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Theory and Methods

Generalized Scalar-on-Image Regression Models via Total Variation

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Pages 1156-1168 | Received 01 Sep 2014, Published online: 13 Apr 2017

References

  • Candès, W., Romberg, J., and Tao, T. (2006a), “Stable Signal Recovery From Incomplete and Inaccurate Measurements,” Communications on Pure and Applied Mathematics, 59, 1027–1023.
  • ——— (2006b), “Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information,” IEEE Transactions on Information Theory, 52, 489–509.
  • Chen, S., Donoho, D. L., and Saunders, M. (1998), “Atomic Decomposition for Basis Pursuit,” SIAM Journal on Scientific Computing, 20, 33–61.
  • Colom, R., Stein, J. L., Rajagopalan, P., Martńez, K., Hermel, D., Wang, Y., Alvarez Linera, J., Burgaleta, M., A., Quiroga, M., Shih, P. C., and Thompson, P. M. (2013), “Hippocampal Structure and Human Cognition: Key Role of Spatial Processing and Evidence Supporting the Efficiency Hypothesis in Females,” Intelligence, 41, 129–140.
  • Crambes, C., Kneip, A., and Sarda, P. (2009), “Smoothing Splines Estimators for Functional Linear Regression,” Annals of Statistics, 37, 35–72.
  • De La Torre, J. C. (2010), “Alzheimer’s Disease is Incurable But Preventable,” Journal of Alzheimer’s Disease, 20, 861–870.
  • Du, P., and Wang, X. (2014), “Penalized Likelihood Functional Regression,” Statistica Sinica, 24, 1017–1041.
  • Fan, J., and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties,” Journal of the American Statistical Association, 96, 1348–1360.
  • Fennema-Notestine, C., Hagler, D. J. Jr, McEvoy, L. K., Fleisher, A. S., Wu, E. H., Karow, D. S., Dale, A. M.; Alzheimer’s Disease Neuroimaging Initiative. (2009), “Structural MRI Biomarkers for Preclinical and Mild Alzheimer’S Disease,” Human Brain Mapping, 30, 3238–3253.
  • Ferraty, F., and Vieu, P. (2006), Nonparametric Functional Data Analysis: Theory and Practice, New York: Springer-Verlag Inc.
  • Friedman, J. T., Hastie, H., and Tibshirani, R. (2007), “Pathwise Coordinate Optimization,” Annals of Applied Statistics, 1, 302–332.
  • Gertheiss, J., Maity, A., and Staicu, A. M. (2013), “Variable Selection in Generalized Functional Linear Model,” Stat, 2, 86–101.
  • Goldsmith, J., Bobb, J., Crainiceanu, C. M., Caffo, B., and Reich, D. (2010), “Penalized Functional Regression,” Journal of Computational and Graphical Statistics, 20, 830–851.
  • Guillas, S., and Lai, M. J. (2010), “Bivariate Splines for Spatial Functional Regression Models,” Journal of Nonparametric Statistics, 22, 477–497.
  • Hall, P., and Horowitz, J. L. (2007), “Methodology and Convergence Rates for Functional Linear Regression,” Annals of Statistics, 35, 70–91.
  • James, G. M. (2002), “Generalized Linear Models With Functional Predictors,” Journal of the Royal Statistical Society, Series B, 64, 411–432.
  • James, G. M., Wang, J., and Zhu, J. (2009), “Functional Linear Regression That’s Interpretable,” Annals of Statistics, 37, 2083–2108.
  • Hestenes, M. R. (1969), “Multiplier and Gradient Methods, Journal of Optimization Theory and Applications,” in Computing Methods in Optimization Problems (vol. 4), eds. L. A. Zadeh, L. W. Neustadt, and A. V. Balakrishnan, New York: Academic Press, pp. 303–320
  • Li, Y., Wang, N., and Carroll, R. J. (2010), “Generalized Functional Linear Models With Semi Parametric Single-Index Interactions,” Journal of the American Statistical Association, 105, 621–633.
  • Li, C. (2013), “Compressive Sensing for 3D Data Processing Tasks: Applications, Model and Algorithms,” Ph.D. Dissertation, Rice University.
  • Lorensen, W. E., and Cline, H. E. (1987), “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” in Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 87, pp. 163–169.0
  • Luders, E., Thompson, P. M., Kurth, F., Hong, J. Y., Phillips, O. R., Wang, Y., Gutman, B. A., Chou, Y. Y., Narr, K. L., and Toga, A. W. (2013), “Global and Regional Alterations of Hippocampal Anatomy in Long-Term Meditation Practitioners,” Human Brain Mapping, 34, 3369–3375.
  • Mammen, E., and van de Geer, S. (1997), “Locally Adaptive Regression Splines,” Annals of Statistics, 25, 387–413.
  • Michel, V., Gramfort, A., Varoquaux, G., Eger, E., and Thirion, B. (2011), “Total Variation Regularization for fMRI-Based Prediction of Behavior,” IEEE Transactions on Medical Imaging, 30, 1328–1340.
  • Mu, Y., and Gage, F. (2011), “Adult Hippocampal Neurogenesis and Its Role in Alzheimer’s Disease,” Molecular Neurodegeneration, 6, 85.
  • Müller, H. G., and Stadtmüller, U. (2005), “Generalized Functional Linear Models,” Annals of Statistics, 33, 774–805.
  • Needell, D., and Ward, R. (2013), “Stable Image Reconstruction Using Total Variation Minimization,” SIAM Journal of Imaging Sciences, 6, 1035–1058.
  • Nelder, J., and Wedderburn, R. (1972), “Generalized Linear Models,” Journal of the Royal Statistical Society, Series A, 135, 370–384.
  • Patenaude, B., Smith, S. M., Kennedy, D. N., and Jenkinson, M. (2011), “A Bayesian Model of Shape and Appearance for Subcortical Brain Segmentation,” NeuroImage, 56, 907–922.
  • Petrushev, P. P., Cohen, A., Xu, H., and DeVore, R. (1999), “Nonlinear Approximation and the Space BV(R2),” American Journal of Mathematics, 121, 587–628.
  • Pizer, S., Fritsch. D., Yushkevich, P., Johnson, C., and Chaney, E. (1999), “Segmentation, Registration, and Measurement of Shape Variation via Image Object Shape,” IEEE Transactions on Medical Imaging, 18, 851–865.
  • Powell, M. J. D. (1969), “A Method for Nonlinear Constraints in Minimization Problems,” in Optimization, ed. R. Fletcher, London, New York: Academic Press, pp. 283–298.
  • Ramsay, J. O., and Silverman, B. W. (2005), Functional Data Analysis, New York: Springer-Verlag Inc.
  • Reiss, P. T., Huo, L., Zhao, Y., Kelly, C., and Ogden, R. T. (2015), “Wavelet-Domain Regression and Predictive Inference in Psychiatric Neuroimaging,” Annals of Applied Statistics, 9, 1076–1101.
  • Reiss, P. T., and Ogden, R. T. (2007), “Functional Principal Component Regression and Functional Partial Least Squares,” Journal of the American Statistical Association, 102, 984–996.
  • ——— (2010), “Functional Generalized Linear Models With Images as Predictors,” Biometrics, 66, 61–69.
  • Rudin, L. I., and Osher, S. (1994), “Total Variation Based Image Restoration With Free Local Constraints,” Proceedings of the 1st IEEE ICIP, 1, 31–35.
  • Rudin, L. I., Osher, S., and Fatemi, E. (1992), “Nonlinear Total Variation Noise Removal Algorithm,” Physica D, 60, 259–268.
  • Shi, J., Lepore, N., Gutman, B., Thompson, P. M., Baxter, L., Caselli, R. J., and Wang, Y. (2014), “Genetic Influence of APOE4 Genotype on Hippocampal Morphometry—An N=725 Surface-Based ADNI Study,” Human Brain Mapping, 35, 3902–3918.
  • Shi, J., Thompson, P. M., Gutman, B., and Wang, Y. (2013), “Surface Fluid Registration of Conformal Representation: Application to Detect Disease Burden and Genetic Influence on Hippocampus,” NeuroImage, 78, 111–134.
  • Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
  • ——— (2014), “Adaptive Piecewise Polynomial Estimation via Trend Filtering,” Annals of Statistics, 42, 285–323.
  • Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., and Knight, K. (2005), “Sparsity and Smoothness via the Fused Lasso,” Journal of the Royal Statistical Society, Series B, 67, 91–108.
  • Vidakovic, B. (1999), Statistical Modeling by Wavelets, New York: Wiley.
  • Wang, X., Nan, B., Zhu, J., Koppe, R., and ADNI (2014), “Regularized 3D Functional Regression for Brain Image Data via Haar Wavelets,” Annals of Applied Statistics, 8, 1045–1064.
  • Wang, Y., Zhang, J., Gutman, B., Chan, T. F., Becker, J. T., Aizenstein, H. J., Lopez, O. L., Tamburo, R. J., Toga, A. W., and Thompson, P. M. (2010), “Multivariate Tensor Based Morphometry on Surfaces: Application to Mapping Ventricular Abnormalities in HIV/AIDS,” NeuroImage, 49, 2141–2157.
  • Weiner, M. W., Veitcha, D. P., Aisen, P. S., Beckett, L. A., Cairnsh, N. J., Green, R. C., Harvey, D., Jack, C. R., Jagust, W., Liu, E., Morris, J. C., Petersen, R. C., Saykino, A. J., Schmidt, M. E., Shaw, L., Siuciak, J. A., Soares, H., Toga, A. W., Trojanowski, J. Q., and ADNI (2012), “The Alzheimer’s Disease Neuroimaging Initiative: A Review of Papers Published Since Its Inception,” Alzheimers and Dementia, 8, S1–S68.
  • Yuan, M., and Cai, T. T. (2010), “A Reproducing Kernel Hilbert Space Approach to Functional Linear Regression,” Annals of Statistics, 38, 3412–3444.
  • Zhao, Y., Ogden, R. T., and Reiss, P. T. (2014), “Wavelet-Based LASSO in Functional Linear Regression,” Journal of Computational and Graphical Statistics, 21, 600–617.
  • Zhou, H., and Li, L. (2014), “Regularized Matrix Regression,” Journal of Royal Statistical Society, Series B, 76, 463–483.
  • Zhou, H., Li, L., and Zhu, H. (2013), “Tensor Regression with Applications in Neuroimaging Data Analysis,” Journal of the American Statistical Association, 108, 540–552.
  • Zhu, H., Fan, J., and Kong, L. (2014), “Spatially Varying Coefficient Model for Neuroimaging Data With Jump Discontinuities,” Journal of the American Statistical Association, 109, 977–990.

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