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Statistical and Computational Methods in Brain Image Analysis [Kõva köide]

4.67/5 (3 hinnangut Goodreads-ist)
(University of Wisconsin-Madison, USA)
Teised raamatud teemal:
Statistical and Computational Methods in Brain Image AnalysisSuurem pilt
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781439836354.html
Märksõnad:
The massive amount of nonstandard high-dimensional brain imaging data being generated is often difficult to analyze using current techniques. This challenge in brain image analysis requires new computational approaches and solutions. But none of the research papers or books in the field describe the quantitative techniques with detailed illustrations of actual imaging data and computer codes. Using MATLAB® and case study data sets, Statistical and Computational Methods in Brain Image Analysis is the first book to explicitly explain how to perform statistical analysis on brain imaging data.

The book focuses on methodological issues in analyzing structural brain imaging modalities such as MRI and DTI. Real imaging applications and examples elucidate the concepts and methods. In addition, most of the brain imaging data sets and MATLAB codes are available on the authors website.

By supplying the data and codes, this book enables researchers to start their statistical analyses immediately. Also suitable for graduate students, it provides an understanding of the various statistical and computational methodologies used in the field as well as important and technically challenging topics.

Arvustused

"The writing style is pleasing and the book has the important virtue of using a consistent mathematical notation and terminology throughout the book, unlike collections of chapters from various authors that are usually published on this kind of topic. One important and interesting aspect of this book is the use of MATLAB code to illustrate the theory that the author is developing. In addition, the data mentioned in the text are provided so that the reader can experiment and learn using the same examples as the ones described in the book. This provides an excellent supplement and will appeal to students starting in the field as well as researchers wanting to refresh their knowledge or learn more about some aspects of brain analysis. a very good book to have in a lab, and it is a pleasure to recommend it." Australian & New Zealand Journal of Statistics, 56(4), 2014

" a great new reference text to the field of structural brain imaging. The presence of MATLAB code will make it easy for people to play around with the various data formats and more easily get involved in this exciting field. As a researcher already involved in neuroimaging data analysis, I have a feeling that this is a book I will return to often as a reference source, and I am happy to have it as part of my library." Martin A. Lindquist, Journal of the American Statistical Association, September 2014, Vol. 109

Preface xv
1 Introduction to Brain and Medical Images
1(20)
1.1 Image Volume Data
2(4)
1.1.1 Amygdala Volume Data
4(2)
1.2 Surface Mesh Data
6(5)
1.2.1 Topology of Surface Data
6(3)
1.2.2 Amygdala Surface Data
9(2)
1.3 Landmark Data
11(4)
1.3.1 Affine Transforms
11(2)
1.3.2 Least Squares Estimation
13(2)
1.4 Vector Data
15(2)
1.5 Tensor and Curve Data
17(2)
1.6 Brain Image Analysis Tools
19(2)
1.6.1 SurfStat
20(1)
1.6.2 Public Image Database
20(1)
2 Bernoulli Models for Binary Images
21(8)
2.1 Sum of Bernoulli Distributions
21(2)
2.2 Inference on Proportion of Activation
23(4)
2.2.1 One Sample Test
23(3)
2.2.2 Two Sample Test
26(1)
2.3 MATLAB Implementation
27(2)
3 General Linear Models
29(22)
3.1 General Linear Models
29(3)
3.1.1 R-square
31(1)
3.1.2 GLM for Whole Brain Images
32(1)
3.2 Voxel-Based Morphometry
32(8)
3.2.1 Mixture Models
34(2)
3.2.2 EM-Algorithm
36(1)
3.2.3 Two-Components Gaussian Mixture
37(3)
3.3 Case Study: VBM in Corpus Callosum
40(9)
3.3.1 White Matter Density Maps
42(1)
3.3.2 Manipulating Density Maps
42(3)
3.3.3 Numerical Implementation
45(4)
3.4 Testing Interactions
49(2)
4 Gaussian Kernel Smoothing
51(16)
4.1 Kernel Smoothing
51(1)
4.2 Gaussian Kernel Smoothing
52(2)
4.2.1 Fullwidth at Half Maximum
53(1)
4.3 Numerical Implementation
54(3)
4.3.1 Smoothing Scalar Functions
54(1)
4.3.2 Smoothing Image Slices
55(2)
4.4 Case Study: Smoothing of DWI Stroke Lesions
57(2)
4.5 Effective FWHM
59(1)
4.6 Checking Gaussianness
60(3)
4.6.1 Quantile-Quantile Plots
60(1)
4.6.2 Quantiles
60(1)
4.6.3 Empirical Distribution
61(1)
4.6.4 Normal Probability Plots
61(1)
4.6.5 MATLAB Implementation
62(1)
4.7 Effect of Gaussianness on Kernel Smoothing
63(4)
5 Random Fields Theory
67(18)
5.1 Random Fields
67(4)
5.1.1 Gaussian Fields
68(1)
5.1.2 Derivative of Gaussian Fields
69(1)
5.1.3 Integration of Gaussian Fields
70(1)
5.1.4 t, F and X2 Fields
70(1)
5.2 Simulating Gaussian Fields
71(2)
5.3 Statistical Inference on Fields
73(5)
5.3.1 Bonferroni Correction
75(1)
5.3.2 Rice Formula
76(2)
5.3.3 Poisson Clumping Heuristic
78(1)
5.4 Expected Euler Characteristics
78(7)
5.4.1 Intrinsic Volumes
79(1)
5.4.2 Euler Characteristic Density
80(2)
5.4.3 Numerical Implementation of Euler Characteristics
82(3)
6 Anisotropic Kernel Smoothing
85(16)
6.1 Anisotropic Gaussian Kernel Smoothing
85(3)
6.1.1 Truncated Gaussian Kernel
87(1)
6.2 Probabilistic Connectivity in DTI
88(1)
6.3 Riemannian Metric Tensors
89(2)
6.4 Chapman-Kolmogorov Equation
91(4)
6.5 Cholesky Factorization of DTI
95(2)
6.6 Experimental Results
97(1)
6.7 Discussion
98(3)
7 Multivariate General Linear Models
101(20)
7.1 Multivariate Normal Distributions
101(4)
7.1.1 Checking Bivariate Normality of Data
103(1)
7.1.2 Covariance Matrix Factorization
104(1)
7.2 Deformation-Based Morphometry (DBM)
105(3)
7.3 Hotelling's T2 Statistic
108(3)
7.4 Multivariate General Linear Models
111(3)
7.4.1 SurfStat
113(1)
7.5 Case Study: Surface Deformation Analysis
114(7)
7.5.1 Univariate Tests in SurfStat
116(3)
7.5.2 Multivariate Tests in SurfStat
119(2)
8 Cortical Surface Analysis
121(28)
8.1 Introduction
121(2)
8.2 Modeling Surface Deformation
123(3)
8.3 Surface Parameterization
126(4)
8.3.1 Quadratic Parameterization
126(3)
8.3.2 Numerical Implementation
129(1)
8.4 Surface-Based Morphological Measures
130(5)
8.4.1 Local Surface Area Change
131(1)
8.4.2 Local Gray Matter Volume Change
132(2)
8.4.3 Cortical Thickness Change
134(1)
8.4.4 Curvature Change
135(1)
8.5 Surface-Based Diffusion Smoothing
135(4)
8.6 Statistical Inference on the Cortical Surface
139(3)
8.7 Results
142(6)
8.7.1 Gray Matter Volume Change
143(1)
8.7.2 Surface Area Change
143(1)
8.7.3 Cortical Thickness Change
144(3)
8.7.4 Curvature Change
147(1)
8.8 Discussion
148(1)
9 Heat Kernel Smoothing on Surfaces
149(14)
9.1 Introduction
149(1)
9.2 Heat Kernel Smoothing
150(6)
9.3 Numerical Implementation
156(3)
9.4 Random Field Theory on Cortical Manifold
159(1)
9.5 Case Study: Cortical Thickness Analysis
160(2)
9.6 Discussion
162(1)
10 Cosine Series Representation of 3D Curves
163(22)
10.1 Introduction
163(3)
10.2 Parameterization of 3D Curves
166(4)
10.2.1 Eigenfunctions of 1D Laplacian
167(1)
10.2.2 Cosine Representation
167(1)
10.2.3 Parameter Estimation
168(1)
10.2.4 Optimal Representation
169(1)
10.3 Numerical Implementation
170(2)
10.4 Modeling a Family of Curves
172(3)
10.4.1 Registering 3D Curves
172(1)
10.4.2 Inference on a Collection of Curves
173(2)
10.5 Case Study: White Matter Fiber Tracts
175(5)
10.5.1 Image Acquisition
175(1)
10.5.2 Image Processing
176(1)
10.5.3 Cosine Series Representation
177(1)
10.5.4 Two Sample T-test
177(1)
10.5.5 Hotelling's T-square Test
178(1)
10.5.6 Simulating Curves
178(2)
10.6 Discussion
180(5)
10.6.1 Similarly Shaped Tracts
180(1)
10.6.2 Gibbs Phenomenon
180(5)
11 Weighted Spherical Harmonic Representation
185(34)
11.1 Introduction
185(2)
11.2 Spherical Coordinates
187(1)
11.3 Spherical Harmonics
188(12)
11.3.1 Weighted Spherical Harmonic Representation
190(4)
11.3.2 Estimating Spherical Harmonic Coefficients
194(2)
11.3.3 Validation Against Heat Kernel Smoothing
196(4)
11.4 Weighted-SPHARM Package
200(5)
11.5 Surface Registration
205(5)
11.5.1 MATLAB Implementation
207(3)
11.6 Encoding Surface Asymmetry
210(4)
11.7 Case Study: Cortical Asymmetry Analysis
214(3)
11.7.1 Descriptions of Data Set
214(2)
11.7.2 Statistical Inference on Surface Asymmetry
216(1)
11.8 Discussion
217(2)
12 Multivariate Surface Shape Analysis
219(28)
12.1 Introduction
219(3)
12.2 Surface Parameterization
222(4)
12.2.1 Flattening of Simulated Cube
224(2)
12.3 Weighted Spherical Harmonic Representation
226(2)
12.3.1 Optimal Degree Selection
226(2)
12.4 Gibbs Phenomenon in SPHARM
228(5)
12.4.1 Overshoot in Gibbs Phenomenon
232(1)
12.4.2 Simulation Study
233(1)
12.5 Surface Normalization
233(4)
12.5.1 Validation
236(1)
12.6 Image and Data Acquisition
237(2)
12.7 Results
239(3)
12.7.1 Amygdala Volumetry
239(1)
12.7.2 Local Shape Difference
239(2)
12.7.3 Brain and Behavior Association
241(1)
12.8 Discussion
242(1)
12.8.1 Anatomical Findings
242(1)
12.9 Numerical Implementation
243(4)
13 Laplace-Beltrami Eigenfunctions for Surface Data
247(28)
13.1 Introduction
247(1)
13.2 Heat Kernel Smoothing
248(4)
13.2.1 Heat Kernel Smoothing in 2D Images
250(2)
13.3 Generalized Eigenvalue Problem
252(5)
13.3.1 Finite Element Method
252(4)
13.3.2 Fourier Coefficients Estimation
256(1)
13.4 Numerical Implementation
257(3)
13.5 Experimental Results
260(5)
13.5.1 Image Acquisition and Preprocessing
260(1)
13.5.2 Validation of Heat Kernel Smoothing
261(4)
13.6 Case Study: Mandible Growth Modeling
265(9)
13.6.1 Diffeomorphic Surface Registration
266(1)
13.6.2 Random Field Theory
267(1)
13.6.3 Numerical Implementation
268(6)
13.7 Conclusion
274(1)
14 Persistent Homology
275(20)
14.1 Introduction
275(2)
14.2 Rips Filtration
277(5)
14.2.1 Topology
277(2)
14.2.2 Simplex
279(1)
14.2.3 Rips Complex
279(1)
14.2.4 Constructing Rips Filtration
280(2)
14.3 Heat Kernel Smoothing of Functional Signal
282(1)
14.4 Min-max Diagram
283(6)
14.4.1 Pairing Rule
286(1)
14.4.2 Algorithm
287(2)
14.5 Case Study: Cortical Thickness Analysis
289(4)
14.5.1 Numerical Implementation
290(2)
14.5.2 Statistical Inference
292(1)
14.6 Discussion
293(2)
15 Sparse Networks
295(24)
15.1 Introduction
295(1)
15.2 Massive Univariate Methods
296(2)
15.3 Why Are Sparse Models Needed?
298(2)
15.4 Persistent Structures for Sparse Correlations
300(6)
15.4.1 Numerical Implementation
304(2)
15.5 Persistent Structures for Sparse Likelihood
306(3)
15.6 Case Study: Application to Persistent Homology
309(3)
15.6.1 MRI Data and Univariate-TBM
309(2)
15.6.2 Multivariate-TBM via Barcodes
311(1)
15.6.3 Connection to DTI Study
311(1)
15.7 Sparse Partial Correlations
312(5)
15.7.1 Partial Correlation Network
312(2)
15.7.2 Sparse Network Recovery
314(1)
15.7.3 Sparse Network Modeling
314(1)
15.7.4 Application to Jacobian Determinant
315(1)
15.7.5 Limitations of Sparse Partial Correlations
316(1)
15.8 Summary
317(2)
16 Sparse Shape Models
319(16)
16.1 Introduction
319(1)
16.2 Amygdala and Hippocampus Shape Models
320(1)
16.3 Data Set
321(1)
16.4 Sparse Shape Representation
322(2)
16.5 Case Study: Subcortical Structure Modeling
324(2)
16.5.1 Traditional Volumetric Analysis
325(1)
16.5.2 Sparse Shape Analysis
325(1)
16.6 Statistical Power
326(3)
16.6.1 Type-II Error
326(1)
16.6.2 Statistical Power for t-Test
327(2)
16.7 Power Under Multiple Comparisons
329(4)
16.7.1 Type-I Error Under Multiple Comparisons
330(1)
16.7.2 Type-II Error Under Multiple Comparisons
330(3)
16.7.3 Statistical Power of Sparse Representation
333(1)
16.8 Conclusion
333(2)
17 Modeling Structural Brain Networks
335(16)
17.1 Introduction
335(1)
17.2 DTI Acquisition and Preprocessing
336(1)
17.3 ε-Neighbor Construction
337(3)
17.4 Node Degrees
340(1)
17.5 Connected Components
341(3)
17.6 ε-Filtration
344(1)
17.7 Numerical Implementation
345(4)
17.7.1 Fiber Bundle Visualization
346(1)
17.7.2 ε-Neighbor Network Construction
346(3)
17.7.3 Network Computation
349(1)
17.8 Discussion
349(2)
18 Mixed Effects Models
351(12)
18.1 Introduction
351(1)
18.2 Mixed Effects Models
352(11)
18.2.1 Fixed Effects Model
353(1)
18.2.2 Random Effects Model
354(2)
18.2.3 Restricted Maximum Likelihood Estimation
356(1)
18.2.4 Case Study: Longitudinal Image Analysis
357(3)
18.2.5 Functional Mixed Effects Models
360(3)
Bibliography 363(34)
Index 397
Moo K. Chung, Ph.D. is an associate professor in the Department of Biostatistics and Medical Informatics at the University of Wisconsin-Madison. He is also affiliated with the Waisman Laboratory for Brain Imaging and Behavior. He has won the Vilas Associate Award for his applied topological research (persistent homology) to medical imaging and the Editors Award for best paper published in Journal of Speech, Language, and Hearing Research. Dr. Chung received a Ph.D. in statistics from McGill University. His main research area is computational neuroanatomy, concentrating on the methodological development required for quantifying and contrasting anatomical shape variations in both normal and clinical populations at the macroscopic level using various mathematical, statistical, and computational techniques.