BME 210
Spring 2008
Name: ____________Solution____________
MIDTERM EXAMINATION #2
(1 hr 15 min)
(15 points)
1.
Consider the 9 element pixel grid shown below with the 10 projections indicted. Write down the
W matrix
for these projects, such that
W
s
μ
=
(
,
s
μ
are the vectors of CT numbers and
projections). When a ray sum goes through a pixel, assume it goes through that pixel’s center and
therefore use a value of 1 for the weight for that pixel.
S
1
S
2
S
3
S
4
S
5
μ
1
μ
2
μ
3
μ
4
μ
5
μ
6
μ
7
μ
8
μ
9
S
6
S
7
S
8
S
9
S
10
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
W
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=
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1
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(15 points)
2.
Solve the following system of equations for
1
2
3
,
, and
μ
μ
μ
using forward and backward
substitution. Follow the process
of the forward and backward substitution algorithms.
1
2
3
1
0
0
3
2
1
4
5
1
11
1
0
0
10
3
3
3
3
1
45
5
1
0
0
3
3
�
� �
�
�
� �
�

μ
� � � �
�
� �
�
� � � �
�
� �
�

μ
=
� � � �
�
� �
�
� � � �
μ

�
� �
�
� � � �
�
� �
�


�
� �
�
Let
1
1
2
2
3
3
3
2
1
1
11
0
3
3
45
0
0
3
y
y
y
μ
μ
μ
�
�

� �
� �
�
�
� �
� �
�
�

=
� �
� �
�
�
� �
� �
�
�
� �
� �
�
�
�
�
Therefore,
1
2
3
1
0
0
4
5
1
0
10
3
3
1
5
1
3
y
y
y
�
�
� � � �
�
�
� � � �
�
�
=
� � � �
�
�
� � � �

�
�
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 Spring '07
 D'Argenio
 matlab, Least Squares, TI, Zürich Hauptbahnhof, backward substitution

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