Ene 206 matlab laboratory
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ENE 206 MATLAB Laboratory. Lab 3: การใช้ MATLAB สำหรับการสร้างแบบจำลองเพื่อวิเคราะห์ (ต่อ). โจทย์ปัญหาการหาค่าสัมประสิทธิ์การลดทอนของรังสีเอกซ์ในตัวกลางที่มีค่าสัมประสิทธิ์ไม่คงที่.

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ENE 206 MATLAB Laboratory

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Ene 206 matlab laboratory

ENE 206 MATLAB Laboratory

Lab 3: MATLAB ()


Ene 206 matlab laboratory

(X-ray)

0.2I0

0.3I0

I0

0.4I0

0.1I0


Ene 206 matlab laboratory

I0 x I0ex

I0

0.2I0 = I0ex

x


Ene 206 matlab laboratory

()

0.2I0 = I0e(1x1 + 2x2 + 3x3 + 4x4)

x

0.2I0 = I0e(1 + 2 + 3 + 4) x

I0

0.2I0

x1

x2

x3

x4


Ene 206 matlab laboratory

I0

16

0.2I0

0.3I0

I0

0.4I0

0.1I0

0.4I0

0.5I0

0.1I0

0.3I0


Ene 206 matlab laboratory


Ene 206 matlab laboratory

()

16


Ene 206 matlab laboratory

Inverse method

= A-1b

inverse A rank(A)

8 8 rank(A) < 16

underdetermined


Algebraic reconstruction technique art

(Algebraic Reconstruction Technique: ART)

I0

underdetermined

(iterative algorithm)

0.2I0

0.3I0

I0

0.4I0

0.1I0

0.4I0

0.5I0

0.1I0

0.3I0


Ene 206 matlab laboratory


Ene 206 matlab laboratory

ART1:

  • 1 (x = 1)

    *** A


Ene 206 matlab laboratory

ART2:

  • ()

  • (update) I1 1

    1 1 + 1

    2 2 + 1

    3 3 + 1

    4 4 + 1

0.2I0 I1

0.3I0 I2

0.4I0 I3

0.1I0 I4

0.4I0

0.5I0

0.1I0

0.3I0


Ene 206 matlab laboratory


Ene 206 matlab laboratory

I1

I2, I3, I4 2, 3, 4


Ene 206 matlab laboratory

ART2:

  • 1, 2, 3, 4 I1, I2, I3, I4

0.2I0 I1

0.3I0 I2

0.4I0 I3

0.1I0 I4


Ene 206 matlab laboratory

ART2:

  • I1, I2, I3, I4 I5, I6, I7, I8

0.2I0 I1

0.3I0 I2

0.4I0 I3

0.1I0 I4

0.22I0

0.22I0

0.22I0

0.22I0


Ene 206 matlab laboratory

  • (Minimized Square Error per pixel)

    MSE/pixel = [(0.2I0 0.2I0)2 + (0.4I0 0.4I0)2 + (0.3I0 0.3I0)2 + (0.1I0 0.1I0)2 + (0.22I0 0.3I0)2 + (0.22I0 0.1I0)2 + (0.22I0 0.5I0)2 + (0.22I0 0.4I0)2 +] / 8

    MSE/pixel = 0.0325I02


Ene 206 matlab laboratory

ART2:

  • I5, I6, I7, I8 ( )

    MSE/pixel = 0.005I02

0.25I0

0.38I0

0.5I0

0.12I0

0.4I0

0.5I0

0.1I0

0.3I0


Ene 206 matlab laboratory

ART2:

  • ( 1)


Ene 206 matlab laboratory

  • ART ART MSE/pixel 0.00001I02 plot MSE/pixel (iteration) ART

I0

0.2I0

0.3I0

I0

0.4I0

0.1I0

0.4I0

0.5I0

0.1I0

0.3I0


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