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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
Receiver Operating Characteristics
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
Prince and Links 2005
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
3rd grade heights 6th grade heights
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
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
Image Quality, T.T. Liu, Spring 2006
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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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