Image Processing Reference
In-Depth Information
4
Estimation of Signal
and Noise Parameters
from MR Data
A.J. den Dekker and J. Sijbers
CONTENTS
4.1
Introduction................................................................................................86
4.2
PDFs in MRI .............................................................................................87
4.2.1
Gaussian PDF ................................................................................87
4.2.1.1
Moments of the Gaussian PDF......................................88
4.2.1.2
Central Moments............................................................88
4.2.2
Rician PDF ....................................................................................88
4.2.2.1
Asymptotic Approximation of the
Rician Distribution .........................................................89
4.2.2.2
Moments of the Rician PDF ..........................................90
4.2.2.3
Moments of the Rayleigh PDF ......................................91
4.2.2.4
Generalized Rician PDF ................................................91
4.2.2.5
Moments of the Generalized Rician PDF .....................92
4.2.2.6
PDF of Squared Magnitude Data ..................................93
4.2.3
PDF of Phase Data ........................................................................94
4.3
Parameter Estimation.................................................................................96
4.3.1
Performance Measures of Estimators ...........................................96
4.3.2
Precision ........................................................................................96
4.3.3
Accuracy ........................................................................................97
4.3.4
MSE ...............................................................................................97
4.3.5
CRLB .............................................................................................97
4.3.6
ML Estimation...............................................................................98
4.4
Signal Amplitude Estimation ....................................................................99
4.4.1
Introduction....................................................................................99
4.4.2
Signal Amplitude Estimation from Complex Data.....................101
4.4.2.1
Region of Constant Amplitude and Phase...................101
4.4.2.2
Region of Constant Amplitude and Different Phases ...103
4.4.3
Signal Amplitude Estimation from Magnitude Data ..................105
4.4.3.1
Region of Constant Amplitude and Known
Noise Variance..............................................................106
85
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