Wavelets on graphs via spectral graph theory

Shapiro, 1993, Embedded image coding using zerotrees of wavelet coefficients, IEEE Trans. Signal Process., 41, 3445, 10.1109/78.258085 Said, 1996, A new, fast, and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans. Circuits Syst. Video Technol., 6, 243, 10.1109/76.499834 Hilton, 1997, Wavelet and wavelet packet compression of electrocardiograms, IEEE Trans. Biomed. Eng., 44, 394, 10.1109/10.568915 Buccigrossi, 1999, Image compression via joint statistical characterization in the wavelet domain, IEEE Trans. Image Process., 8, 1688, 10.1109/83.806616 Taubman, 2002 Donoho, 1994, Ideal spatial adaptation by wavelet shrinkage, Biometrika, 81, 425, 10.1093/biomet/81.3.425 Chang, 2000, Adaptive wavelet thresholding for image denoising and compression, IEEE Trans. Image Process., 9, 1532, 10.1109/83.862633 Sendur, 2002, Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency, IEEE Trans. Signal Process., 50, 2744, 10.1109/TSP.2002.804091 Portilla, 2003, Image denoising using scale mixtures of Gaussians in the wavelet domain, IEEE Trans. Image Process., 12, 1338, 10.1109/TIP.2003.818640 Daubechies, 2005, Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising, Appl. Comput. Harmon. Anal., 19, 1, 10.1016/j.acha.2004.12.004 Starck, 1994, Filtering and deconvolution by the wavelet transform, Signal Process., 35, 195, 10.1016/0165-1684(94)90211-9 Donoho, 1995, Nonlinear solution of linear inverse problems by wavelet-vaguelette decomposition, Appl. Comput. Harmon. Anal., 2, 101, 10.1006/acha.1995.1008 Miller, 1995, A multiscale approach to sensor fusion and the solution of linear inverse problems, Appl. Comput. Harmon. Anal., 2, 127, 10.1006/acha.1995.1009 Nowak, 2000, A statistical multiscale framework for Poisson inverse problems, IEEE Trans. Inform. Theory, 46, 1811, 10.1109/18.857793 Bioucas-Dias, 2006, Bayesian wavelet-based image deconvolution: A GEM algorithm exploiting a class of heavy-tailed priors, IEEE Trans. Image Process., 15, 937, 10.1109/TIP.2005.863972 Manthalkar, 2003, Rotation and scale invariant texture features using discrete wavelet packet transform, Pattern Recognit. Lett., 24, 2455, 10.1016/S0167-8655(03)00090-4 Flandrin, 1992, Wavelet analysis and synthesis of fractional Brownian motion, IEEE Trans. Inform. Theory, 38, 910, 10.1109/18.119751 D. Lowe, Object recognition from local scale-invariant features, in: Proceedings of the Seventh IEEE International Conference on Computer Vision, vol. 2, 1999, pp. 1150–1157. Apté, 1994, Automated learning of decision rules for text categorization, ACM Trans. Inf. Syst., 12, 233, 10.1145/183422.183423 Chung, 1997, Spectral Graph Theory, vol. 92 Mallat, 1998 Burt, 1983, The Laplacian pyramid as a compact image code, IEEE Trans. Commun., 31, 532, 10.1109/TCOM.1983.1095851 Simoncelli, 1992, Shiftable multi-scale transforms, IEEE Trans. Inform. Theory, 38, 587, 10.1109/18.119725 Kingsbury, 2001, Complex wavelets for shift invariant analysis and filtering of signals, Appl. Comput. Harmon. Anal., 10, 234, 10.1006/acha.2000.0343 Candes, 2003, New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities, Comm. Pure Appl. Math., 57, 219, 10.1002/cpa.10116 Peyré, 2008, Orthogonal bandlet bases for geometric images approximation, Comm. Pure Appl. Math., 61, 1173, 10.1002/cpa.20242 Antoine, 1999, Wavelets on the 2-sphere: A group-theoretical approach, Appl. Comput. Harmon. Anal., 7, 262, 10.1006/acha.1999.0272 Wiaux, 2008, Exact reconstruction with directional wavelets on the sphere, Mon. Not. R. Astron. Soc., 388, 770, 10.1111/j.1365-2966.2008.13448.x Antoine, 2008, The continuous wavelet transform on conic sections, Int. J. Wavelets Multiresolut. Inf. Process., 6, 137, 10.1142/S0219691308002288 M. Crovella, E. Kolaczyk, Graph wavelets for spatial traffic analysis, in: INFOCOM 2003, Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies, vol. 3, 2003, pp. 1848–1857. Smalter, 2009, Graph wavelet alignment kernels for drug virtual screening, J. Bioinform. Comput. Biol., 7, 473, 10.1142/S0219720009004187 Jansen, 2009, Multiscale methods for data on graphs and irregular multidimensional situations, J. R. Stat. Soc. Ser. B Stat. Methodol., 71, 97, 10.1111/j.1467-9868.2008.00672.x Murtagh, 2007, The Haar wavelet transform of a dendrogram, J. Classification, 24, 3, 10.1007/s00357-007-0007-9 Lee, 2008, Treelets an adaptive multi-scale basis for sparse unordered data, Ann. Appl. Stat., 2, 435, 10.1214/07-AOAS137 Coifman, 2006, Diffusion wavelets, Appl. Comput. Harmon. Anal., 21, 53, 10.1016/j.acha.2006.04.004 Maggioni, 2008, Diffusion polynomial frames on metric measure spaces, Appl. Comput. Harmon. Anal., 24, 329, 10.1016/j.acha.2007.07.001 Geller, 2009, Continuous wavelets on compact manifolds, Math. Z., 262, 895, 10.1007/s00209-008-0405-7 Grossmann, 1984, Decomposition of Hardy functions into square integrable wavelets of constant shape, SIAM J. Math. Anal., 15, 723, 10.1137/0515056 Hein, 2005, From graphs to manifolds – weak and strong pointwise consistency of graph Laplacians, vol. 3559, 470 Singer, 2006, From graph to manifold Laplacian: The convergence rate, Appl. Comput. Harmon. Anal., 21, 128, 10.1016/j.acha.2006.03.004 Belkin, 2008, Towards a theoretical foundation for Laplacian-based manifold methods, J. Comput. System Sci., 74, 1289, 10.1016/j.jcss.2007.08.006 Reed, 1980 Daubechies, 1992 Heil, 1989, Continuous and discrete wavelet transforms, SIAM Rev., 31, 628, 10.1137/1031129 Watkins, 2007 Sleijpen, 1996, A Jacobi–Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl., 17, 401, 10.1137/S0895479894270427 Cheney, 1966 Fraser, 1965, A survey of methods of computing minimax and near-minimax polynomial approximations for functions of a single independent variable, J. Assoc. Comput. Mach., 12, 295, 10.1145/321281.321282 Geddes, 1978, Near-minimax polynomial approximation in an elliptical region, SIAM J. Numer. Anal., 15, 1225, 10.1137/0715083 Phillips, 2003, Interpolation and Approximation by Polynomials, 10.1007/b97417 Grochenig, 1993, Acceleration of the frame algorithm, IEEE Trans. Signal Process., 41, 3331, 10.1109/78.258077 Zaroubi, 2000, Complex denoising of MR data via wavelet analysis: Application for functional MRI, Magnetic Resonance Imaging, 18, 59, 10.1016/S0730-725X(99)00100-9 Ruttimann, 1998, Statistical analysis of functional MRI data in the wavelet domain, IEEE Trans. Medical Imaging, 17, 142, 10.1109/42.700727 Ville, 2004, Integrated wavelet processing and spatial statistical testing of fMRI data, Neuroimage, 23, 1472, 10.1016/j.neuroimage.2004.07.056 Hagmann, 2008, Mapping the structural core of human cerebral cortex, PLoS Comput. Biol., 6, e159, 10.1371/journal.pbio.0060159 Wessel, 1996, A global, self-consistent, hierarchical, high-resolution shoreline database, J. Geophys. Res., 101, 8741, 10.1029/96JB00104 R.I. Kondor, J. Lafferty, Diffusion kernels on graphs and other discrete input spaces, in: Proceedings of the 19th International Conference on Machine Learning, 2002.