EE640 STOCHASTIC SYSTEMS
SPRING 2016
COMPUTER PROJECT 1B
PART B: ANALYSIS (updated 4-20-16)
Use the ui and gi Nx1 lexicographical vectors from Project 1A for the following problems.
1.
(a) Generate independent identically distributed test vectors. The target vectors are:
t I 1  g1  3
tI 2  g2  4
(B-1a)
t I 3  g3  2
and the clutter vectors are:
cI 1  g 4 1
cI 2  g 5 1
(B-1b)
cI 3  g 6 1
(b) Generate correlated test vectors. Three vectors will represent target class data and
three vectors will represent clutter class data. The 3 target vectors are:
t 1  4 g 1  2 g 2  g 3  10
t 2  g 1  4 g 2  2 g 3  21
(B-2a)
t 3  2 g 1  g 2  4 g 3  28
and the clutter vectors are:
c1  4 g 4  2 g 5  g 6  7
c2  g 4  4g 5  2g 6  7
(B-2b)
c3  2g 4  g 5  4g 6  7
2.
Histogram: Design a program, or use the MATLAB function hist.m, that will estimate
the histogram of random image intensity values. Have the program use specified M bin
intervals. Run the program and plot for:
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u1 , g 1
PlotB - 2 s1 , s 2 , s3 , s4 , s5
PlotB - 3
t I1 , c I1
PlotB - 4
t I2 , c I2
histogram
PlotB - 5
histogram
PlotB - 1
3.
t I3 , c I3
histogram
histogram
histogram
Covariance estimate: Estimate covariance matrices (3x3)
Kt from t1,t2,t3
Kc from c1,c2,c3
KtI from tI1,tI2,tI3
KcI from cI1,cI2,cI3
such that:
K(m,n) 
1
( xm -  m )T ( xn -  n )
N  1
(B-3)
where m is an Nx1 vector with all elements equal to the mean value of the vector xm and K(m,n)
is the mth, nth element of the matrix K.
4.
Estimate mean vectors (3x1) from
t I1 , t I2 , t I3
(B-4)
such that
  t ,1 


 t   t ,2 
  t ,3 
(B-5)
where
 t ,i 
1 N
 t I ,i  m 
N m 1
(B-6)
likewise for clutter, use
c I1 , c I2 , c I3
(B-7)
to generate
  c,1 


 c   c,2 
  c,3 
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5. Use one of the target images and corresponding control noise image from Project 1.A.2. Find
the histogram of the deterministic image intensity and also find the histogram of the associated
control noise intensity. Are these histograms different? Why?
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