positively correlated, e.g. C (u, u)0) Due to the initial attenuation image mu for the PET image reconstruction u-u0| ^20The value remains constant throughout the operation, then when μ and μ0The smaller the difference between them, the smaller the penalty function β C (μ, μ)0) The smaller.
It can be seen that in the above example of the present invention, the new penalty function β C (μ, μ) is subtracted from the numerator and denominator of the updated quantity respectively based on the original formula (4)0) The first and second derivatives of (c) can be derived as equation (5) so that the final convergence value of the algorithm is not far from the initial attenuation image generated from the CT estimation image, thereby increasing the stability of the estimation.
Meanwhile, in the above embodiment of the present invention, the ordered subset method is adopted to continuously update the PET radiation image and the attenuation image by using the equations (1) to (4) for each subset, and meanwhile, since the attenuation image for PET image reconstruction has a smaller deviation from the true attenuation image, the iterative reconstruction process can be shortened to a great extent, and only a few iterative processes are required, so that the accurate PET radiation image and attenuation image can be obtained, and therefore, the number of times and time required by iteration can be reduced, and the image reconstruction speed can be increased.
Referring to fig. 3 to 5, fig. 3A and 3B respectively show an attenuation image obtained by CT scanning and a PET reconstructed image obtained by using the attenuation image, fig. 4A and 4B respectively show an attenuation image obtained by MR image processing and a PET reconstructed image obtained by using the attenuation image, and fig. 5A and 5B respectively show a modified attenuation image and a PET reconstructed image obtained by image reconstruction method according to an embodiment of the present invention.
Comparing fig. 3 and 4, it can be seen that the attenuation image lacking arm information results in an underestimation of the final radiation image in the lung, very insignificant cardiac imaging, and an underestimation in the arm region. Comparing fig. 3 and 5, it can be seen that the two radiological images are very similar in structure, and the cardiac and arm imaging are evident, only with a slight difference in image noise due to the difference in the number of iterations. Therefore, the image reconstruction method in the embodiment of the invention can obtain more accurate attenuation images and radiation images.
Fig. 6 is a schematic structural diagram of an image reconstruction apparatus in an embodiment of the present invention. The image reconstruction apparatus 600 as shown in fig. 6 may comprise a first acquisition unit 601, a second acquisition unit 602, and a generation unit 603, wherein:
a first acquisition unit 601 adapted for acquiring MR images of the scanned object by means of an MR scan.
A second acquisition unit 602, adapted to acquire a CT estimation image corresponding to the MR image.
A generating unit 603 adapted to generate a corresponding initial attenuation image using said CT estimate image.
In a specific implementation, the image reconstruction apparatus 600 shown in fig. 6 may further include a third obtaining unit 604 and a reconstruction unit 605, where:
a third acquisition unit 604 adapted for acquiring PET radiation data of the scan object by means of a PET scan.
A reconstruction unit 605 adapted for iteratively reconstructing a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image.
In a specific implementation, the reconstruction unit 605 is adapted for iteratively reconstructing a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image using an ordered subset approach.
In an embodiment of the invention, the reconstruction unit 605 is adapted to iteratively reconstruct a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image by establishing a penalty function positively correlated to a difference between the iteratively reconstructed attenuation image and the initial attenuation image.
Fig. 7 shows a schematic structural diagram of a second obtaining unit in the embodiment of the present invention. The second obtaining unit 700 shown in fig. 7 may include a first establishing subunit 701, a first querying subunit 702, and a first obtaining subunit 703, where:
a first establishing subunit 701 adapted to establish a joint dictionary of MR images and CT images.
A first querying subunit 702, adapted to query the joint dictionary, obtaining a sparse solution of the MR image of the scanned object.
A first obtaining subunit 703 is adapted to obtain a CT estimation image corresponding to the MR image of the scanned object based on the sparse solution and the joint dictionary.
Fig. 8 shows a schematic structural diagram of another second acquisition unit in the embodiment of the present invention. The second obtaining unit 800 as shown in fig. 4 may include a second establishing subunit 801, a dividing subunit 802, a second querying subunit 803, a second obtaining subunit 804, and an aggregating subunit 805, where:
a second establishing subunit 801 adapted to establish a joint dictionary of MR images and CT images. Wherein the second establishing subunit is adapted to obtain the joint dictionary of the MR images and the CT images through learning of a training set, the training set comprising a plurality of pairs of spatially registered MR image blocks and CT image blocks.
A segmentation unit 802 adapted to extract a plurality of MR image patches from an MR image of the scanned object. Wherein at least some of the MR image patches overlap.
A second querying subunit 803, adapted to query the joint dictionary to obtain sparse solutions of the MR image blocks.
A second obtaining subunit 804, adapted to obtain, based on the sparse solution and the joint dictionary, CT image blocks corresponding to the MR image blocks.
An aggregating subunit 805 adapted to aggregate the acquired CT image blocks to acquire a CT estimation image, wherein the CT estimation image corresponds to an MR image of the scanned object.
Those skilled in the art will appreciate that all or part of the steps in the methods of the above embodiments may be implemented by instructions associated with hardware via a program, which may be stored in a computer-readable storage medium, and the storage medium may include: ROM, RAM, magnetic or optical disks, and the like.
The method and system of the embodiments of the present invention have been described in detail, but the present invention is not limited thereto. Various changes and modifications may be effected therein by one skilled in the art without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (14)

1. An image reconstruction method, comprising:
acquiring an MR image of a scanning object through MR scanning;
acquiring a CT estimated value image corresponding to the MR image;
generating a corresponding initial attenuation image by using the CT estimation image;
acquiring PET emission data of the scanning object through PET scanning;
iteratively reconstruct a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image.
2. The image reconstruction method according to claim 1, wherein said obtaining a CT estimation image corresponding to said MR image comprises:
establishing a joint dictionary of the MR image and the CT image;
inquiring the joint dictionary to obtain the sparse solution of the MR image of the scanning object;
and acquiring a CT estimated value image corresponding to the MR image of the scanning object based on the sparse solution and the joint dictionary.
3. The image reconstruction method according to claim 1, wherein said obtaining a CT estimation image corresponding to said MR image comprises:
establishing a joint dictionary of the MR image and the CT image;
extracting a plurality of MR image blocks from an MR image of the scanned object;
inquiring the joint dictionary to obtain sparse solutions of the MR image blocks;
acquiring CT image blocks corresponding to the MR image blocks based on the sparse solution and the joint dictionary;
and aggregating the obtained CT image blocks to obtain a CT estimated image, wherein the CT estimated image corresponds to the MR image of the scanning object.
4. Method for image reconstruction according to claim 3 characterized in that at least some of the MR image blocks overlap each other.
5. The image reconstruction method according to claim 3 or 4, wherein the establishing of the joint dictionary of the MR image and the CT image comprises: and acquiring a joint dictionary of the MR images and the CT images through learning of a training set, wherein the training set comprises a plurality of pairs of MR image blocks and CT image blocks which are registered in space.
6. The image reconstruction method of claim 1, wherein iteratively reconstructing a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image comprises: iteratively reconstructing a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image using an ordered subset approach.
7. The image reconstruction method of claim 1, wherein iteratively reconstructing a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image comprises: and iteratively reconstructing a PET radiation image and an attenuation image of the scanning object by using the PET radiation data and the initial attenuation image by establishing a penalty function positively correlated with the difference between the attenuation image obtained by iterative reconstruction and the initial attenuation image.
8. An image reconstruction apparatus, comprising:
a first acquisition unit adapted to acquire an MR image of a scan object by MR scanning;
a second acquisition unit, adapted to acquire a CT estimation image corresponding to the MR image;
a generating unit adapted to generate a corresponding initial attenuation image using the CT estimate image;
a third acquisition unit adapted to acquire PET radiation data of the scan object by a PET scan;
a reconstruction unit adapted for iteratively reconstructing a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image.
9. The image reconstruction apparatus according to claim 8, wherein the second acquisition unit includes:
a first establishing subunit adapted to establish a joint dictionary of the MR image and the CT image;
a first query subunit, adapted to query the joint dictionary, to obtain a sparse solution of the MR image of the scanning object;
a first obtaining subunit, adapted to obtain a CT estimation image corresponding to the MR image of the scanned object based on the sparse solution and the joint dictionary.
10. The image reconstruction apparatus according to claim 8, wherein the second acquisition unit includes:
a second establishing subunit, adapted to establish a joint dictionary of the MR image and the CT image;
a molecular segmentation unit adapted to extract a plurality of MR image patches from an MR image of the scan object;
the second query subunit is suitable for querying the joint dictionary to obtain sparse solutions of the MR image blocks;
the second acquisition subunit is suitable for acquiring CT image blocks corresponding to the MR image blocks on the basis of the sparse solution and the joint dictionary;
and the aggregation subunit is suitable for aggregating the obtained CT image blocks to obtain a CT estimated image, and the CT estimated image corresponds to the MR image of the scanning object.
11. Image reconstruction apparatus according to claim 10, characterized in that at least some of said MR image blocks overlap each other.
12. Image reconstruction apparatus according to claim 9 or 10, characterized in that the first and second establishing sub-units are adapted to acquire the joint dictionary of MR images and CT images by learning of a training set comprising pairs of spatially registered MR image blocks and CT image blocks.
13. The image reconstruction apparatus as claimed in claim 8, characterized in that the reconstruction unit is adapted to iteratively reconstruct a PET radiation image and an attenuation image of the scanned object using the PET radiation data and the initial attenuation image using an ordered subset method.
14. The image reconstruction apparatus according to claim 8, characterized in that the reconstruction unit is adapted to iteratively reconstruct a PET radiation image and an attenuation image of the scan object using the PET radiation data and the initial attenuation image by establishing a penalty function positively correlated to a difference between the iteratively reconstructed attenuation image and the initial attenuation image.
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