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MATLAB and Numerical Analysis
- Dual-energy imaging -
Radiological Imaging SciencesSchool of Mechanical Engineering
Pusan National University
dongwoonkim@pusan.ac.kr
MATLAB and Numerical Analysis
Radiological Imaging Lab
X-ray imaging
2
Mrs. Roentgen, 22 Dec. 1895Taken from I. A. Cunningham’s Slides 22 Sept. 2009
MATLAB and Numerical Analysis
Radiological Imaging Lab
X-ray imaging
digital camera
film camera
film
photodiodearray
Photo+graphy
digital radiography
X-ray ???
Radio+graphy
film radiography / computed radiography
MATLAB and Numerical Analysis
Radiological Imaging Lab
X-ray imaging
4
E (keV)
0 30 60 90 120 150
(cm
-1)
10 -1
10 0
10 1
10 2
10 3
10 4
Cortical bone
Soft tissue
Thickness (cm)0 3 6 9 12 15
Rel
ativ
e si
gnal
0
0.2
0.4
0.6
0.8
1
Cortical bone
Soft tissue
MATLAB and Numerical Analysis
Radiological Imaging Lab
Dual-energy imaging
5
MATLAB and Numerical Analysis
Radiological Imaging Lab
Dual-energy imaging
6
Tissue Bone
Low energy
Tissue Bone
Weighted
Bone enhancedLow energy High energy
Tissue Bone
High energy
Tissue Bone
Enhanced
-
-
=
=
MATLAB and Numerical Analysis
Radiological Imaging Lab
Dual-energy imaging
7
Tissue Bone
Low energy
Tissue enhancedLow energy High energy
Tissue Bone
High energy
Tissue Bone
Enhanced
Tissue Bone
Weighted
-
-
=
=
MATLAB and Numerical Analysis
Radiological Imaging Lab
Single-shot dual-energy imaging
8
Dual-energy imaging is vulnerable to motion artifacts during registration of two successive images
The sandwich detector can avoid motion artifacts by acquiring the high and low images at the same time
Motion artifact Image quality – kVp, 𝑡𝑡𝐼𝐼𝐼𝐼
J. C. Han et al., Curr. Appl. Phys. (2014)
MATLAB and Numerical Analysis
Radiological Imaging Lab
Modeling
A cascaded-systems model describing the signal and noise propagation in sandwich detector
9
D. W. Kim et al., J. Instrum. (2016)
MATLAB and Numerical Analysis
Radiological Imaging Lab
Mouse image using sandwich detector
MATLAB and Numerical Analysis
Radiological Imaging Lab
Neural network
𝑤𝑤 ×− =
𝑊𝑊𝐷𝐷𝐷𝐷𝐷𝐷 ∗𝑤𝑤×
− =
HE LE
HE HE
DE
DNN-DE
MATLAB and Numerical Analysis
Radiological Imaging Lab
Type of neural network
Hidden layer = 1
• Shallow neural network
Hidden layer > 1
• Deep neural network
Regression
MATLAB and Numerical Analysis
Radiological Imaging Lab
Input Image Teaching image
DNN (Deep neural network)
𝑒𝑒
Case 1 Case 2 Case 3 Case 1 Case 2 Case 3
MATLAB and Numerical Analysis
Radiological Imaging Lab
DNN (Parameters)
𝑒𝑒𝑒𝑒
𝑒𝑒
𝑒𝑒
Number of Hidden layers (Nhl)
Number of Hidden nodes (Nhn)Batch size (Sb)
Inputdata
Inputdata
Inputdata
Inputdata
Labeldata
Labeldata
Labeldata
Labeldata
Batch size (Sb)
MATLAB and Numerical Analysis
Radiological Imaging Lab
DNN results
DE images
DNN images
Output images
MATLAB and Numerical Analysis
Radiological Imaging Lab
Assign #2
MATLAB and Numerical Analysis
Radiological Imaging Lab
Assign #2
load Image
data 타입변환
I0 추출
figure,imshow(Image,[low high]) 영상확인
MATLAB and Numerical Analysis
Radiological Imaging Lab
Assign #2영상의좌표및값확인
x, y를자리바꿔입력
MATLAB and Numerical Analysis
Radiological Imaging Lab
Assign #2
𝐼𝐼𝐻𝐻 → Image_H, 𝐼𝐼𝐿𝐿 → Image_L
𝐼𝐼𝐻𝐻0 → I_H0, 𝐼𝐼𝐿𝐿0 → I_L0
write it here 부분구현
• −ln 𝐼𝐼𝐻𝐻𝐼𝐼𝐻𝐻𝐻
+ ln 𝐼𝐼𝐿𝐿𝐼𝐼𝐿𝐿𝐻
또는 ln 𝐼𝐼𝐻𝐻𝐼𝐼𝐻𝐻𝐻
− ln 𝐼𝐼𝐿𝐿𝐼𝐼𝐿𝐿𝐻
𝐴𝐴 = −ln 𝐼𝐼𝐻𝐻𝐼𝐼𝐻𝐻𝐻
+ ln 𝐼𝐼𝐿𝐿𝐼𝐼𝐿𝐿𝐻
;
𝐵𝐵 = −ln 𝐼𝐼𝐻𝐻𝐼𝐼𝐻𝐻𝐻
+ ln 𝐼𝐼𝐿𝐿𝐼𝐼𝐿𝐿𝐻
;
MATLAB and Numerical Analysis
Radiological Imaging Lab
Assign #2
MATLAB and Numerical Analysis
Radiological Imaging Lab
Assign #2
영상정의
weighting factor 정의
반복문을이용하여w에대한 contrast 연산w 간격을바꿔보고영역을바꿔볼것
bgn 영역평균계산 tissue 영역평균계산
수식 (2)
w에따른그래프및 DE 영상
두값을수정하여적절히 display 할것
예시: [𝑚𝑚 − 𝑛𝑛 × 𝜎𝜎 𝑚𝑚 + 𝑛𝑛 × 𝜎𝜎]
𝑚𝑚: 평균𝑛𝑛: 배수
𝜎𝜎:표준편차
최소 w 좌표계산
MATLAB and Numerical Analysis
Radiological Imaging Lab
Assign #2
MATLAB and Numerical Analysis
Radiological Imaging Lab
Assign #2영상 load 및 matrix화수식 (4)의 P matrix
수식 (4)의mu matrix
𝑃𝑃𝐿𝐿𝑃𝑃𝐻𝐻
=𝜇𝜇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝐿𝐿 𝜇𝜇𝑏𝑏𝑏𝑏𝑏𝑏𝑡𝑡𝐿𝐿
𝜇𝜇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝐻𝐻 𝜇𝜇𝑏𝑏𝑏𝑏𝑏𝑏𝑡𝑡𝐻𝐻𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑏𝑏𝑏𝑏𝑏𝑏𝑡𝑡
𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑏𝑏𝑏𝑏𝑏𝑏𝑡𝑡
=𝜇𝜇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝐿𝐿 𝜇𝜇𝑏𝑏𝑏𝑏𝑏𝑏𝑡𝑡𝐿𝐿
𝜇𝜇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝐻𝐻 𝜇𝜇𝑏𝑏𝑏𝑏𝑏𝑏𝑡𝑡𝐻𝐻
−1𝑃𝑃𝐿𝐿𝑃𝑃𝐻𝐻
invMu = 역행렬내장함수(Mu) ;t = invMu*P;
𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑏𝑏𝑏𝑏𝑏𝑏𝑡𝑡
주어진 Gauss.m 파일을이용하여𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑏𝑏𝑏𝑏𝑏𝑏𝑡𝑡
계산
매트랩내장함수를이용하여determinant, condition number를계산
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