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E-raamat: Statistical Analysis of Noise in MRI: Modeling, Filtering and Estimation

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 12-Jul-2016
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319399348
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Statistical Analysis of Noise in MRI: Modeling, Filtering and EstimationSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 12-Jul-2016
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319399348
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This unique text presents a comprehensive review of methods for modeling signal and noise in magnetic resonance imaging (MRI), providing a systematic study, classifying and comparing the numerous and varied estimation and filtering techniques. Features: provides a complete framework for the modeling and analysis of noise in MRI, considering different modalities and acquisition techniques; describes noise and signal estimation for MRI from a statistical signal processing perspective; surveys the different methods to remove noise in MRI acquisitions from a practical point of view; reviews different techniques for estimating noise from MRI data in single- and multiple-coil systems for fully sampled acquisitions; examines the issue of noise estimation when accelerated acquisitions are considered, and parallel imaging methods are used to reconstruct the signal; includes appendices covering probability density functions, combinations of random variables used to derive estimators, and us

eful MRI datasets.

The Problem of Noise in MRIPart I: Noise Models and the Noise Analysis ProblemAcquisition and Reconstruction of Magnetic Resonance ImagingStatistical Noise Models for MRINoise Analysis in MRI: OverviewNoise Filtering in MRIPart II: Noise Analysis in Non-Accelerated AcquisitionsNoise Estimation in the Complex DomainNoise Estimation in Single-Coil MR DataNoise Estimation in Multiple-Coil MR DataParametric Noise Analysis from Correlated Multiple-Coil MR DataPart III: Noise Estimators in pMRIParametric Noise Analysis in Parallel MRIBlind Estimation of Non-Stationary Noise in MRIAppendix A: Probability Distributions and Combination of Random VariablesAppendix B: Variance Stabilizing TransformationAppendix C: Data Sets Used in the Experiments

Arvustused

The book is presented in a simple and lucid manner, starting with the basics of MRI noise and its analysis with simple models, progressing to an analysis using complex models and the noise issues in multi-coil and parallel acquisition schemes. Overall the book is self-contained to help the beginners . (Pramod Kumar Pisharady, IAPR Newsletter , Vol. 40 (2), 2018)

1 The Problem of Noise in MRI
1(8)
1.1 Thermal Noise in Magnetic Resonance Imaging
1(3)
1.2 Organization of the Book
4(5)
Part I Noise Models and the Noise Analysis Problem
2 Acquisition and Reconstruction of Magnetic Resonance Imaging
9(22)
2.1 Physics of Magnetic Resonance Imaging
10(2)
2.2 The k-Space and the x-Space
12(2)
2.3 Single-Coil Acquisition Process
14(1)
2.4 Multiple-Coil Acquisition Process
15(4)
2.5 Accelerated Acquisitions: Parallel Imaging
19(10)
2.5.1 The Problem of Acceleration: Subsampling
19(4)
2.5.2 Sensitivity Encoding (SENSE)
23(2)
2.5.3 Generalized Autocalibrating Partially Parallel Acquisition (GRAPPA)
25(2)
2.5.4 Other pMRI Methods
27(2)
2.6 Final Remarks
29(2)
3 Statistical Noise Models for MRI
31(42)
3.1 Complex Single-and Multiple-Coil MR Signals
31(2)
3.2 Single-Coil MRI Data
33(2)
3.3 Fully Sampled Multiple-Coil Acquisition
35(7)
3.3.1 Uncorrected Multiple-Coil with SoS
35(2)
3.3.2 Correlated Multiple-Coil with SoS
37(3)
3.3.3 Multiple-Coil with SMF Reconstruction
40(2)
3.4 Statistical Models for pMRI Acquisitions
42(12)
3.4.1 General Noise Models in pMRI
42(4)
3.4.2 Statistical Model in SENSE Reconstructed Images
46(2)
3.4.3 Statistical Model in GRAPPA Reconstructed Images
48(6)
3.5 Some Practical Examples
54(15)
3.5.1 Single-Coil Acquisitions
54(1)
3.5.2 Multiple-Coil Acquisitions
54(6)
3.5.3 pMRI Acquisitions
60(9)
3.6 Final Remarks
69(4)
4 Noise Analysis in MRI: Overview
73(16)
4.1 The Problem of Noise Estimation: An Introductory Example
74(4)
4.1.1 A Practical Problem
74(1)
4.1.2 Analysis of the Data
74(1)
4.1.3 Estimation Procedure
75(2)
4.1.4 Other Estimation Issues
77(1)
4.2 Main Issues About Noise Analysis in MRI
78(7)
4.2.1 The Noise Model of the Data
78(1)
4.2.2 The Stationarity of the Noise
79(2)
4.2.3 The Background
81(1)
4.2.4 Quantification of Data
82(1)
4.2.5 Single Versus Multiple Sample Estimation
83(1)
4.2.6 Practical Implementation
83(2)
4.3 Noise Analysis Practical Methodology
85(4)
5 Noise Filtering in MRI
89(34)
5.1 Noise Filtering and Signal Estimation in MRI
89(3)
5.2 The Importance of Noise Filtering
92(4)
5.3 Noise Suppression/Reduction Methods
96(15)
5.3.1 Noise Correction During the Acquisition
96(2)
5.3.2 Generic Filtering Algorithms
98(5)
5.3.3 Transform Domain Filters
103(2)
5.3.4 Statistical Methods
105(4)
5.3.5 Some Examples
109(2)
5.4 Case Study: The LMMSE Signal Estimator
111(8)
5.4.1 Original Formulation: Signal Estimation for the General Rician Model
111(2)
5.4.2 Extension to Multiple Samples
113(1)
5.4.3 Recursive LMMSE Filter
114(1)
5.4.4 Extension to nc-Χ Data
114(1)
5.4.5 Extension for an Specific Application: DWI Filtering
115(4)
5.5 Some Final Remarks
119(4)
Part II Noise Analysis in Nonaccelerated Acquisitions
6 Noise Estimation in the Complex Domain
123(88)
6.1 Single-Coil Estimation
124(7)
6.2 Multiple-Coil Estimation
131(3)
6.2.1 Variance in Each Coil
131(1)
6.2.2 Covariance Matrix and Correlation Coefficient
131(2)
6.2.3 Reconstruction Process
133(1)
6.3 Non-stationary Noise Analysis
134(1)
6.4 Examples and Performance Evaluation
134(7)
7 Noise Estimation in Single-Coil MR Data
141(32)
7.1 Noise Estimators for Rayleigh/Rician Data
142(11)
7.1.1 Estimators Based on a Rayleigh Background
142(5)
7.1.2 Estimators Based on the Signal Area
147(6)
7.2 Estimators Based on Local Moments: A Detailed Study
153(7)
7.3 Performance of the Estimators
160(10)
7.3.1 Performance Evaluation with Synthetic Data
160(4)
7.3.2 Performance Evaluation Over Real Data
164(6)
7.4 Final Remarks
170(3)
8 Noise Estimation in Multiple-Coil MR Data
173(14)
8.1 Uncorrelated Data and SMF Reconstruction
174(1)
8.2 Noise Estimation Assuming a nc-Χ Distribution
174(6)
8.2.1 Estimators Based on a c-Χ Background
175(2)
8.2.2 Estimators Based on the Signal Area
177(3)
8.3 Performance of the Estimators
180(5)
8.3.1 Performance Evaluation with Synthetic Data
180(3)
8.3.2 Performance Evaluation Over Real Data
183(2)
8.4 Final Remarks About the Estimators
185(2)
9 Parametric Noise Analysis from Correlated Multiple-Coil MR Data
187(24)
9.1 Parametric Noise Estimation for Correlated Multiple-Coil with SMF
188(3)
9.1.1 Background-Based Estimation
189(1)
9.1.2 Estimation Based on Signal Area
190(1)
9.2 Noise Estimation for Correlated SoS
191(6)
9.2.1 Estimation of σ
193(1)
9.2.2 Estimation of Effective Values
194(2)
9.2.3 Simplified Estimation
196(1)
9.3 Performance of the Estimators
197(9)
9.3.1 Correlated Coils with SMF
197(3)
9.3.2 Correlated Coils with SoS
200(2)
9.3.3 In Vivo Data
202(4)
9.4 Final Remarks
206(5)
Part III Noise Estimators in pMRI
10 Parametric Noise Analysis in Parallel MRI
211(18)
10.1 Noise Estimation in SENSE
212(3)
10.2 Noise Estimation in GRAPPA with SMF Reconstruction
215(1)
10.3 Noise Estimation in GRAPPA with SoS Reconstruction
215(5)
10.3.1 Practical Simplifications over the GRAPPA Model
216(1)
10.3.2 Noise Estimator
217(1)
10.3.3 Estimation of Effective Values in GRAPPA
218(1)
10.3.4 Gaussian Simplification
219(1)
10.4 Examples and Performance of the Estimators
220(7)
10.4.1 Noise Estimation in SENSE
220(3)
10.4.2 Noise Estimation in GRAPPA
223(4)
10.5 Final Remarks
227(2)
11 Blind Estimation of Non-stationary Noise in MRI
229(46)
11.1 Non-stationary Noise Estimation in MRI
230(19)
11.1.1 Non-stationary Gaussian Noise Estimators
231(5)
11.1.2 Rician Estimators
236(9)
11.1.3 Noncentral Χ Estimation
245(2)
11.1.4 Estimation Along Multiple MR Scans
247(2)
11.2 A Homomorphic Approach to Non-stationary Noise Estimation
249(7)
11.2.1 The Gaussian Case
249(2)
11.2.2 The Rayleigh Case
251(2)
11.2.3 The Rician Case
253(3)
11.3 Performance of the Estimators
256(17)
11.3.1 Non-stationary Rician Noise
256(13)
11.3.2 Non-stationary Nc-Χ Noise
269(4)
11.4 Final Remarks
273(2)
Appendix A Probability Distributions and Combination of Random Variables 275(20)
Appendix B Variance-Stabilizing Transformation 295(10)
Appendix C Data Sets Used in the Experiments 305(6)
References 311(12)
Index 323
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