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Digital Image Processing Homework 4: ML and MMSE Estimation, Exercises of Digital Signal Processing

Sam Higginbottom Institute of Agriculture, Technology and SciencesDigital Signal Processing

Two problems related to maximum likelihood (ml) and minimum mean squared error (mmse) estimation in the context of digital image processing. The first problem involves estimating the parameter θ from i.i.d. Random variables xi with given probabilities. The second problem deals with estimating x when the observed data y is a noisy version of x.

Typology: Exercises

2012/2013

Uploaded on 05/18/2013

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ECE-S490 Digital Image Processing
Homework 4
1. Let {Xi}Ni=1 be i.i.d. R.V. with distribution
P(Xi=1) = θ
P(Xi=0) = 1-θ
Compute the ML estimate of θ.
2. Let X, N, Y be random vectors such that
X ~ N(0,Rx)
N ~ N(0,Rn)
θ deterministic
a) Compute ML estimate of θ when Y= θ+N
b) Compute MMSE estimate of X when Y=X+N
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ECE-S490 Digital Image Processing

Homework 4

  1. Let {Xi}Ni=1 be i.i.d. R.V. with distribution P(Xi=1) = θ P(Xi=0) = 1-θ Compute the ML estimate of θ.
  2. Let X, N, Y be random vectors such that X ~ N(0,Rx) N ~ N(0,Rn) θ deterministic a) Compute ML estimate of θ when Y= θ+N b) Compute MMSE estimate of X when Y=X+N

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