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

Lab 3: MATLAB ()


(X-ray)

0.2I0

0.3I0

I0

0.4I0

0.1I0


I0 x I0ex

I0

0.2I0 = I0ex

x


()

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

x

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

I0

0.2I0

x1

x2

x3

x4


I0

16

0.2I0

0.3I0

I0

0.4I0

0.1I0

0.4I0

0.5I0

0.1I0

0.3I0



()

16


Inverse method

= A-1b

inverse A rank(A)

8 8 rank(A) < 16

underdetermined


(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



ART1:

  • 1 (x = 1)

    *** A


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



I1

I2, I3, I4 2, 3, 4


ART2:

  • 1, 2, 3, 4 I1, I2, I3, I4

0.2I0 I1

0.3I0 I2

0.4I0 I3

0.1I0 I4


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


  • (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


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


ART2:

  • ( 1)


  • 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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