WO2018220686A1 - 吸収係数画像推定方法、吸収係数画像推定プログラム並びにそれを搭載したポジトロンct装置 - Google Patents
吸収係数画像推定方法、吸収係数画像推定プログラム並びにそれを搭載したポジトロンct装置 Download PDFInfo
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- 238000010521 absorption reaction Methods 0.000 title claims abstract description 335
- 238000000034 method Methods 0.000 title claims abstract description 155
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T11/00—2D [Two Dimensional] image generation
- G06T11/003—Reconstruction from projections, e.g. tomography
- G06T11/008—Specific post-processing after tomographic reconstruction, e.g. voxelisation, metal artifact correction
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Definitions
- the present invention relates to an absorption coefficient image estimation method, an absorption coefficient image estimation program for estimating an absorption coefficient image from measurement data of a positron CT apparatus (positron emission tomography apparatus), and a positron CT apparatus equipped with the absorption coefficient image estimation program.
- a positron CT device or PET (Positron Emission Tomography) device, is effective only when two ⁇ -rays generated by the annihilation of positron (Positron) are detected simultaneously by multiple detectors (that is, only when they are counted simultaneously). It is configured to measure the signal as a simple signal and reconstruct a tomographic image of the subject based on the measurement data.
- a radiopharmaceutical containing a positron emitting nuclide is administered to a subject, and 511 keV paired annihilation gamma rays released from the administered subject are detected by a group of detector elements (for example, scintillators). Detect with instrument.
- positron CT In positron CT (PET), various data correction processes are required to quantitatively measure the radioactivity concentration in the subject. Typical correction processes include sensitivity correction, scattering correction, random correction, attenuation correction, dead time correction, and absorption correction.
- the present invention relates to an absorption correction for preventing deterioration in image quantitativeness due to absorption of ⁇ rays emitted from a radiopharmaceutical (radioisotope). In order to perform the absorption correction, it is necessary to estimate an absorption coefficient image obtained by imaging the absorption coefficient distribution in the subject.
- the transmittance of ⁇ rays is obtained from the estimated absorption coefficient image, and the transmittance is divided from the measurement data of PET, and converted to data from which the influence of absorption of ⁇ rays has been eliminated.
- the estimated absorption coefficient image is incorporated into an image reconstruction calculation formula to obtain a reconstructed image from which the influence of ⁇ -ray absorption is eliminated.
- transmission data obtained by irradiating an external source of positron emitting nuclides is necessary.
- CT data obtained from an X-ray CT (Computed Tomography) apparatus instead of transmission data.
- Non-Patent Documents 1 and 2 there are reconstruction algorithms that do not require such transmission data (for example, see Non-Patent Documents 1 and 2).
- TOF-PET the measurement data of PET
- TOF time difference
- the distribution shape of the absorption coefficient sinogram can be estimated.
- the radioactivity image and the absorption coefficient sinogram can be estimated simultaneously.
- the reconstruction algorithms in Non-Patent Documents 1 and 2 are also called “simultaneous reconstruction algorithms” because they simultaneously estimate the radioactivity image and the data related to the absorption coefficient (for example, absorption coefficient sinogram).
- the simultaneous reconstruction algorithm that simultaneously estimates the radioactivity image and the absorption coefficient sinogram is also called the MLACF method.
- the radioactivity concentration is distributed as shown in FIG. 9 in the target region of the subject.
- the radioactivity distribution is developed into a two-dimensional distribution consisting of TOF information t and radial direction s
- the projection direction ⁇ is in the range of 0 ° to 180 °, a two-dimensional distribution for each projection angle ⁇ is obtained as measurement data.
- the following technologies are indispensable. That is, a technique for estimating an absorption coefficient image with a correct absolute value from an absorption coefficient sinogram with a correct distribution shape but an incorrect absolute value is indispensable.
- Non-Patent Document 2 there is a method of directly quantifying a radioactivity image without directly quantifying an absorption coefficient sinogram.
- the processing steps are as follows. (1) A radioactivity image without absorption correction is created, and an object mask image is created from the radioactivity image. (2) Substituting a known absorption coefficient (for example, water absorption coefficient or bone absorption coefficient) into each pixel value of the subject mask image, and abbreviated as a pseudo absorption coefficient image (hereinafter referred to as “pseudo absorption coefficient image”). Create). (3) Using the pseudo absorption coefficient image, a radioactivity image is created by a conventional reconstruction algorithm, and the total pixel value is calculated for each slice in the body axis direction. As shown in FIG.
- z is the body axis direction
- the xy plane is a plane (axial plane) orthogonal to the body axis direction z
- P (x, y) is the pixel value
- S (z) is the body axis direction z.
- the total pixel value is calculated for each slice in the body axis direction in the same manner as in step (3).
- S ′ (z) is the total pixel value for each z-slice in the body axis direction.
- Step (4) so that the total pixel value S ′ (z) obtained in step (5) matches the total pixel value S (z) obtained in step (3) for each slice in the body axis direction.
- Non-Patent Document 2 has a problem that it cannot be guaranteed in principle that the finally obtained radioactivity image is quantitative.
- the present invention has been made in view of such circumstances, and an absorption coefficient image estimation method, an absorption coefficient image estimation program capable of creating a quantitative absorption coefficient image, and a positron CT apparatus equipped with the absorption coefficient image estimation program are provided.
- the purpose is to provide.
- the inventors have obtained the following knowledge. That is, the above-described conventional technique assumes that the total pixel value for each slice in the body axis direction obtained in the procedure (3) is true (that is, correct).
- the absorption coefficient image estimation method is a method for estimating an absorption coefficient image from positron CT measurement data including time-of-flight information of annihilation radiation, and quantitatively determines ⁇ ′.
- a reconstruction calculation step for calculating the image ⁇ ′ based on optimization of an evaluation function related to the measurement data, and an image obtained by adding an uneven offset value to the absorption coefficient image
- a mask calculation step for calculating subject mask projection data, which is subject mask data in the projection data space, and forward projection data of the offset image ⁇ off is subject mask projection data when ⁇ off is a non-uniform offset image.
- the configured reconstruction algorithm to approximate the offset estimation step of estimating the offset image mu off, the ⁇ with known absorption coefficients
- an absorption coefficient value correcting step of correcting, as an absorption coefficient value, a value obtained by adding ⁇ ⁇ ⁇ off obtained by multiplying off by the coefficient ⁇ .
- the evaluation function of the positron CT measurement data (TOF-PET measurement data) including the time-of-flight difference (Time Of Flight) information of annihilation radiation is calculated. Based on the optimization, an image in which a non-uniform offset value is added to the quantitative absorption coefficient image is calculated.
- ⁇ ′ is a non-quantitative radioactivity image
- the radioactivity image ⁇ ′ is calculated in the reconstruction calculation step.
- the reconstruction algorithm in the reconstruction calculation step here is the simultaneous reconstruction algorithm described above.
- subject mask projection data in the projection data space (hereinafter referred to as “subject mask projection data”) is calculated based on the measurement data.
- subject mask projection data in the projection data space
- the offset estimation step the reconstruction algorithm forward projection data of the offset image mu off is configured to approximate the object mask projection data, an offset image mu off presume.
- the reference region extraction step uses an image that is calculated based on the measurement data and can recognize the subject region. Extract one or more.
- the image calculated based on the measurement data and capable of recognizing the subject region is, for example, the above-described image ⁇ ′, the above-described radioactivity image ⁇ ′, and the reconstruction in the above-described reconstruction calculation step.
- These are non-quantitative images estimated by a reconstruction algorithm different from the algorithm (simultaneous reconstruction algorithm), and object mask images estimated from the above-described object mask projection data.
- the image is not limited to these exemplified images, and may be any image that can be recognized based on the measurement data and that can recognize the subject region.
- extracting at least one region ⁇ using an image that can be recognized by the subject region calculated based on the measurement data means that the region ⁇ is extracted using single image information. In addition to this, extracting the region ⁇ using a combination of a plurality of pieces of image information (for example, logical sum or logical product) is also included.
- the following coefficient calculation step and absorption coefficient value correction step are performed using the image ⁇ ′, the offset image ⁇ off and the region ⁇ obtained in the above-described steps.
- ⁇ is an unknown true absorption coefficient image value (absorption coefficient value)
- ⁇ is a coefficient
- the coefficient calculation process reduces the error between the image ⁇ ′ value and the known absorption coefficient value in the region ⁇ .
- the coefficient ⁇ to be calculated is calculated.
- the absorption coefficient value correcting step a value obtained by adding ⁇ ⁇ ⁇ off obtained by multiplying the offset image ⁇ off by a coefficient ⁇ to the value of the image ⁇ ′ is corrected as an absorption coefficient value.
- the difference between the value of the non-quantitative image ⁇ ′ in the region ⁇ and the known absorption coefficient value (the value of the true absorption coefficient image) is approximated by ⁇ ⁇ ⁇ off, which is obtained by multiplying the offset image ⁇ off by a coefficient ⁇ .
- the absorption coefficient value is corrected in the absorption coefficient value correction step based on a mathematical relationship that is possible (that is, ⁇ ′ + ⁇ ⁇ ⁇ off ). Therefore, the absorption coefficient image having the absorption coefficient value corrected in the absorption coefficient value correction step has a small systematic error. As a result, since a quantitative absorption coefficient image can be created, accurate absorption correction of the radioactivity image becomes possible.
- the above-described reconstruction calculation process may be performed with a calculation algorithm including (a) the image ⁇ ′ as an unknown.
- the above-described reconstruction calculation step may be performed by a combination of (b) a calculation algorithm including absorption coefficient projection data as an unknown and an algorithm in which an image obtained by reconstructing absorption coefficient projection data is an image ⁇ ′.
- the former algorithm (a) is an MLAA method in which a non-quantitative radioactivity image ⁇ ′ and an image ⁇ ′ (non-quantitative absorption coefficient image) are simultaneously reconstructed.
- the latter algorithm (b) uses the MLACF method described in Non-Patent Document 1 for simultaneous estimation of non-quantitative radioactivity image ⁇ ′ and non-quantitative absorption coefficient projection data (for example, absorption coefficient sinogram), and absorption.
- This is a combination with an algorithm in which an image obtained by reconstructing coefficient projection data is an image ⁇ ′.
- the algorithm in which the image ⁇ ′ is an image obtained by reconstructing the absorption coefficient projection data in the latter (b) is not particularly limited as long as it is a reconstruction algorithm.
- An example of the mask calculating step described above includes a step of calculating a binarized image of the image ⁇ ′ as a subject mask image, a step of calculating projection data of the subject mask image, and a projection data of the subject mask image. And a step of calculating the value data as subject mask projection data (aspect (A)). Further, the mask calculation step may be a mode of (B) including a step of calculating projection data of the image ⁇ ′ and a step of calculating binarized data of the projection data of the image ⁇ ′ as subject mask projection data. .
- the projection data is calculated after binarizing the image ⁇ ′ first, and the projection data is binarized.
- the projection data of the image ⁇ ′ is binarized after being calculated first.
- the image ⁇ ′ is a non-quantitative absorption coefficient image, but the object mask projection data can be calculated by binarizing the image other than the absorption coefficient image and the projection data.
- Another example of the mask calculation step includes a step of calculating data obtained by binarizing the above-described TOF-PET measurement data converted into a projection data format as subject mask projection data.
- the TOF-PET measurement data is directly used, and binarized data converted into the projection data format can be calculated as the subject mask projection data.
- the mask calculation step is a step of calculating a radioactivity image based on optimization of an evaluation function related to the measurement data of TOF-PET (described above) and a projection data of the radioactivity image. And a step of calculating data obtained by binarizing projection data (of a radioactivity image) as subject mask projection data (aspect (C)).
- the mask calculation step is a step of calculating a radioactivity image based on optimization of the evaluation function related to the measurement data of TOF-PET (described above), a step of calculating a binarized image of the radioactivity image,
- the aspect of (D) may include a step of calculating projection data of a binarized image and a step of calculating data obtained by binarizing the projection data of the binarized image as subject mask projection data.
- the projection data of the radioactivity image is binarized after previously calculated.
- the projection data is calculated after binarizing the radioactivity image first, and the projection data is binarized.
- the reconstruction algorithm for calculating the radioactivity image is not particularly limited.
- the subject mask projection data can be calculated using the above-described radioactivity image ⁇ ′ estimated by the simultaneous reconstruction algorithm.
- the subject mask projection data may be calculated using a radioactivity image estimated by a reconstruction algorithm (for example, ML-EM method) different from the above-described simultaneous reconstruction algorithm (MLACF method or MLAA method). .
- the reconstruction processing performed in the offset estimation step described above may be performed by any one of analytical reconstruction, statistical reconstruction, and algebraic reconstruction.
- analytical reconstruction for example, there is an FBP (Filtered Back Projection) method.
- statistical reconstruction for example, the above-described ML-EM (Maximum Likelihood- ⁇ Expectation Maximization) method is available.
- algebraic reconstruction for example, there is an ART (Algebraic Reconstruction Technique) method.
- the at least one region ⁇ extracted in the above-described reference region extraction step is a tissue region in which the absorption coefficient can be regarded as known.
- the “region of tissue whose absorption coefficient can be regarded as known” means, for example, a region that can be approximated by water, a region that can be approximated by air, a region that can be approximated by brain tissue, a region that can be approximated by bone, and lung tissue The region that can be approximated by, and the region that can be approximated by soft tissue.
- any structure can be used as long as an approximate value of the absorption coefficient can be understood.
- the water absorption coefficient value of 0.0096 / mm can be used.
- K ( ⁇ 1) is the number of regions that can be approximated by a known absorption coefficient value
- ⁇ n is the n-th region ⁇
- n is a known absorption coefficient value
- S (X; ⁇ n ) is a statistic of image X in region ⁇ n or a value calculated from the statistic is a representative value
- the representative value is, for example, an average value, a median value, a trimmed average value, a trimmed median value, or a weighted average value of two or more values thereof.
- the value is not limited to these exemplified values, and may be “a statistic or a value calculated from the statistic”.
- S ( ⁇ ′; ⁇ n ) is a representative value of image ⁇ ′ in region ⁇ n
- S ( ⁇ off ; ⁇ n ) is a representative value of the offset image ⁇ off ′ in the region ⁇ n .
- n 1, ..., each region K Omega 1, ..., coefficient alpha 1 in Omega K, ..., an alpha K after calculating each coefficient ⁇ 1, ..., ⁇ K representative value T
- the coefficient ⁇ can be calculated by setting ⁇ 1 , ⁇ 2 ,..., ⁇ K ) as the coefficient ⁇ .
- K ( ⁇ 1) is the number of regions that can be approximated with a known absorption coefficient value
- ⁇ n is the nth region ⁇
- image set the known absorption coefficient in n, the error evaluation function D ⁇ n (X, Y) image X and image Y about the region ⁇ n, w n (n 1, ..., K) 0
- the coefficient is 1 or less.
- Image X is obtained by replacing image X n known by setting a known absorption coefficient in region ⁇ n and adding image Y to image ⁇ ′ by multiplying offset image ⁇ off ′ by ⁇ ⁇ ⁇ off.
- D ⁇ n ( ⁇ n known, ⁇ value ⁇ )' + ⁇ ⁇ ⁇ off ) includes an image mu n known set of known absorption coefficient for region Omega n, This is an error evaluation function with an image ( ⁇ ′ + ⁇ ⁇ ⁇ off ) obtained by adding a non-uniform offset value to a quantitative absorption coefficient image.
- the coefficient ⁇ can be calculated by calculating ⁇ that minimizes known , ⁇ ′ + ⁇ ⁇ ⁇ off )]).
- the absorption coefficient image estimation program according to the present invention causes a computer to execute the absorption coefficient image estimation method according to the present invention.
- the absorption coefficient image estimation program by causing a computer to execute the absorption coefficient image estimation method according to the present invention, a non-quantitative image ⁇ ′ value in a region ⁇ and a known absorption coefficient value (true The absorption coefficient value is corrected in the absorption coefficient value correcting step based on a mathematical relationship that the difference from the absorption coefficient image value) can be approximated by ⁇ ⁇ ⁇ off obtained by multiplying the offset image ⁇ off by a coefficient ⁇ . . Therefore, the absorption coefficient image having the absorption coefficient value corrected in the absorption coefficient value correction step has a small systematic error. As a result, since a quantitative absorption coefficient image can be created, accurate absorption correction of the radioactivity image becomes possible.
- the positron CT apparatus is a positron CT apparatus equipped with the absorption coefficient image estimation program according to the present invention, and includes a calculation means for executing the absorption coefficient image estimation program.
- the positron CT apparatus by including a calculation unit that executes the absorption coefficient image estimation program according to the present invention, the value of the non-quantitative image ⁇ ′ in the region ⁇ and the known absorption coefficient value (true The absorption coefficient value is corrected in the absorption coefficient value correcting step based on a mathematical relationship that the difference from the absorption coefficient image value) can be approximated by ⁇ ⁇ ⁇ off obtained by multiplying the offset image ⁇ off by a coefficient ⁇ . . Therefore, the absorption coefficient image having the absorption coefficient value corrected in the absorption coefficient value correction step has a small systematic error. As a result, since a quantitative absorption coefficient image can be created, accurate absorption correction of the radioactivity image becomes possible.
- the value of the non-quantitative image ⁇ ′ in the region ⁇ and the known absorption coefficient value (true
- the absorption coefficient value is corrected in the absorption coefficient value correction step based on the mathematical relationship that the offset image ⁇ off can be approximated by ⁇ ⁇ ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ . Therefore, the absorption coefficient image having the absorption coefficient value corrected in the absorption coefficient value correction step has a small systematic error. As a result, since a quantitative absorption coefficient image can be created, accurate absorption correction of the radioactivity image becomes possible.
- FIG. 3 is a flowchart illustrating a processing procedure and a data flow of an absorption coefficient image estimation method according to the first embodiment.
- 10 is a flowchart illustrating a processing procedure and a data flow of an absorption coefficient image estimation method according to the second embodiment.
- 10 is a flowchart showing a processing procedure and a data flow of an absorption coefficient image estimation method according to Example 3 when subject mask projection data is calculated using a radioactivity image estimated by the MLACF method.
- FIG. 14 is a flowchart illustrating a processing procedure and a data flow of an absorption coefficient image estimation method according to a fourth embodiment.
- 10 is a flowchart showing a processing procedure and data flow of an absorption coefficient image estimation method according to Embodiment 5. It is a conceptual diagram with which the principle in the MLACF method is provided.
- FIG. 6 is a schematic diagram of a profile when a total pixel value for each slice in the body axis direction, a horizontal axis is a body axis direction, and a vertical axis is a total pixel value.
- FIG. 1 is a schematic perspective view and a block diagram of a PET apparatus according to each embodiment
- FIG. 2 is a schematic perspective view of a ⁇ -ray detector. 1 and 2 have the same configuration in each embodiment.
- the PET apparatus 1 includes a detector ring 2 that surrounds the periphery of the subject in a stacked arrangement in the body axis direction of the subject.
- a plurality of ⁇ -ray detectors 3 are embedded in the detector ring 2.
- the PET apparatus 1 corresponds to the positron CT apparatus in the present invention.
- the ⁇ -ray detector 3 corresponds to the detector in the present invention.
- the PET apparatus 1 includes a coincidence counting circuit 4 and an arithmetic circuit 5.
- a coincidence counting circuit 4 includes a coincidence counting circuit 4 and an arithmetic circuit 5.
- FIG. 1 only two connections from the ⁇ -ray detector 3 to the coincidence counting circuit 4 are shown, but actually, a photomultiplier tube (PMT: Photo Multiplier Tube) 33 of the ⁇ -ray detector 3 ( Are connected to the coincidence counting circuit 4 by the total number of channels (see FIG. 2).
- the arithmetic circuit 5 executes processing of an absorption coefficient image estimation method shown in FIG. 3 described later by the absorption coefficient image estimation program 6.
- the arithmetic circuit 5 corresponds to the arithmetic means in the present invention.
- a ⁇ -ray generated from a subject (not shown) to which a radiopharmaceutical has been administered is converted into light by a scintillator block 31 (see FIG. 2) of the ⁇ -ray detector 3, and the converted light is converted into a ⁇ -ray detector.
- 3 photomultiplier tube (PMT) 33 (see FIG. 2) is multiplied and converted into an electrical signal. The electrical signal is sent to the coincidence counting circuit 4 to generate count value detection signal data.
- the coincidence circuit 4 checks the position of the scintillator block 31 (see FIG. 2) and the incident timing of the ⁇ -ray, and sends it only when ⁇ -rays are simultaneously incident on the two scintillator blocks 31 on both sides of the subject. The determined electrical signal is determined as appropriate data.
- the coincidence counting circuit 4 rejects. That is, the coincidence counting circuit 4 detects that ⁇ rays are simultaneously observed (that is, coincidence counting) by the two ⁇ ray detectors 3 based on the above-described electrical signal.
- the detection signal data (count value) composed of appropriate data determined to be coincidence by the coincidence circuit 4 is sent to the arithmetic circuit 5.
- the arithmetic circuit 5 performs steps S1 to S8 (see FIG. 3) to be described later, and estimates an absorption coefficient image from detection signal data of a subject (not shown) obtained by the PET apparatus 1. Specific functions of the arithmetic circuit 5 will be described later.
- An absorption coefficient image estimation program 6 is stored in a storage medium (not shown) represented by ROM (Read-only Memory), and the absorption coefficient image estimation program 6 is read from the storage medium to the arithmetic circuit 5. Then, the calculation circuit 5 executes the absorption coefficient image estimation program 6 to perform the process of the absorption coefficient image estimation method shown in the flowchart of FIG.
- the arithmetic circuit 5 is a GPU (Graphics Processing Unit), a central processing unit (CPU), or a programmable device (for example, an FPGA (Field Programmable Gate) that can change a hardware circuit (for example, a logic circuit) used in accordance with program data. Array)).
- the ⁇ -ray detector 3 includes a scintillator block 31, a light guide 32 optically coupled to the scintillator block 31, and photoelectrons optically coupled to the light guide 32.
- a multiplier (hereinafter simply abbreviated as “PMT”) 33 is provided.
- Each scintillator element constituting the scintillator block 31 converts ⁇ rays into light by emitting light with the incidence of ⁇ rays. By this conversion, the scintillator element detects ⁇ rays.
- Light emitted from the scintillator element is sufficiently diffused by the scintillator block 31 and input to the PMT 33 via the light guide 32.
- the PMT 33 multiplies the light converted by the scintillator block 31 and converts it into an electric signal.
- the electric signal is sent to the coincidence counting circuit 4 (see FIG. 1) as a pixel value.
- the ⁇ -ray detector 3 is a DOI detector composed of scintillator elements arranged three-dimensionally and composed of a plurality of layers in the depth direction.
- a four-layer DOI detector is illustrated, but the number of layers is not particularly limited as long as it is plural.
- the DOI detector is constructed by laminating the respective scintillator elements in the radiation depth direction, and the interaction depth (DOI: Depth of Interaction) direction and lateral direction (incident surface). Coordinate information with a direction parallel to the center of gravity).
- DOI Depth of Interaction
- lateral direction incident surface
- FIG. 3 is a flowchart illustrating the processing procedure and the data flow of the absorption coefficient image estimation method according to the first embodiment.
- the subject is imaged by the PET apparatus 1 shown in FIG. 1, and list mode data is acquired by the coincidence counting circuit 4 (see FIG. 1).
- the list mode data energy information of detected photons is recorded.
- ⁇ a normal energy window (for example, 400 keV-600 keV), that is, an energy window for reconstruction data, and a measurement range and bin width in the TOF direction of TOF measurement data.
- bin means binarization (separation).
- a pixel corresponds to a bin.
- the TOF bin means a temporal separation of TOF information. For example, when the TOF bin is 100 [ps], the detection time difference is temporally separated with an accuracy of 100 [ps].
- MLACF ⁇ ′ is an image obtained by adding a non-uniform offset value to a quantitative absorption coefficient image
- ⁇ ′ is a non-quantitative radioactivity image. Based on the optimization of the evaluation function regarding the measurement data, the image ⁇ ′ and the radioactivity image ⁇ ′ are calculated simultaneously. As described in the section “Means for Solving the Problems”, the image ⁇ ′ is also an absorption coefficient image. However, it is simply referred to as “image ⁇ ′” to distinguish it from the quantitative absorption coefficient image finally obtained. .
- the reconstruction algorithm in Step S1 is a simultaneous reconstruction algorithm in Non-Patent Document 1.
- the MLACF method described in Non-Patent Document 1 is applied as the simultaneous reconstruction algorithm.
- the specific method of the MLACF method see Non-Patent Document 1 described above.
- a ′ is the absorption coefficient sinogram. Radioactivity image ⁇ ′ and absorption coefficient sinogram A ′ are estimated by MLACF method. The absorption coefficient sinogram A ′ corresponds to the absorption coefficient projection data in the present invention.
- Step S2 ML-TR or ML-EM
- the absorption coefficient sinogram A ′ is reconstructed by a reconstruction algorithm (for example, ML-TR method or ML-EM method) to create a non-quantitative image ⁇ ′.
- a reconstruction algorithm for example, ML-TR method or ML-EM method
- log conversion of the absorption coefficient sinogram A ′ is performed in advance.
- Reference 1 Reference 1
- Reference 2 Reference 2
- Reference 2 Reference 2
- Step 2 Reference 2: LA Shepp and Y. Vardi. Maximum likelihood reconstruction for emission tomography. IEEE Trans. Med. Imaging, Vol. 1 , pp. 113-122, 1982.
- Steps S1 and S2 correspond to a reconstruction calculation step in the present invention.
- Step S3 Binarization Processing
- the image ⁇ ′ is binarized by threshold processing. Then, a binarized image in which the subject region is “1” and the other regions are “0” is calculated as a subject mask image. Let m img be the subject mask image.
- Step S4 Projection + Binarization Processing Line integral data (projection data) of the subject mask image m img is calculated (Projection). Then, the projection data of the subject mask image m img is binarized by threshold processing, so that the projection line passing through the subject becomes “1” and the other projection lines become “0”. The digitized data is calculated as subject mask projection data. Let m proj be subject mask projection data. Steps S3 and S4 correspond to a mask calculation step in the present invention.
- Step S5 ML-EM Let ⁇ off be a non-uniform offset image.
- the configured reconstruction algorithm as the forward projection data of the offset image mu off approximates the subject mask projection data m proj, estimates the offset image mu off. That is, the subject mask projection data m proj is converted into image data by a reconstruction algorithm (for example, ML-EM method). This image data is set as an offset image ⁇ off .
- Step S5 corresponds to the offset estimation step in the present invention.
- Step S6 Extraction Let ⁇ be a region that can be approximated by a known absorption coefficient value. At least one region ⁇ is extracted (Extraction) using an image recognizable from the subject region calculated based on the measurement data.
- K ( ⁇ 1) is the number of regions that can be approximated by a known absorption coefficient value
- ⁇ n is the n-th region ⁇
- each region ⁇ 1 ,..., ⁇ K is extracted from a region that can be approximated by air, a region that can be approximated by brain tissue, and a region that can be approximated by bone.
- Examples of the image that can be recognized based on the measurement data that can recognize the subject region include the image ⁇ ′ created in step S2, the radioactivity image ⁇ ′ obtained in step S1, and the reconstruction algorithm in step S1 ( A non-quantitative image estimated by a different reconstruction algorithm (for example, ML-EM method), and a subject mask image m img estimated from the above-described subject mask projection data m proj .
- Step S6 corresponds to the reference region extraction step in the present invention.
- ⁇ is a coefficient.
- the representative value is, for example, an average value, a median value, a trimmed average value, a trimmed median value, or a weighted average value of two or more values thereof.
- the “trimmed average value” means an average value of the remaining data from which data having extremely large / small values is removed.
- the “trimmed median” means the median of the remaining data obtained by removing data with extremely large / small values.
- Step S7 corresponds to a coefficient calculation step in the present invention.
- Step S8 corresponds to an absorption coefficient value correcting step in the present invention.
- the absorption correction is performed using the absorption coefficient image having the absorption coefficient value ⁇ obtained in step S8.
- the transmittance of ⁇ rays is obtained from the estimated absorption coefficient image, and the transmittance is divided from the PET measurement data, thereby eliminating the influence of the absorption of ⁇ rays.
- Absorption correction is performed by conversion.
- the absorption correction is performed by incorporating the estimated absorption coefficient image into a calculation formula for image reconstruction to obtain a reconstructed image from which the influence of ⁇ -ray absorption is eliminated.
- step S1 the evaluation of the positron CT measurement data (TOF-PET measurement data) including the time-of-flight difference (Time ⁇ Of ⁇ Flight) information of the annihilation radiation is performed.
- TOF-PET measurement data the time-of-flight difference
- step S1 a radioactivity image ⁇ ′ is calculated.
- the reconstruction algorithm in step S1 is the above-described simultaneous reconstruction algorithm.
- step S3 subject mask data in the projection data space (that is, subject mask projection data m proj ) is calculated based on the measurement data.
- step S5 the offset image ⁇ off is estimated by a reconstruction algorithm configured such that the forward projection data of the offset image ⁇ off approximates the subject mask projection data.
- At least one region ⁇ is extracted in step S6 using an image that can be recognized based on the measurement data and that can recognize the subject region.
- the image that can be recognized based on the measurement data and in which the subject region can be recognized is, for example, the image created in step S2.
- ⁇ ′, radioactivity image ⁇ ′ obtained in step S1 non-quantitative image estimated by a reconstruction algorithm (for example, ML-EM method) different from the reconstruction algorithm (simultaneous reconstruction algorithm) in step S1,
- a subject mask image m img estimated from the subject mask projection data m proj is not limited to these exemplified images, and may be any image that can be recognized based on the measurement data and that can recognize the subject region.
- At least one region ⁇ is extracted using an image recognizable from the subject region calculated based on the measurement data”. “Not only extracting the region ⁇ using a single image information but also extracting the region ⁇ using a combination of a plurality of pieces of image information (for example, logical sum or logical product).
- Steps S7 and S8 are performed using the image ⁇ ′, the offset image ⁇ off and the region ⁇ obtained in the above steps S1 to S6.
- step S7 a coefficient ⁇ that reduces the error between the value of the image ⁇ ′ in the region ⁇ and the known absorption coefficient value is calculated.
- step S8 as described above (3), the value of the image mu ', corrects the value obtained by adding the alpha ⁇ mu off that coefficient alpha multiplying the offset image mu off as the absorption coefficient mu To do.
- the difference between the value of the non-quantitative image ⁇ ′ in the region ⁇ and the known absorption coefficient value (the value of the true absorption coefficient image) is approximated by ⁇ ⁇ ⁇ off, which is obtained by multiplying the offset image ⁇ off by a coefficient ⁇ .
- the absorption coefficient value is corrected in step S8. Therefore, the absorption coefficient image having the absorption coefficient value ⁇ corrected in step S8 has a small systematic error. As a result, since a quantitative absorption coefficient image can be created, accurate absorption correction of the radioactivity image becomes possible.
- steps S1 and S2 corresponding to the above-described reconstruction calculation step are performed as follows: (b) a calculation algorithm including absorption coefficient projection data in an unknown and absorption coefficient projection data This is implemented by a combination of algorithms that make the image reconstructed as an image ⁇ ′.
- Non-Patent Document 1 which simultaneously estimates a non-quantitative radioactivity image ⁇ ′ and non-quantitative absorption coefficient projection data (absorption coefficient sinogram A ′ in each of Examples 1 to 3).
- This is a combination of the MLACF method and an algorithm in which an image obtained by reconstructing the absorption coefficient projection data (absorption coefficient sinogram A ′) is an image ⁇ ′.
- the algorithm for reconstructing the image obtained by reconstructing the absorption coefficient projection data (absorption coefficient sinogram A ′) in (b) is the image ⁇ ′. If it is an algorithm, it will not specifically limit.
- step S2 the absorption coefficient sinogram A ′ is reconstructed by the ML-TR method or the ML-EM method, and an image ⁇ ′ is created.
- the mask calculation step includes a step of calculating a binarized image of the image ⁇ ′ as the subject mask image m img (step S3) and a step of calculating projection data of the subject mask image m img (the first half of step S4).
- the process of calculating the binarized data of the projection data of the subject mask image m img as the subject mask projection data m proj (“Binarization Processing” in the latter half of step S4).
- the image ⁇ ′ is a non-quantitative absorption coefficient image.
- an image other than the absorption coefficient image for example, the radioactivity image ⁇ ′ of Example 3 or the radioactivity image ⁇ 2 ′.
- the object mask projection data m proj can also be calculated by binarizing the projection data.
- the reconstruction process performed in step S5 corresponding to the offset estimation process described above is performed by a statistical reconstruction calculation method typified by the ML-EM (Maximum-Likelihood--Expectation-Maximization) method in the first embodiment. Yes.
- the reconstruction process performed in step S5 is not limited to the statistical reconstruction as in the first embodiment. What is necessary is just to implement by any one of analytical reconstruction, statistical reconstruction, and algebraic reconstruction.
- analytical reconstruction for example, there is an FBP (Filtered Back Projection) method.
- an algebraic reconstruction for example, there is an ART (Algebraic Reconstruction Technique) method.
- the at least one region ⁇ extracted in step S6 corresponding to the above-described reference region extraction step is a tissue region in which the absorption coefficient can be regarded as known.
- the region of the tissue whose absorption coefficient can be regarded as known means, for example, a region that can be approximated by water, a region that can be approximated by air, These include areas that can be approximated by brain tissue, areas that can be approximated by bone, areas that can be approximated by lung tissue, and areas that can be approximated by soft tissue.
- any structure can be used as long as an approximate value of the absorption coefficient can be understood.
- the water absorption coefficient value of 0.0096 / mm can be used.
- step S7 corresponding to the coefficient calculation step described above is performed. That is, the coefficient ⁇ is calculated based on the representative value in the first embodiment, including later-described second to fourth embodiments.
- the representative value is, for example, an average value, a median value, a trimmed average value, a trimmed median value, or a weighted average value of two or more values thereof.
- the value is not limited to these exemplified values, and may be “a statistic or a value calculated from the statistic”.
- S ( ⁇ ′; ⁇ n ) is a representative value of image ⁇ ′ in region ⁇ n
- S ( ⁇ off ; ⁇ n ) is a representative value of the offset image ⁇ off ′ in the region ⁇ n .
- the coefficients ⁇ 1 ,. ..., ⁇ K can be calculated by setting the representative value T ( ⁇ 1 , ⁇ 2 ,..., ⁇ K ) as the coefficient ⁇ .
- the absorption coefficient image estimation program 6 is configured by a computer (in each embodiment, the arithmetic circuit 5 shown in FIG. 1 is configured).
- the absorption coefficient value is corrected in step S8 based on the mathematical relationship that it is possible to approximate with ⁇ ⁇ ⁇ off multiplied by ⁇ . Therefore, the absorption coefficient image having the absorption coefficient value ⁇ corrected in step S8 has a small systematic error. As a result, since a quantitative absorption coefficient image can be created, accurate absorption correction of the radioactivity image becomes possible.
- arithmetic means for executing the absorption coefficient image estimation program 6 according to the first embodiment (in each embodiment, the arithmetic circuit 5 shown in FIG. 1 is configured).
- the difference between the non-quantitative image ⁇ ′ value in the region ⁇ and the known absorption coefficient value (the true absorption coefficient image value) is the coefficient of the offset image ⁇ off .
- the absorption coefficient value is corrected in step S8 based on the mathematical relationship that it is possible to approximate with ⁇ ⁇ ⁇ off multiplied by ⁇ . Therefore, the absorption coefficient image having the absorption coefficient value ⁇ corrected in step S8 has a small systematic error. As a result, since a quantitative absorption coefficient image can be created, accurate absorption correction of the radioactivity image becomes possible.
- FIG. 4 is a flowchart illustrating a processing procedure and a data flow of the absorption coefficient image estimation method according to the second embodiment.
- the binarized image of the image mu ' is calculated as a subject mask image m img, calculate the projection data of the object mask image m img, the projection data of the object mask image m img two The value data was calculated as the subject mask projection data m proj .
- data obtained by binarizing the TOF-PET measurement data converted into the projection data format is calculated as the subject mask projection data m proj .
- Step S11 MLACF Since step S11 in FIG. 4 is the same as step S1 in the first embodiment described above, description thereof is omitted.
- Step S12 ML-TR or ML-EM Since step S12 in FIG. 4 is the same as step S2 in the first embodiment described above, description thereof is omitted. Steps S11 and S12 correspond to a reconstruction calculation step in the present invention.
- Step S14 Projection + Binarization Processing
- steps S3 and S4 in FIG. 3 are performed to calculate the subject mask image m img from the image ⁇ ′.
- step S14 in FIG. 4 is performed in order to calculate the subject mask image m img from the measurement data instead of the image ⁇ ′.
- the measurement data is converted into a projection data format (Conversion).
- binarization processing of the projection data of the measurement data by threshold processing binarization data in which the projection line passing through the subject is “1” and the other projection lines are “0” is obtained.
- subject mask projection data m proj Step S14 corresponds to a mask calculation step in the present invention.
- Step S15 ML-EM Since step S15 in FIG. 4 is the same as step S5 in the first embodiment described above, description thereof is omitted. Step S15 corresponds to the offset estimation step in the present invention.
- Step S16 Extraction Since step S16 in FIG. 4 is the same as step S6 in the first embodiment described above, description thereof is omitted. Step S16 corresponds to the reference region extraction step in the present invention.
- the value of the non-quantitative image ⁇ ′ in the region ⁇ and the known absorption coefficient value (value of the true absorption coefficient image).
- the absorption coefficient value is corrected in step S18 based on a mathematical relationship that the offset image ⁇ off can be approximated by ⁇ ⁇ ⁇ off obtained by multiplying the offset image ⁇ off by a coefficient ⁇ . Therefore, the absorption coefficient image having the absorption coefficient value ⁇ corrected in step S18 has a small systematic error. As a result, since a quantitative absorption coefficient image can be created, accurate absorption correction of the radioactivity image becomes possible.
- step S14 corresponding to the mask calculation process described above is performed. That is, the mask calculation step includes a step (step S14) of calculating, as object mask projection data, binary data obtained by converting the above-described TOF-PET measurement data into a projection data format.
- step S14 data obtained by binarizing the data converted into the projection data format using the TOF-PET measurement data directly can be calculated as the subject mask projection data m proj .
- the binarized image of the image mu ' is calculated as a subject mask image m img, calculate the projection data of the object mask image m img, the projection data of the object mask image m img two The value data was calculated as the subject mask projection data m proj .
- data obtained by binarizing the TOF-PET measurement data converted into the projection data format is calculated as the subject mask projection data m proj .
- the radioactivity image is calculated, the projection data of the radioactivity image is calculated, (of the radioactivity image)
- Data obtained by binarizing the projection data is calculated as subject mask projection data m proj .
- Step S21 MLACF Step S21 of FIG. 5 is the same as step S1 of the first embodiment described above and step S11 of the second embodiment described above, and thus description thereof is omitted.
- Step S22 ML-TR or ML-EM Step S22 in FIG. 5 is the same as step S2 in the first embodiment described above and step S12 in the second embodiment described above, and therefore description thereof is omitted. Steps S21 and S22 correspond to a reconstruction calculation step in the present invention.
- the line integral data (projection data) of the radioactivity image ⁇ ′ estimated based on the optimization of the evaluation function related to the measurement data in the MLACF method is calculated (Projection). That is, in FIG. 5, the projection data of the radioactivity image ⁇ ′ may be calculated using the radioactivity image ⁇ ′ estimated by the MLACF method in step S21. Then, by performing binarization processing on the projection data of the radioactivity image ⁇ ′ by threshold processing, the projection line passing through the subject is “1”, and the other projection lines are “0”. Data is calculated as subject mask projection data m proj . Step S24 corresponds to a mask calculation step in the present invention.
- Step S25 ML-EM Step S25 in FIG. 5 is the same as step S5 in the first embodiment described above and step S15 in the second embodiment described above, and thus description thereof is omitted. Step S25 corresponds to an offset estimation step in the present invention.
- Step S26 Extraction Step S26 in FIG. 5 is the same as step S6 in the first embodiment described above and step S16 in the second embodiment described above, and therefore description thereof is omitted. Step S26 corresponds to the reference region extraction step in the present invention.
- Step S27 in FIG. 5 is the same as step S7 in the first embodiment described above and step S17 in the second embodiment described above, and thus description thereof is omitted.
- Step S27 corresponds to a coefficient calculation step in the present invention.
- Step S31 MLACF Since step S31 in FIG. 6 is the same as step S21 in FIG. 5, the description thereof is omitted.
- Step S32 ML-TR or ML-EM Since step S32 in FIG. 6 is the same as step S22 in FIG. 5, the description thereof is omitted. Steps S31 and S32 correspond to a reconstruction calculation step in the present invention.
- Step S33 ML-EM
- step S24 in FIG. 5 is performed to calculate the subject mask projection data m proj using the radioactivity image ⁇ ′ estimated by the MLACF method.
- steps S33 and S34 of FIG. 6 are performed in order to calculate the subject mask projection data m proj using a radioactivity image estimated by a reconstruction algorithm different from the MLACF method.
- a radioactivity image is estimated based on optimization of an evaluation function related to measurement data in a reconstruction algorithm (for example, ML-EM method) different from the MLACF method.
- a reconstruction algorithm for example, ML-EM method
- the radioactivity image estimated by the reconstruction algorithm different from that of the MLACF method is defined as ⁇ 2 ′ in distinction from the radioactivity image ⁇ ′ estimated by the MLACF method.
- Step S34 Projection + Binarization Processing
- the line integral data (projection data) of the radioactivity image ⁇ 2 ′ estimated based on the optimization of the evaluation function for the measurement data in the reconstruction algorithm different from the MLACF method is calculated (Projection).
- the projection data of the radioactivity image ⁇ 2 ′ is binarized by threshold processing, so that the projection line passing through the subject becomes “1” and the other projection lines become “0”.
- the digitized data is calculated as subject mask projection data m proj .
- Steps S33 and S34 correspond to a mask calculation step in the present invention.
- Step S35 ML-EM Since step S35 in FIG. 6 is the same as step S25 in FIG. 5, the description thereof is omitted. Step S35 corresponds to an offset estimation step in the present invention.
- Step S36 Extraction Since step S36 in FIG. 6 is the same as step S26 in FIG. 5, the description thereof is omitted. Step S36 corresponds to the reference region extraction step in the present invention.
- Step S37 in FIG. 6 is the same as step S27 in FIG. Step S37 corresponds to a coefficient calculation step in the present invention.
- the value of the non-quantitative image ⁇ ′ in the region ⁇ and the known absorption coefficient value is based on the mathematical relationship that the offset image ⁇ off can be approximated by ⁇ ⁇ ⁇ off obtained by multiplying the offset image ⁇ off by the coefficient ⁇ , and the absorption coefficient value in step S28 of FIG. 5 or step S38 of FIG. Correct. Therefore, the systematic error of the absorption coefficient image having the absorption coefficient value ⁇ corrected in step S28 of FIG. 5 or step S38 of FIG. 6 is reduced. As a result, since a quantitative absorption coefficient image can be created, accurate absorption correction of the radioactivity image becomes possible.
- step S24 in FIG. 5 or steps S33 and S34 in FIG. 6 corresponding to the above-described mask calculation step is performed. That is, the mask calculation step is a step of calculating a radioactivity image ( ⁇ ′ in FIG. 5 and ⁇ 2 ′ in FIG. 6) based on optimization of the evaluation function related to the measurement data of TOF-PET (described above) (FIG. 6).
- 5 is step S21
- FIG. 6 is step S33
- a step of calculating projection data of the radioactivity image ⁇ ′ in FIG. 5 and ⁇ 2 ′ in FIG. 6) (“Projection” in the first half of step S24 in FIG. In FIG.
- the reconstruction algorithm for calculating the radioactivity image is not particularly limited. As shown in FIG. 5, when the above-described simultaneous reconstruction algorithm (MLACF method or MLAA method) is used, subject mask projection data is obtained using the above-described radioactivity image ⁇ ′ estimated by the simultaneous reconstruction algorithm. m proj can be calculated. Further, as shown in FIG.
- Radioactivity image lambda 2 'estimated in the, subject Mask projection data m proj may be calculated.
- FIG. 7 is a flowchart illustrating the processing procedure and the data flow of the absorption coefficient image estimation method according to the fourth embodiment.
- Step S41 MLAA
- the radioactivity image ⁇ ′ and the absorption coefficient sinogram A ′ are estimated by the MLACF method in step S1 (in Example 2).
- Step S11, Step S21 or S31 in Example 3 After Step S21 or S31), an image obtained by reconstructing the absorption coefficient sinogram A ′ is set as an image ⁇ ′ (Step S12 in Example 2, Step S22 or S32 in Example 3) Had been implemented.
- the radioactivity image ⁇ ′ and the image ⁇ ′ are simultaneously calculated by the MLAA method.
- steps S1 and S2 using the MLACF method steps S11 and S12 in the second embodiment, steps S21 and S22 or S31 and S32 in the third embodiment
- the MLAA method is used. Is integrated into one step S41.
- Reference 3 Reference 3: A. Rezaei (KU Leuven), M. Defrise, G. Bal et. Al., “Simultaneous reconstruction of activity and attenuation in time-of-flight (PET), IEEE Trans. (Med.) Imag., (31) (12), (2224-2233, 2012).
- Step S41 corresponds to a reconstruction calculation step in the present invention.
- Step S43 Binarization Processing Since step S43 in FIG. 7 is the same as step S3 in the first embodiment described above, description thereof is omitted.
- Step S44 Projection + Binarization Processing Since step S44 of FIG. 7 is the same as step S4 of the first embodiment described above, description thereof is omitted. Steps S43 and S44 correspond to a mask calculation step in the present invention.
- Step S45 ML-EM Step S45 in FIG. 7 is the same as Step S5 in Embodiment 1 described above, Step S15 in Embodiment 2 described above, and Step 3 in Embodiment 3 described above (Step S25 in FIG. 5 and Step S35 in FIG. 6). The description is omitted. Step S45 corresponds to an offset estimation step in the present invention.
- Step S46 Extraction Step S46 in FIG. 7 is the same as step S6 in the first embodiment described above, step S16 in the second embodiment described above, and step S3 in the third embodiment described above (step S26 in FIG. 5 and step S36 in FIG. 6). The description is omitted. Step S46 corresponds to the reference region extraction step in the present invention.
- Step S47 in FIG. 7 is the same as Step S7 in Embodiment 1 described above, Step S17 in Embodiment 2 described above, and Step 3 in Embodiment 3 described above (Step S27 in FIG. 5 and Step S37 in FIG. 6). The description is omitted.
- Step S47 corresponds to a coefficient calculation step in the present invention.
- FIG. 7 is a flowchart of the fourth embodiment when applied to the case where steps S1 and S2 in FIG. 3 of the first embodiment described above are integrated into step S43.
- the fourth embodiment may be applied when the steps S11 and S12 in FIG. 4 of the second embodiment described above are integrated into the step S43, or the steps S21 and S22 in FIG.
- the fourth embodiment may be applied when the steps are integrated into steps S31 and S32.
- step S41 corresponding to the above-described reconstruction calculation step is performed by a calculation algorithm including (a) the image ⁇ ′ as an unknown.
- the algorithm (a) is an MLAA method that simultaneously reconstructs a non-quantitative radioactivity image ⁇ ′ and an image ⁇ ′ (non-quantitative absorption coefficient image).
- FIG. 8 is a flowchart illustrating the processing procedure and data flow of the absorption coefficient image estimation method according to the fifth embodiment.
- the coefficient ⁇ is calculated based on the representative value.
- the coefficient ⁇ is calculated based on the error evaluation function.
- Step S51 MLACF Step S51 in FIG. 8 is the same as Step S1 in Embodiment 1 described above, Step S11 in Embodiment 2 described above, and Step 3 in Embodiment 3 described above (Step S21 in FIG. 5 and Step S31 in FIG. 6). The description is omitted.
- Step S52 ML-TR or ML-EM Step S52 in FIG. 8 is the same as Step S2 in Embodiment 1 described above, Step S12 in Embodiment 2 described above, and Step 3 in Embodiment 3 described above (Step S22 in FIG. 5 and Step S32 in FIG. 6). The description is omitted. Steps S51 and S52 correspond to a reconstruction calculation step in the present invention.
- Step S53 Binarization Processing Step S53 in FIG. 8 is the same as step S3 in the first embodiment described above and step S43 in the fourth embodiment described above, and thus description thereof is omitted.
- Step S54 Projection + Binarization Processing Step S54 in FIG. 8 is the same as step S4 in the first embodiment described above and step S44 in the fourth embodiment described above, and therefore description thereof is omitted. Steps S53 and S54 correspond to the mask calculation step in the present invention.
- Step S55 ML-EM Step S55 in FIG. 8 includes step S5 in the first embodiment described above, step S15 in the second embodiment described above, step S3 in the third embodiment described above (step S25 in FIG. 5, step S35 in FIG. 6), and the embodiment described above. Since this is the same as step S45 in FIG. Step S55 corresponds to the offset estimation step in the present invention.
- Step S56 of Extraction Step S56 of FIG. 8 includes step S6 of the first embodiment described above, step S16 of the second embodiment described above, step S3 of the third embodiment described above (step S26 in FIG. 5 and step S36 in FIG. 6), and the embodiment described above. Since this is the same as step S46 in FIG. Step S56 corresponds to the reference region extraction step in the present invention.
- f ( ⁇ ) D ⁇ ( ⁇ known , ⁇ ′ + ⁇ ⁇ ⁇ off )
- the coefficient ⁇ is calculated based on the representative value.
- the coefficient ⁇ is calculated based on the error evaluation function.
- ⁇ known is an image in which a known absorption coefficient is set in the region ⁇
- D ⁇ (X, Y) is an error evaluation function of the image X and the image Y related to the region ⁇ .
- D ⁇ ( ⁇ known , ⁇ ' + ⁇ ⁇ ⁇ off ) is an image ⁇ known with a known absorption coefficient in the region ⁇ and a quantitative absorption coefficient
- This is an error evaluation function for an image ( ⁇ ′ + ⁇ ⁇ ⁇ off ) obtained by adding a non-uniform offset value to the image.
- f ( ⁇ ) D ⁇ ( ⁇ known , ⁇ '+ ⁇ ⁇ ⁇ off ) (4)
- Step S57 corresponds to a coefficient calculation step in the present invention.
- Step S48 in FIG. 8 includes step S8 in the above-described first embodiment, step S18 in the above-described second embodiment, step in the above-described third embodiment (step S28 in FIG. 5, step S38 in FIG. 6), and the above-described embodiment. Since this is the same as step S48 in FIG. Step S58 corresponds to the absorption coefficient value correcting step in the present invention.
- FIG. 8 shows an implementation when the calculation of the coefficient ⁇ based on the representative value in step S7 in FIG. 3 of the first embodiment described above is replaced with the calculation of the coefficient ⁇ based on the error evaluation function in step S57.
- 10 is a flowchart of Example 5.
- the fifth embodiment may be applied when the calculation of the coefficient ⁇ based on the representative value in step S17 in FIG. 4 of the second embodiment described above is replaced with the calculation of the coefficient ⁇ based on the error evaluation function in step S57.
- the calculation of the coefficient ⁇ based on the representative value in step S27 in FIG. 5 or the step S37 in FIG. 6 of the third embodiment described above is replaced with the calculation of the coefficient ⁇ based on the error evaluation function in step S57.
- the calculation of the coefficient ⁇ based on the representative value in step S47 in FIG. 7 in the fourth embodiment described above is replaced with the calculation of the coefficient ⁇ based on the error evaluation function in step S57. May be applied.
- the value of the non-quantitative image ⁇ ′ in the region ⁇ and the known absorption coefficient value (the true absorption coefficient image
- the absorption coefficient value is corrected in step S58 on the basis of a mathematical relationship that the offset image ⁇ off can be approximated by ⁇ ⁇ ⁇ off obtained by multiplying the offset image ⁇ off by a coefficient ⁇ . Therefore, the absorption coefficient image having the absorption coefficient value ⁇ corrected in step S58 has a small systematic error. As a result, since a quantitative absorption coefficient image can be created, accurate absorption correction of the radioactivity image becomes possible.
- the coefficient ⁇ is calculated based on the error evaluation function.
- K ( ⁇ 1) be the number of regions that can be approximated by a known absorption coefficient value
- ⁇ n is the nth region ⁇
- w n (n 1, ..., K) and the 0 to 1 inclusive coefficients To do.
- Image X is obtained by replacing image X n known by setting a known absorption coefficient in region ⁇ n and adding image Y to image ⁇ ′ by multiplying offset image ⁇ off ′ by ⁇ ⁇ ⁇ off.
- 'be replaced with (+ ⁇ ⁇ ⁇ off, D ⁇ n ( ⁇ n known, ⁇ value ⁇ )' + ⁇ ⁇ ⁇ off ) includes an image mu n known set of known absorption coefficient for region Omega n, This is an error evaluation function with an image ( ⁇ ′ + ⁇ ⁇ ⁇ off ) obtained by adding a non-uniform offset value to a quantitative absorption coefficient image.
- the present invention is not limited to the above embodiment, and can be modified as follows.
- the subject to be photographed in each of the embodiments described above is not particularly limited. You may apply to the apparatus which image
- the DOI detector is used, but it may be applied to a detector that does not distinguish the depth direction.
- the detector rings are stacked in the body axis direction of the subject.
- the detector ring may have only one configuration.
- the data format is sinogram, but is not limited to sinogram. If it is projection data, for example, the data format may be a histogram. Therefore, in Examples 1 to 3 described above, the absorption coefficient projection data estimated by the MLACF method is the absorption coefficient sinogram A ′, but the absorption coefficient projection data estimated by the MLACF method may be an absorption coefficient histogram.
- the projection data is calculated after binarizing the image ⁇ ′ first, and the projection data is binarized, but the object mask projection data m proj is calculated as follows. May be. That is, the mask calculation step may be an aspect including a step of calculating projection data of the image ⁇ ′ and a step of calculating binarized data of the projection data of the image ⁇ ′ as the subject mask projection data m proj . In this embodiment, the projection data of the image ⁇ ′ is binarized after being calculated first.
- the radioactivity image in FIG. 5 lambda ', lambda 2 in Fig. 6'
- the projection data m proj may be calculated. That is, the mask calculation step is a step of calculating a radioactivity image based on optimization of the evaluation function related to the measurement data of TOF-PET (described above), a step of calculating a binarized image of the radioactivity image,
- the aspect which consists of the process of calculating the projection data of a binarized image and the process of calculating the data which binarized the projection data of the binarized image as object mask projection data m proj may be sufficient.
- the projection data is calculated after binarizing the radioactivity image first, and the projection data is binarized.
- the reconstruction algorithm for calculating the radioactivity image is not particularly limited, and a simultaneous reconstruction algorithm (MLACF method or MLAA method) as shown in FIG.
- a reconstruction algorithm for example, ML-EM method
- MCACF method or MLAA method different from the simultaneous reconstruction algorithm (MLACF method or MLAA method) as shown in FIG. 6 may be used.
- the present invention is suitable for estimation of an absorption coefficient image using measurement data measured by a TOF measurement type PET apparatus.
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Abstract
Description
(1)吸収補正なしの放射能画像を作成し、当該放射能画像から被検体マスク画像を作成する。
(2)被検体マスク画像の各画素値に既知の吸収係数(例えば、水の吸収係数や骨の吸収係数)を代入し、疑似的な吸収係数画像(以下、「疑似吸収係数画像」と略記する)を作成する。
(3)疑似吸収係数画像を用いて、従来の再構成アルゴリズムで放射能画像を作成し、体軸方向スライス毎に合計画素値を計算する。図10に示すようにzを体軸方向とし、xy平面を体軸方向zに直交する平面(アキシャル面)とし、P(x,y)を画素値とし、S(z)を体軸方向zスライス毎の合計画素値とすると、S(z)=ΣyΣxP(x,y)となる。横軸を体軸方向z,縦軸を合計画素値S(z)とすると、図10の右図のようなプロファイルが作成される。
(4)同時再構成アルゴリズムによって、定量的でない放射能画像および定量的でない吸収係数サイノグラムを推定する。
(5)手順(4)で求めた定量的でない放射能画像に対しても、手順(3)と同様にして、体軸方向スライス毎に合計画素値を計算する。ここでは、S'(z)を体軸方向zスライス毎の合計画素値とする。
(6)手順(5)で求めた合計画素値S'(z)と手順(3)で求めた合計画素値S(z)とが体軸方向スライス毎に一致するように、手順(4)で求めた定量的でない放射能画像をスケーリングし、定量化する。具体的には、手順(4)で求めた定量的でない放射能画像の各画素値にS(z)/ S'(z)を体軸方向スライス毎にそれぞれ乗算することで、当該放射能画像をスケーリングする。
すなわち、上述した従来技術は、手順(3)で求めた体軸方向スライス毎の合計画素値が真である(すなわち正しい)ということを仮定している。
すなわち、本発明に係る吸収係数画像推定方法は、消滅放射線の飛行時間差(Time Of Flight)情報を含んだポジトロンCTの計測データから吸収係数画像を推定する方法であって、μ'を定量的な吸収係数画像に対して不均一なオフセット値が加算された画像とし、前記計測データに関する評価関数の最適化に基づいて、前記画像μ'を計算する再構成計算工程と、前記計測データに基づいて投影データ空間における被検体マスクデータである被検体マスク投影データを算出するマスク算出工程と、μoffを不均一なオフセット画像としたときに、オフセット画像μoffの順投影データが被検体マスク投影データを近似するように構成された再構成アルゴリズムによって、前記オフセット画像μoffを推定するオフセット推定工程と、Ωを既知の吸収係数値で近似可能な領域としたときに、前記計測データに基づいて計算された、被検体領域が認識可能な画像を用いて、前記領域Ωを少なくとも1つ以上抽出する参照領域抽出工程と、αを係数としたときに、前記領域Ωにおける前記画像μ'の値と既知の吸収係数値との誤差を減少させる前記係数αを算出する係数算出工程と、前記画像μ'の値に、前記オフセット画像μoffを前記係数α倍したα×μoffを加算して得られた値を吸収係数値として補正する吸収係数値補正工程とを備えるものである。
μ'を定量的な吸収係数画像に対して不均一なオフセット値が加算された画像とし、λ'を非定量的な放射能画像とする。計測データに関する評価関数の最適化に基づいて、画像μ'および放射能画像λ'を同時に計算する。「課題を解決するための手段」の欄でも述べたように、画像μ'も吸収係数画像となるが、最終的に求まる定量的な吸収係数画像と区別して、単に「画像μ'」とする。
吸収係数サイノグラムA'を再構成アルゴリズム(例えばML-TR法やML-EM法)で再構成し、定量的でない画像μ'を作成する。ML-EM法を利用する場合は、吸収係数サイノグラムA’を事前にログ変換する。ML-TR法の具体的な手法については、参考文献1を参照されたい(参考文献1:Erdo?an H, Fessler JA: Ordered subsets algorithms for transmission tomography. Phys Med Biol 44: 2835-2851, 1999)。また、ML-EM法の具体的な手法については、参考文献2を参照されたい(参考文献2:L.A. Shepp and Y. Vardi. Maximum likelihood reconstruction for emission tomography. IEEE Trans. Med. Imaging, Vol. 1, pp. 113-122, 1982)。ステップS1,S2は、本発明における再構成計算工程に相当する。
閾値処理によって画像μ'を二値化処理(Binarization Processing)する。そして、被検体領域を“1”,その他の領域を“0”となる二値化画像を被検体マスク画像として算出する。mimgを被検体マスク画像とする。
被検体マスク画像mimgの線積分データ(投影データ)を算出する(Projection)。そして、閾値処理によって被検体マスク画像mimgの投影データを二値化処理(Binarization Processing)することで、被検体を通過する投影線を“1”,その他の投影線を“0”となる二値化データを被検体マスク投影データとして算出する。mprojを被検体マスク投影データとする。ステップS3,S4は、本発明におけるマスク算出工程に相当する。
μoffを不均一なオフセット画像とする。オフセット画像μoffの順投影データが被検体マスク投影データmprojを近似するように構成された再構成アルゴリズムによって、オフセット画像μoffを推定する。つまり、被検体マスク投影データmprojを再構成アルゴリズム(例えばML-EM法)で画像データに変換する。この画像データをオフセット画像μoffとする。ステップS5は、本発明におけるオフセット推定工程に相当する。
Ωを既知の吸収係数値で近似可能な領域とする。計測データに基づいて計算された、被検体領域が認識可能な画像を用いて、領域Ωを少なくとも1つ以上抽出する(Extraction)。後述する実施例2~4も含めて、本実施例1では、K(≧1)を既知の吸収係数値で近似可能な領域数とし、Ωnをn番目の領域Ωとしたときに、n=1,…,Kで各領域Ω1,…,ΩKをそれぞれ抽出する。例えば、被検体の頭部を撮影する場合には、空気で近似可能な領域,脳組織で近似可能な領域,骨で近似可能な領域で各領域Ω1,…,ΩKをそれぞれ抽出する。
μn known(n=1,…,K)を領域Ωnの既知の吸収係数値とし、S(X;Ωn)を、領域Ωnにおける画像Xの統計量または統計量から算出される値を代表値とし、T(x1,x2,…,xK)を任意のK個の値x1,x2,…,xKの統計量または統計量から算出される値を代表値とし、αnを領域Ωnにおける係数αとする。なお、αは係数である。ここで、代表値としては、例えば、平均値,中央値,トリムド平均値,トリムド中央値またはそれらの2つ以上の値の重み付き平均値である。ここで、「トリムド平均値」とは、値が極端に大きい/小さいデータを取り除いた残りのデータの平均値を意味する。「トリムド中央値」とは、値が極端に大きい/小さいデータを取り除いた残りのデータの中央値を意味する。
αn=(μn known-S(μ';Ωn))/S(μoff;Ωn) …(1)
α=T(α1,α2,…,αK) …(2)
μを未知の真の吸収係数画像の値(吸収係数値)とする。吸収係数値μは下記(3)式のように表される。
μ=μ'+α×μoff …(3)
図4のステップS11は、上述した実施例1のステップS1と同じであるので、その説明については省略する。
図4のステップS12は、上述した実施例1のステップS2と同じであるので、その説明については省略する。ステップS11,S12は、本発明における再構成計算工程に相当する。
上述した実施例1では、画像μ'から被検体マスク画像mimgを算出するのに、図3のステップS3,S4を実施していた。本実施例2では、画像μ'の替わりに、計測データから被検体マスク画像mimgを算出するために、図4のステップS14を実施する。先ず、計測データを投影データ形式に変換する(Conversion)。そして、閾値処理によって計測データの投影データを二値化処理(Binarization Processing)することで、被検体を通過する投影線を“1”,その他の投影線を“0”となる二値化データを被検体マスク投影データmprojとして算出する。ステップS14は、本発明におけるマスク算出工程に相当する。
図4のステップS15は、上述した実施例1のステップS5と同じであるので、その説明については省略する。ステップS15は、本発明におけるオフセット推定工程に相当する。
図4のステップS16は、上述した実施例1のステップS6と同じであるので、その説明については省略する。ステップS16は、本発明における参照領域抽出工程に相当する。
図4のステップS17は、上述した実施例1のステップS7と同じであるので、その説明については省略する。ステップS17は、本発明における係数算出工程に相当する。
図4のステップS18は、上述した実施例1のステップS8と同じであるので、その説明については省略する。ステップS18は、本発明における吸収係数値補正工程に相当する。
図5のステップS21は、上述した実施例1のステップS1,上述した実施例2のステップS11と同じであるので、その説明については省略する。
図5のステップS22は、上述した実施例1のステップS2,上述した実施例2のステップS12と同じであるので、その説明については省略する。ステップS21,S22は、本発明における再構成計算工程に相当する。
上述した実施例1では、画像μ'から被検体マスク画像mimgを算出するのに、図3のステップS3,S4を実施していた。また、上述した実施例2では、計測データから被検体マスク画像mimgを算出するのに、図4のステップS14を実施していた。本実施例3では、実施例1の画像μ',実施例2の計測データの替わりに、計測データに関する評価関数の最適化に基づいて推定した放射能画像から被検体マスク画像mimgを算出するために、図5のステップS24を実施する。
図5のステップS25は、上述した実施例1のステップS5,上述した実施例2のステップS15と同じであるので、その説明については省略する。ステップS25は、本発明におけるオフセット推定工程に相当する。
図5のステップS26は、上述した実施例1のステップS6,上述した実施例2のステップS16と同じであるので、その説明については省略する。ステップS26は、本発明における参照領域抽出工程に相当する。
図5のステップS27は、上述した実施例1のステップS7,上述した実施例2のステップS17と同じであるので、その説明については省略する。ステップS27は、本発明における係数算出工程に相当する。
図5のステップS28は、上述した実施例1のステップS8,上述した実施例2のステップS18と同じであるので、その説明については省略する。ステップS28は、本発明における吸収係数値補正工程に相当する。
図6のステップS31は、図5のステップS21と同じであるので、その説明については省略する。
図6のステップS32は、図5のステップS22と同じであるので、その説明については省略する。ステップS31,S32は、本発明における再構成計算工程に相当する。
図5ではMLACF法で推定した放射能画像λ'を利用して被検体マスク投影データmprojを算出するのに、図5のステップS24を実施していた。図6では、MLACF法とは異なる再構成アルゴリズムで推定した放射能画像を利用して被検体マスク投影データmprojを算出するために、図6のステップS33,S34を実施する。
MLACF法とは異なる再構成アルゴリズムにおける計測データに関する評価関数の最適化に基づいて推定した放射能画像λ2'の線積分データ(投影データ)を算出する(Projection)。そして、閾値処理によって放射能画像λ2'の投影データを二値化処理(Binarization Processing)することで、被検体を通過する投影線を“1”,その他の投影線を“0”となる二値化データを被検体マスク投影データmprojとして算出する。ステップS33,S34は、本発明におけるマスク算出工程に相当する。
図6のステップS35は、図5のステップS25と同じであるので、その説明については省略する。ステップS35は、本発明におけるオフセット推定工程に相当する。
図6のステップS36は、図5のステップS26と同じであるので、その説明については省略する。ステップS36は、本発明における参照領域抽出工程に相当する。
図6のステップS37は、図5のステップS27と同じであるので、その説明については省略する。ステップS37は、本発明における係数算出工程に相当する。
図6のステップS38は、図5のステップS28と同じであるので、その説明については省略する。ステップS38は、本発明における吸収係数値補正工程に相当する。
上述した実施例1~3では、画像μ'および放射能画像λ'を同時に計算するために、MLACF法によって、放射能画像λ'および吸収係数サイノグラムA'を推定したステップS1(実施例2ではステップS11,実施例3ではステップS21またはS31)の後に、吸収係数サイノグラムA'を再構成した画像を画像μ'とするステップS2(実施例2ではステップS12,実施例3ではステップS22またはS32)を実施していた。本実施例4では、MLAA法によって、放射能画像λ'および画像μ'を同時に計算する。
図7のステップS43は、上述した実施例1のステップS3と同じであるので、その説明については省略する。
図7のステップS44は、上述した実施例1のステップS4と同じであるので、その説明については省略する。ステップS43,S44は、本発明におけるマスク算出工程に相当する。
図7のステップS45は、上述した実施例1のステップS5,上述した実施例2のステップS15,上述した実施例3のステップ(図5ではステップS25,図6ではステップS35)と同じであるので、その説明については省略する。ステップS45は、本発明におけるオフセット推定工程に相当する。
図7のステップS46は、上述した実施例1のステップS6,上述した実施例2のステップS16,上述した実施例3のステップ(図5ではステップS26,図6ではステップS36)と同じであるので、その説明については省略する。ステップS46は、本発明における参照領域抽出工程に相当する。
図7のステップS47は、上述した実施例1のステップS7,上述した実施例2のステップS17,上述した実施例3のステップ(図5ではステップS27,図6ではステップS37)と同じであるので、その説明については省略する。ステップS47は、本発明における係数算出工程に相当する。
図7のステップS48は、上述した実施例1のステップS8,上述した実施例2のステップS18,上述した実施例3のステップ(図5ではステップS28,図6ではステップS38)と同じであるので、その説明については省略する。ステップS48は、本発明における吸収係数値補正工程に相当する。
図8のステップS51は、上述した実施例1のステップS1,上述した実施例2のステップS11,上述した実施例3のステップ(図5ではステップS21,図6ではステップS31)と同じであるので、その説明については省略する。
図8のステップS52は、上述した実施例1のステップS2,上述した実施例2のステップS12,上述した実施例3のステップ(図5ではステップS22,図6ではステップS32)と同じであるので、その説明については省略する。ステップS51,S52は、本発明における再構成計算工程に相当する。
図8のステップS53は、上述した実施例1のステップS3,上述した実施例4のステップS43と同じであるので、その説明については省略する。
図8のステップS54は、上述した実施例1のステップS4,上述した実施例4のステップS44と同じであるので、その説明については省略する。ステップS53,S54は、本発明におけるマスク算出工程に相当する。
図8のステップS55は、上述した実施例1のステップS5,上述した実施例2のステップS15,上述した実施例3のステップ(図5ではステップS25,図6ではステップS35),上述した実施例4のステップS45と同じであるので、その説明については省略する。ステップS55は、本発明におけるオフセット推定工程に相当する。
図8のステップS56は、上述した実施例1のステップS6,上述した実施例2のステップS16,上述した実施例3のステップ(図5ではステップS26,図6ではステップS36),上述した実施例4のステップS46と同じであるので、その説明については省略する。ステップS56は、本発明における参照領域抽出工程に相当する。
上述した実施例1~4では、代表値に基づいて係数αを算出していた。本実施例5では、誤差評価関数に基づいて係数αを算出する。なお、K(≧1)を既知の吸収係数値で近似可能な領域数とし、wn (n=1,…,K)を0以上1以下の係数としたときに、図8では、K=1(つまり、n=1のみ)として領域数を1つのみとし、係数w1=1として説明する。一般化した式については、後述する。
f(α)=DΩ(μknown,μ'+α×μoff) …(4)
図8のステップS48は、上述した実施例1のステップS8,上述した実施例2のステップS18,上述した実施例3のステップ(図5ではステップS28,図6ではステップS38),上述した実施例4のステップS48と同じであるので、その説明については省略する。ステップS58は、本発明における吸収係数値補正工程に相当する。
f(α)=Σn=1,…,K[wn×DΩn(μn known,μ'+α×μoff)] …(5)
3 … γ線検出器
5 … 演算回路
6 … 吸収係数画像推定プログラム
λ',λ2' … 放射能画像
A' … 吸収係数サイノグラム
μ' … (定量的な吸収係数画像に対して不均一なオフセット値が加算された)画像
mimg … 被検体マスク画像
mproj … 被検体マスク投影データ
μoff … (不均一な)オフセット画像
Ω … (既知の吸収係数値で近似可能な)領域
K … 既知の吸収係数値で近似可能な領域数
Ωn … n番目の領域Ω
μn known … 領域Ωnの既知の吸収係数値
S(μ';Ωn) … 領域Ωnにおける画像μ'の代表値
S(μoff;Ωn) … 領域Ωnにおけるオフセット画像μoff'の代表値
α … 係数
αn … 領域Ωnにおける係数α
T(α1,α2,…,αK) … 係数α1,α2,…,αKの代表値
μ … 真の吸収係数画像の値(吸収係数値)
DΩ(μknown,μ'+α×μoff) … 領域Ω内に既知の吸収係数を設定した画像μknownと、定量的な吸収係数画像に対して不均一なオフセット値が加算された画像(μ'+α×μoff)との誤差評価関数
DΩn(μn known,μ'+α×μoff) … 領域Ωn内に既知の吸収係数を設定した画像μn knownと、定量的な吸収係数画像に対して不均一なオフセット値が加算された画像(μ'+α×μoff)との誤差評価関数
wn … (0以上1以下の)係数
f(α) … (係数αを変数とした)関数
Claims (11)
- 消滅放射線の飛行時間差(Time Of Flight)情報を含んだポジトロンCTの計測データから吸収係数画像を推定する方法であって、
μ'を定量的な吸収係数画像に対して不均一なオフセット値が加算された画像とし、前記計測データに関する評価関数の最適化に基づいて、前記画像μ'を計算する再構成計算工程と、
前記計測データに基づいて投影データ空間における被検体マスクデータである被検体マスク投影データを算出するマスク算出工程と、
μoffを不均一なオフセット画像としたときに、オフセット画像μoffの順投影データが被検体マスク投影データを近似するように構成された再構成アルゴリズムによって、前記オフセット画像μoffを推定するオフセット推定工程と、
Ωを既知の吸収係数値で近似可能な領域としたときに、前記計測データに基づいて計算された、被検体領域が認識可能な画像を用いて、前記領域Ωを少なくとも1つ以上抽出する参照領域抽出工程と、
αを係数としたときに、前記領域Ωにおける前記画像μ'の値と既知の吸収係数値との誤差を減少させる前記係数αを算出する係数算出工程と、
前記画像μ'の値に、前記オフセット画像μoffを前記係数α倍したα×μoffを加算して得られた値を吸収係数値として補正する吸収係数値補正工程と
を備える、
吸収係数画像推定方法。 - 請求項1に記載の吸収係数画像推定方法において、
前記再構成計算工程を、(a)前記画像μ'を未知数に含む計算アルゴリズムで実施する、または(b)吸収係数投影データを未知数に含む計算アルゴリズムおよび前記吸収係数投影データを再構成した画像を前記画像μ'とするアルゴリズムの組み合わせで実施する、
吸収係数画像推定方法。 - 請求項1または請求項2に記載の吸収係数画像推定方法において、
(A)前記マスク算出工程は、
前記画像μ'の二値化画像を被検体マスク画像として算出する工程と、
前記被検体マスク画像の投影データを算出する工程と、
前記被検体マスク画像の投影データの二値化データを前記被検体マスク投影データとして算出する工程と
からなる、
または
(B)前記マスク算出工程は、
前記画像μ'の投影データを算出する工程と、
前記画像μ'の投影データの二値化データを前記被検体マスク投影データとして算出する工程と
からなる、
吸収係数画像推定方法。 - 請求項1または請求項2に記載の吸収係数画像推定方法において、
前記マスク算出工程は、
前記計測データを投影データ形式に変換したものを二値化したデータを前記被検体マスク投影データとして算出する工程からなる、
吸収係数画像推定方法。 - 請求項1または請求項2に記載の吸収係数画像推定方法において、
(C)前記マスク算出工程は、
前記計測データに関する評価関数の最適化に基づいて、放射能画像を算出する工程と、
前記放射能画像の投影データを算出する工程と、
前記投影データを二値化したデータを前記被検体マスク投影データとして算出する工程と
からなる、
または
(D)前記マスク算出工程は、
前記計測データに関する評価関数の最適化に基づいて、放射能画像を算出する工程と、
前記放射能画像の二値化画像を算出する工程と、
前記二値化画像の投影データを算出する工程と、
前記二値化画像の投影データを二値化したデータを前記被検体マスク投影データとして算出する工程と
からなる、
吸収係数画像推定方法。 - 請求項1から請求項5のいずれかに記載の吸収係数画像推定方法において、
前記オフセット推定工程で実施する再構成処理は、解析的再構成,統計的再構成,代数的再構成のいずれかの計算方式で実施する、
吸収係数画像推定方法。 - 請求項1から請求項6のいずれかに記載の吸収係数画像推定方法において、
前記参照領域抽出工程において抽出される少なくとも1つ以上の領域Ωは、吸収係数を既知と見なせる組織の領域である、
吸収係数画像推定方法。 - 請求項1から請求項7のいずれかに記載の吸収係数画像推定方法において、
K(≧1)を既知の吸収係数値で近似可能な領域数とし、Ωnをn番目の前記領域Ωとし、μn known (n=1,…,K)を前記領域Ωnの既知の吸収係数値とし、S(X;Ωn)を、前記領域Ωnにおける画像Xの統計量または統計量から算出される値を代表値とし、T(x1,x2,…,xK)を任意のK個の値x1,x2,…,xKの統計量または統計量から算出される値を代表値とし、αnを前記領域Ωnにおける前記係数αとしたときに、前記係数算出工程における前記係数αは、α= T(α1,α2,…,αK),αn=(μn known-S(μ';Ωn))/S(μoff;Ωn) (n=1,…,K)である、
吸収係数画像推定方法。 - 請求項1から請求項7のいずれかに記載の吸収係数画像推定方法において、
K(≧1)を既知の吸収係数値で近似可能な領域数とし、Ωnをn番目の前記領域Ωとし、μn known (n=1,…,K)を前記領域Ωn内に既知の吸収係数を設定した画像とし、DΩn(X,Y)を前記領域Ωn内に関する画像Xおよび画像Yの誤差評価関数とし、wn(n=1,…,K)を0以上1以下の係数としたときに、前記係数算出工程における前記係数αは、関数f(α)= Σn=1,…,K[wn×DΩn(μn known,μ'+α×μoff)]を最小化するαである、
吸収係数画像推定方法。 - 請求項1から請求項9のいずれかに記載の吸収係数画像推定方法をコンピュータに実行させる、吸収係数画像推定プログラム。
- 請求項10に記載の吸収係数画像推定プログラムを搭載したポジトロンCT装置において、
当該吸収係数画像推定プログラムを実行する演算手段を備える、ポジトロンCT装置。
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