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MATLAB and Numerical Analysis - Dual-energy imaging - Radiological Imaging Sciences School of Mechanical Engineering Pusan National University [email protected]

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Page 1: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

MATLAB and Numerical Analysis

- Dual-energy imaging -

Radiological Imaging SciencesSchool of Mechanical Engineering

Pusan National University

[email protected]

Page 2: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

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

Page 3: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

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

Page 4: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

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

Page 5: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

MATLAB and Numerical Analysis

Radiological Imaging Lab

Dual-energy imaging

5

Page 6: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

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

-

-

=

=

Page 7: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

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

-

-

=

=

Page 8: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

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)

Page 9: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

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)

Page 10: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

MATLAB and Numerical Analysis

Radiological Imaging Lab

Mouse image using sandwich detector

Page 11: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

MATLAB and Numerical Analysis

Radiological Imaging Lab

Neural network

𝑤𝑤 ×− =

𝑊𝑊𝐷𝐷𝐷𝐷𝐷𝐷 ∗𝑤𝑤×

− =

HE LE

HE HE

DE

DNN-DE

Page 12: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

MATLAB and Numerical Analysis

Radiological Imaging Lab

Type of neural network

Hidden layer = 1

• Shallow neural network

Hidden layer > 1

• Deep neural network

Regression

Page 13: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

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

Page 14: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

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)

Page 15: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

MATLAB and Numerical Analysis

Radiological Imaging Lab

DNN results

DE images

DNN images

Output images

Page 16: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

MATLAB and Numerical Analysis

Radiological Imaging Lab

Assign #2

Page 17: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

MATLAB and Numerical Analysis

Radiological Imaging Lab

Assign #2

load Image

data 타입변환

I0 추출

figure,imshow(Image,[low high]) 영상확인

Page 18: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

MATLAB and Numerical Analysis

Radiological Imaging Lab

Assign #2영상의좌표및값확인

x, y를자리바꿔입력

Page 19: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

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

;

Page 20: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

MATLAB and Numerical Analysis

Radiological Imaging Lab

Assign #2

Page 21: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

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

Page 22: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

MATLAB and Numerical Analysis

Radiological Imaging Lab

Assign #2

Page 23: MATLAB and Numerical Analysisbml.pusan.ac.kr/LectureFrame/Lecture/Undergraduates... · 2018-04-24 · MATLAB and Numerical Analysis. Radiological Imaging Lab. Single-shot dual-energy

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