# Image Quality Lecture 2

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```					                                       Image Quality
Lecture 2

Thomas Liu
UCSD Center for Functional MRI
Resident Physics Course
April 3, 2006

Image Quality, T.T. Liu, Spring 2006

Topics

Review MTF question
Noise
Sampling and Aliasing

Image Quality, T.T. Liu, Spring 2006

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MTF = Fourier Transform (LTF)

Bushberg et al 2001
Image Quality, T.T. Liu, Spring 2006

Image Quality, T.T. Liu, Spring 2006

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Noise and Image Quality

Bushberg et al 2001

Image Quality, T.T. Liu, Spring 2006

What is Noise?
Fluctuations in either the imaging system or the object
being imaged.
Quantization Noise: Due to conversion from analog
waveform to digital number.
Quantum Noise: Random ﬂuctuation in the number of
photons emitted and recorded.
Thermal Noise: Random ﬂuctuations present in all
electronic systems. Also, sample noise in MRI
Other types: ﬂicker, burst, avalanche - observed in
semiconductor devices.
Structured Noise: physiological sources, interference

Image Quality, T.T. Liu, Spring 2006

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Histograms and Distributions

Bushberg et al 2001

Image Quality, T.T. Liu, Spring 2006

Gaussian Distribution

Bushberg et al 2001

1, 2, and 3 standard deviation intervals correspond to 68%,
95%, and 99% of the observations
Image Quality, T.T. Liu, Spring 2006

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Poisson Process
Events occur at random instants of time at an average rate
of λ events per second.
Examples: arrival of customers to an ATM, emission of
photons from an x-ray source, lightning strikes in a
thunderstorm.

" = Average rate of events per second
"t = Average number of events at time t
"t = Variance in number of events

! Image Quality, T.T. Liu, Spring 2006

Quantum Noise

For a Poisson process, the mean = variance, i.e. X = " 2
Therefore, the standard deviation is given by " = X

For X - ray systems, if the mean number of counts is N, then the
standard deviation in the number of counts is " = N .

N
SNR =        = N.
"

!
Image Quality, T.T. Liu, Spring 2006

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Image Quality, T.T. Liu, Spring 2006

Bushberg et al 2001

Poisson Distribution describes x - ray counting statistics.
Gaussian distribution is good approximation to Poisson when " = X

Image Quality, T.T. Liu, Spring 2006
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Image Quality, T.T. Liu, Spring 2006

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Image Quality, T.T. Liu, Spring 2006

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Contrast Resolution

Bushberg et al 2001
Lower row shows effect of structure noise

Image Quality, T.T. Liu, Spring 2006

Image Quality, T.T. Liu, Spring 2006

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TP
Sensitivity =
TP + FN
= Fraction of people who have the disease who test positive

TN
Specificity =
TN + FP
= Fraction of people who do not have the disease who test negative

TP
Positive Predictive Value =
TP + FP
= Probability patient is actually abnormal when diagnosed as abnormal

TN
Negative Predictive Value =
TN + FN
= Probability patient is actually normal when diagnosed as normal.

!
Image Quality, T.T. Liu, Spring 2006

TP
True Positive Fraction =
TP + FN
= Sensitivity
= Probability of Detection

FP
False Positive Fraction =
FP + TN
=1-Specificity
= Probability of False Alarm

!        Receiver operating characteristic (ROC) curve plots True
Positive Fraction vs. False Positive Fraction

Image Quality, T.T. Liu, Spring 2006

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Detection

Image Quality, T.T. Liu, Spring 2006

Detection

Area is a measure of detectability
Image Quality, T.T. Liu, Spring 2006

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Image Quality, T.T. Liu, Spring 2006

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1
Nyquist Frequency = FN =               Sampling Pitch
2"
If f > FN , then aliasing will occur

!

Image Quality, T.T. Liu, Spring 2006

Image Quality, T.T. Liu, Spring 2006

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Image Quality, T.T. Liu, Spring 2006

Sampling in Image Space

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Sampling in k-space

Image Quality, T.T. Liu, Spring 2006

Image Quality, T.T. Liu, Spring 2006

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Smoothing of Projections in CT

Projection

Beam                                     W= 2/(Δs)
Width                                    δ=1/W= Δs/2
2/(Δs)

Smoothed
Projection

Image Quality, T.T. Liu, Spring 2006                  Suetens 2002

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