Deconvolution When Classifying Noisy Data Involving Transformations

REFERENCES

• Besag , J. 1986 . “On the Statistical-Analysis of Dirty Pictures,” . Journal of the Royal Statistical Society, Series B , 48 : 259 – 302 .
   Google Scholar
• Cannon , M. 1976 . “Blind Deconvolution of Spatially Invariant Image Blurs With Phase,” . IEEE Transactions on Acoustics, Speech and Signal Processing , 24 : 58 – 63 .
   Google Scholar
• Cannon , T. M. and Hunt , B. R. 1981 . “Image Processing by Computer,” . Scientific American , 245 : 214 – 225 .
   Web of Science ®Google Scholar
• Carasso , A. S. 2001 . “Direct Blind Deconvolution,” . SIAM Journal on Applied Mathematics , 61 : 1980 – 2007 .
   Web of Science ®Google Scholar
• Cressie , N. and Kornak , J. 2003 . “Spatial Statistics in the Presence of Location Error With an Application to Remote Sensing of the Environment,” . Statistical Science , 18 : 436 – 456 .
   Web of Science ®Google Scholar
• Crosilla , F. , Visintini , D. and Sepic , F. 2007 . “An Automatic Classification and Robust Segmentation Procedure of Spatial Objects,” . Statistical Methods and Applications , 15 : 329 – 341 .
   Google Scholar
• Dass , S. C. and Nair , V. N. 2003 . “Edge Detection, Spatial Smoothing, and Image Reconstruction with Partially Observed Multivariate Data,” . Journal of the American Statistical Association , 98 : 77 – 89 .
   Web of Science ®Google Scholar
• Delaigle , A. and Hall , P. 2012a . “Methodology and Theory for Partial Least Squares Applied to Functional Data,” . The Annals of Statistics , 40 : 322 – 352 .
   Web of Science ®Google Scholar
• Delaigle , A. and Hall , P. 2012b . “Componentwise Classification and Clustering of Functional Data,” . Biometrika , 99 ( 2 ) : 299 – 313 .
   Web of Science ®Google Scholar
• Donoho , D. L. 1994 . “Statistical Estimation and Optimal Recovery,” . The Annals of Statistics , 22 : 238 – 270 .
   Web of Science ®Google Scholar
• Figueiredo , M. A. T. and Nowak , R. D. 2003 . “An EM Algorithm for Wavelet-Based Image Restoration,” . IEEE Transactions on Image Processing , 12 : 906 – 916 .
   PubMed Web of Science ®Google Scholar
• Friedman , J. H. 1996 . “Another Approach to Polychotomous Classification,” . Technical Report, available at http://www-stat.stanford.edu/jhf/ftp/poly.pdf
   Google Scholar
• Galatsanos , N. P. , Mesarović , V. Z. , Molina , R. , Katsaggelos , A. K. and Mateos , J. 2002 . “Hyperparameter Estimation in Image Restoration Problems With Partially Known Blurs,” . Optical Engineering , 41 : 1845 – 1854 .
   Web of Science ®Google Scholar
• Hall , P. 1990 . “Optimal Convergence Rates in Signal Recovery,” . The Annals of Probability , 18 : 887 – 900 .
   Web of Science ®Google Scholar
• Hall , P. and Qiu , P. 2007a . “Blind Deconvolution and Deblurring in Image Analysis,” . Statistica Sinica , 17 : 1483 – 1509 .
   Web of Science ®Google Scholar
• Hall , P. and Qiu , P. 2007b . “Nonparametric Estimation of a Point Spread Function in Multivariate Problems,” . The Annals of Statistics , 35 : 1512 – 1534 .
   Web of Science ®Google Scholar
• Huang , H. C. and Cressie , N. 2000 . “Deterministic/Stochastic Wavelet Decomposition for Recovery of Signal From Noisy Data,” . Technometrics , 42 : 262 – 276 .
   Web of Science ®Google Scholar
• Huang , X. F. and Qiu , P. 2010 . “Blind Deconvolution for Jump-Preserving Curve Estimation,” . Mathematical Problems in Engineering , [online], Article No. 350849, doi 10.1155/2010/350849
   Web of Science ®Google Scholar
• James , G. and Hastie , T. 2001 . “Functional Linear Discriminant Analysis for Irregularly Sampled Curves,” . Journal of the Royal Statistical Society, Series B , 63 : 533 – 550 .
   Google Scholar
• Johnstone , I. M. 1990 . “Speed of Estimation in Positron Emission Tomography and Related Inverse Problems,” . The Annals of Statistics , 18 : 251 – 280 .
   Web of Science ®Google Scholar
• Joshi , M. V. and Chaudhuri , S. 2005 . “Joint Blind Restoration and Surface Recovery in Photometric Stereo,” . Journal of the Optical Society of America , A22 : 1066 – 1076 .
   Google Scholar
• Klein , R. and Press , S. J. 1992 . “Adaptive Bayesian Classification of Spatial Data,” . Journal of the American Statistical Association , 87 : 844 – 851 .
   Web of Science ®Google Scholar
• Kundur , D. and Hatzinakos , D. 1998 . “A Novel Blind Deconvolution Scheme for Image Restoration Using Recursive Filtering,” . IEEE Transactions on Signal Processing , 46 : 375 – 389 .
   Web of Science ®Google Scholar
• McLachlan , G. J. , Do , K. A. and Ambroise , C. 2004 . Analyzing Microarray Gene Expression Data , Hoboken, , NJ : Wiley .
   Google Scholar
• Mukherjee , P. S. and Qiu , P. 2011 . “3-D Image Denoising by Local Smoothing and Nonparametric Regression,” . Technometrics , 53 : 196 – 208 .
   Web of Science ®Google Scholar
• Popescu , D. C. and Hellicar , A. D. 2010 . “Point Spread Function Estimation for a Terahertz Imaging System,” . EURASIP Journal on Advances in Signal Processing , [online], Article No. 575817, doi 10.1155/2010/575817
   Web of Science ®Google Scholar
• Qiu , P. 2005 . Image Processing and Jump Regression Analysis , New York : Wiley .
   Google Scholar
• Qiu , P. 2007 . “Jump Surface Estimation, Edge Detection, and Image Restoration,” . Journal of the American Statistical Association , 102 : 745 – 756 .
   Web of Science ®Google Scholar
• Qiu , P. 2008 . “A Nonparametric Procedure for Blind Image Deblurring,” . Computational Statistics and Data Analysis , 52 : 4828 – 4841 .
   Web of Science ®Google Scholar
• Shi , T. and Cressie , N. 2007 . “Global Statistical Analysis of MISR Aerosol Data: A Massive Data Product From NASA's Terra Satellite,” . Environmetrics , 18 : 665 – 680 .
   Web of Science ®Google Scholar
• Shin , H. 2008 . “An Extension of Fisher's Discriminant Analysis for Stochastic Processes,” . Journal of Multivariate Analysis , 99 : 1191 – 1216 .
   Web of Science ®Google Scholar
• Warren , R. E. , Vanderbeek , R. G. , Ben-David , A. and Ahl , J. L. 2008 . “Simultaneous Estimation of Aerosol Cloud Concentration and Spectral Backscatter From Multiple-Wavelength Lidar Data,” . Applied Optics , 47 : 4309 – 4320 .
   PubMed Web of Science ®Google Scholar