Instructor

Moo K. Chung, Associate Professor of Biostatistics and Medical Informatics
Office: Waisman Center #437
Email: mkchung@wisc.edu
Personal Webpage: www.stat.wisc.edu/~mchung
 
Guest lecturers

Vikas Singh, Chalres Dyer, Michael Coen and Andrew Alexander.

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Prerequisites

Two semesters of statistics (Statistics 309-310)  or  Biostatistics (571-572) courses, or the consent of instructor.


Target Audience

The course is designed for graduate and advanced undergraduate students, and researchers with strong quantitative skills. The course material is applicable to a wide variety of statistical problems in medical and biological images.


Motivation for Course

There is no course of this kind currently offered in the campus although Moo Chung has previously offered several topics courses (Stat 692: Medical Image Analysis, Stat 992: Statistical Methods in Signal and Image Analysis). Stat 992 mainly focused on the mathematical/statistical modeling aspect of medical image analysis while Stat 692 focused more on the applied aspects of medical image analysis. The proposed course will be based on a combination of course materials from the two courses. The demand from students, staff and faculty is exploding as many are increasingly involved in collecting various medical imaging data, but there are no courses to train students and researchers on how to analyze medical images quantitatively. Most imaging courses from other department deal mainly with image processing or image acquisition and do not provide relevant in-depth statistical content to students.

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Course Aim

Present statistical and other quantitative techniques used in analyzing various medical images. A concise review of relevant methodological background will be presented. Basic concepts of key methods will be developed with considerable attention to analysis of real imaging data of various types and problems. Students and researchers should gain a deeper understanding of statistical methods used in medical image analysis. Course projects will be designed to apply methods learned from classes to medical images provided by an instructor or students themselves.

Course Content

This course will give a concise review of relevant statistical background needed in advanced medical image analysis. Students will be introduced to key concepts and methods used in analyzing various medical images and imaging related problems. Statistical concepts include general linear model, mixture model, maximum likelihood, discriminant analysis, longitudinal analysis, time series, multiple comparisons (permutation test, false discovery rates, random fields theory), Fourier and wavelet methods. The concepts will be applied to various medical imaging data and problems. Aimed at any graduate and senior undergraduate students, and researchers with strong quantitative skills seeking to gain a deeper understanding of quantitative medical image analysis techniques.

Course Evaluation

Students are required to do homework (15%), submit a final research project report (70%) and do an oral presentation (15%) at the end of the semester. Students can use their own medical images for the final project after consultation with the instructor. For students without their own data set, the final project topics and data set will be provided. Sample final project reports can be found here.

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Course Outline
Below is an outline of 7 topics that will be covered for 45 hours of lectures.

Statistical computing: Image data format and data import/export. Statistical computing in R and MATLAB including Bootstrap and MCMC. Application to medical image simulation (7 hours).

Hilbert space methods: Introduction to Hilbert space theory. Karhunen-Loeve expansion and functional principal component analysis (PCA). Partial differential equations (PDE) used in image analysis. Fourier and wavelet analyses. Application to modeling various anatomical objects (7 hours)

Multiple comparisons: General linear model (GLM), Bonferroni correction, Worsley’s random field theory, permutation tests and false discovery rates (FDR). Sample size computation in correlated images, Application to statistical parametric mapping (SPM) technique (6 hours)

Time series analysis: AR models. Nonparametric regression. Fourier transform, Application to functional imaging (4 hours)

Correlation methods: Multiple, partial and canonical correlations. Nonparametric correlations. Application to correlating imaging to nonimaging measures (5 hours)

Multivariate methods: Gaussian and Poisson mixture models, maximum likelihood techniques, linear and logistic discriminant analysis, cross-validation. Application to classifying clinical image population (6 hours)

Longitudinal analysis: Mixed effect models, functional data analysis, Application to longitudinal image modeling (4 hours)

Guest lectures: three guest lecturers will talk about their research on medical image analysis (3 hours)

Student presentation: Students will present their final research projects at the end of semester (3 hours).

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Reading List
Important reading materials are marked with *.

*1.    Dalgaard, P. 2002. Introductory Statistics with R. Springer.

2.    Dougherty, E.R. 1999. Random Processes for Image and Signal Processing. IEEE Press.

3.    Adler, R.J. and Taylor, J.E. 2008. Random Fields and Geometry, Springer.

*4.    Poline, J.-B., Friston, K.J., Worsley, K.J. and Frackowiak, R.S.J. 1995. Estimating Smoothness in Statistical Parametric Maps: Confidence Intervals on p-Values. Journal of Computer Assisted Tomography 19(5):788-796.

5.    F. Riesz and B. Sz.-Nagy, 1955. Functional Analysis, Dover.

6.    Wahba, G. 1990. Spline Models for Observational Data. SIAM.

7.    Rao, C.R. and Toutenburg, H. 1999. Linear Models, Springer-Verlag. NewYork.

*8.    Genovese, C.R., Lazar, N.A. and Nichols, T.E. 2002. Thresholding of statistical maps in functional neuroimaging using the false discovery rate. NeuroImage. 15:870-878.

*9.    Nichols, T.E. and Holmes, A.P. 2002. Nonparametric permutation tests for functional neuroimaging experiments: a primer with examples. Human Brain Mapping. 15:1-25.

*10.    Friston, K.J., Holmes, A.P., Worsley, K.J.,  Poline, J.B., Frith, C., Frackowiak., R.S.J. 1995. Statistical Parametric Maps in Functional Imaging: A General Linear Approach. Human Brain Mapping, 2:189-210.

11.    Robert, C.P and Casella, G. 1999. Monte Carlo Statistical Methods, Springer.

12.    Sapiro, G. 2001. Geometric Partial Differential Equations and Image Analysis. Cambridge University Press.

13.    Boothby, W.M. 1986. An Introduction to Differential Manifolds and Riemannian Geometry. Academic Press, London, 2nd. Edition

14.    Joshi, S.C., Miller, M.I., Grenander, U. 1997. On the geometry and shape of brain sub-manifolds, Int. J. Pattern Recog. Art. Intell. 11:1317-1343.

15.    Sochen, N., Kimmel, R. and Malladi, R. A. 1999. General Framework for Low Level Vision. IEEE Transactions on Image Processing, 7:310-318

16.    Staib, L.H. 1996. Model based deformable surface finding for medical images. IEEE Transactions on Medical Imaging 15:720-731.

*17.    Taubin, G. 1995. Curve and surface smoothing without shrinkage. The Proceedings of the Fifth International Conference on Computer Vision, 852-857, 1995.

*18.    Friston K.J., Holmes A.P., Poline J.B., Grasby P.J., Williams S.C.R., Frackowiak R.S.J., Turner R. 1995. Analysis of fMRI Time Series Revisited. Neuroimage 2:45-53.

*19.    Worsley, K.J. 2003. Detecting activation in fMRI data. Statistical Methods in Medical Research, 12:401-418.

*20.    Worsley, K.J.1997. An overview and some new developments in the statistical analysis of PET and fMRI data Human Brain Mapping. 5:254-258.

21.    Ozkan, M., Dawant, B.M., and Maciunas, R.J. 1993. Neural-Network-Based Segmentation of Multi-Modal Medical Images: a Comparative and Prospective Study. IEEE Trans. Med. Imaging, 12:534—544.

22.    Sled, J.G., Zijdenbos, A.P., and Evans, A.C. 1988. A Nonparametric Method for Automatic Correction of Intensity Nonuniformity in MRI Data. IEEE Trans. on Medical Imaging, 17:87-97.

23.    Sethian., J. A. 1996. Level Set Methods and Fast Marching Methods. Cambridge University Press.

*24.    Hastie, T., Tibshirani, R., Friedman, J. 2001. The elements of statistical learning. Springer. New York.

25.    Lafferty, J. and Lebanon, G. 2004. Diffusion kernels on statistical manifolds by Technical Report CMU-CS-04-101, School of Computer Science, CMU.

*26.    Ramsay and Silverman, 1997. Functional Data Analysis. Springer.

*27.    Muller, H.-G. 2005. Functional modeling and classification of longitudinal data. Scandinavian Journal of Statistics. 32:223-240.

28.    Kirby, M. 2001. Geometric data analysis. John Wiley & Sons, Inc.

*29.    Martinez, W.L, Martinez, A.R. 2007. Computational Statistics Handbook with MATLAB, 2nd edition. Chapman & Hall/CRC.

*30.    Friston, K. 2007. Statistical parametric mapping. Academic Press.

*31.     Mallat, S. 1999. A wavelet tour of signal processing.  Academic Press.