1. 核醫游離輻射偵測與成像原理
Rad iatio n D etectio n an d I n str u men tation o f N M
Camus C.Y. Wu 吳志毅
Medical radiation technologist 醫事放射師
Department of Nuclear Medicine and Molecular Imaging C.G.M.H. 長庚醫院核子醫學科
46. PET影像構成必須包括三組資訊:
① Emission data
② Attenuation correction factor (ACF)
μ Transmission scan
μ blank scan
③ Normalization data
average count rate for entire scanner
measured count rate for this LOR
=
=
50. 2~3 nS
1. True events
2. Random B
~ CTW max
1. Scatter
2. Randoms :
2-1. Rand. A + Rand. B
2-2. ∵ Rand. B >>> Rand. A, ∴Randoms≒Rand.B
2-3. RAB = 2τNANB
Essential Nuclear Medicine Physics, Rachel A. Powsner and Edward R. Powsner, Blackwell Publishing Ltd
52. 由PEC(PET electronics cabinet;
bucket controllerGIM)送出的訊
號頻率約160MHz,這些訊號
(包含經放大的衰減校正訊號)必須
透過CDA(clock distribution
assembly)平均分配並且透過光
纖以固定週期(一般約100nS)
傳送給各個bucket或DEA.
SIEMENSCTI ECAT ACCEL training course
GE DLSDST training course
61. Image of t2
EmissionCT
t
Image of t1
Raw
sinogram
LOR(x,y,z,t)
PositronEmissionTomograpgy
Acq. Mode: Frame List
Matrix size: 128x128, 256x256, 344x344
stop conditions: Preset Time
70. Simple is not Easy
Easy is a minimum amount of effort to produce a result.
Simple is very hard. Simple is the removal of everything except what matters.
73. Iterative Reconstruction
• Treat imaging as just another statistical estimation problem:
– I is the image vector (one point per pixel, or N2 elements).
– P is the data vector (one point per sinogram element, ~N2 long).
– H is a matrix:
• H represents a probability transition matrix (“from a pixel in the I matrix, what is
the probability I will put a count into bin m of the P matrix?”).
• Projection geometry embedded in H.
• A large matrix (~N4 elements), but relatively sparse (kN3 elements populated).
– n is the noise vector.
.
n
HI
P
74. ML-EM Algorithm
• Algorithm Task: Given P, find I that gives the “best fit” to the
available data.
• If we consider “best fit” to mean “statistical likelihood”, and we
assume all elements of P to be independent Poisson variables, then
an iterative procedure described by:
will converge to the maximum likelihood image.
.
n
HI
P
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75. 1. Forward project image to estimate what data should be.
2. Compare data estimate to actual data by taking ratio.
3. Backproject ratio to compute updates to image space.
☆ Each iteration represents one forward projection and one backprojection.
4. Update image by multiplication.
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76. 25
25
1.00 1.167
1.333 1.5
Backprojected ratios
1.25
0.75
1.75
1.00 1.50 1.25
5 10
15 20
“True Image”
15
35 Data (noiseless)
10 10
10 10
First Image
20
20
20 20
20 20
Forward-Projected Data
0.75
1.75
1.00 1.50
1.25 1.25
Ratio of Data to Estimate
10.00 11.67
13.33 15.00
Updated Image
20 30
78. Ordered Subsets EM (OSEM) Algorithm
• Concept: Do forward and backprojection over a subset of
the projections at once.
• One pass through all subsets is equivalent to one iteration of
MLEM.
• Using updated image on subsequent subsets improves
convergence
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79. OSEM convergence
☆ OSEM convergence is typically accelerated by the
number of subsets per iteration. (A little faster in this idealized case)
MLEM convergence