#
Naoki's Selected Publications

"On a nonlocal integral operator commuting with the Laplacian and the Sturm-Liouville problem: Low rank perturbations of the operator" (with L. Hermi), *Journal of Mathematical Physics*, vol. 65, Article #043503, 2024.

"Multiscale Hodge scattering networks for data analysis" (with S. Schonsheck and E. Shvarts), submitted for publication, 2023.

"Multiscale transforms for signals on simplicial complexes" (with S. Schonsheck and E. Shvarts), *Sampling Theory, Signal Processing, and Data Analysis*,vol. 22, no. 1, Article #2, 2024.

"Monogenic wavelet scattering network for texture image classification" (with W. H. Chak), *Japan SIAM Letters*, vol. 15, pp. 21-24, 2023.

"The scattering transform network with generalized Morse wavelets and its application to music genre classification" (with W. H. Chak and D. Weber), in *Proceedings of 2022 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR)*, pp.25-30, 2022.

"WaveletsExt.jl: Extending the boundaries of wavelets in Julia" (with Z. F. Liew and S. Dan), *The Journal of Open Source Software*, vol. 7, no. 69, Article #3937, 2022.

"eGHWT: The extended Generalized Haar-Walsh Transform" (with Y. Shao), *Journal of Mathematical Imaging and Vision*, vol. 64, no. 3, pp. 261-283, 2022.

"Natural graph wavelet packet dictionaries" (with A. Cloninger and H. Li), Topical Collection: "Harmonic Analysis on Combinatorial Graphs," *Journal of Fourier Analysis and Applications*, vol. 27, Article #41, 2021.

"Metrics of graph Laplacian eigenvectors" (with H. Li), in *Wavelets and Sparsity XVIII* (D. Van De Ville, M. Papadakis, and Y. M. Lu, eds.), Proc. SPIE 11138, Paper #111381K, 2019.

"The extended Generalized Haar-Walsh Transform and applications" (with Y. Shao), in *Wavelets and Sparsity XVIII* (D. Van De Ville, M. Papadakis, and Y. M. Lu, eds.), Proc. SPIE 11138, Paper #111380C, 2019.

"The use of mutual coherence to prove *l*^{1}/*l*^{0}-equivalence in classification problems" (with C. Weaver), submitted for publication, 2019.

"How can we naturally order and organize graph Laplacian eigenvectors?" *Proc. 2018 IEEE Workshop on Statistical Signal Processing*, pp. 483-487, 2018.

"Improving sparse representation-based classification using local principal component analysis" (with C. Weaver), in *Computational Intelligence for Pattern Recognition* (W. Pedrycz and S.-M. Chen, eds.), pp. 165-206, Springer, 2018.

"On Rayleigh-type formulas for a non-local boundary value problem associated with an integral operator commuting with the Laplacian" (with L. Hermi), *Applied and Computational Harmonic Analysis*, vol. 45, no. 1, pp. 59-83, 2018.

"Adaptive synchrosqueezing based on a quilted short-time Fourier transform" (with A. Berrian), in *Wavelets and Sparsity XVII* (Y. M. Lu, D. Van De Ville, and M. Papadakis, eds.), Proc. SPIE 10394, Paper #1039420, 2017.

"Underwater object classification using scattering transform of sonar signals" (with D. Weber), in *Wavelets and Sparsity XVII* (Y. M. Lu, D. Van De Ville, and M. Papadakis, eds.), Proc. SPIE 10394, Paper #103940K, 2017.

"Efficient approximation and denoising of graph signals using the multiscale basis dictionaries" (with J. Irion), *IEEE Transactions on Signal and Information Processing over Networks*, vol. 3, no. 3, pp. 607-616, 2017.

"Laplacian eigenfunctions and their application to image data analysis," *Journal of Plasma and Fusion Research*, vol. 92, no. 12, pp. 904-911, 2016 (in Japanese). Invited paper.

"Learning sparsity and structure of matrices with multiscale graph basis dictionaries" (with J. Irion), *Proc. 2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP)*, 2016.

"Applied and computational harmonic analysis on graphs and networks" (with J. Irion), in *Wavelets and Sparsity XVI* (M. Papadakis, V. K. Goyal, and D. Van De Ville, eds.), Proc. SPIE 9597, Paper #95971F, 2015. Invited paper.

"Applied harmonic analysis on graphs and networks," *Bulletin of the Japan Society for Industrial and Applied Mathematics*, vol. 25, no. 3, pp. 102-111, 2015 (in Japanese). Invited paper.

"Tree simplification and the 'plateaux' phenomenon of graph Laplacian eigenvalues" (with E. Woei), *Linear Algebra and its Applications*, vol. 481, pp. 263-279, 2015.

"The generalized Haar-Walsh transform" (with J. Irion), *Proc. 2014 IEEE Workshop on Statistical Signal Processing*, pp. 472-475, 2014.

"Hierarchical graph Laplacian eigen transforms" (with J. Irion), *Japan SIAM Letters*, vol. 6, pp. 21-24, 2014.

"PHLST with adaptive tiling and its application to Antarctic remote sensing image approximation" (with Z. Zhang), *Inverse Problems and Imaging*, vol. 8, no. 1, pp. 321-337, 2014.

"Wavelets for image processing," in *Handbook of Applied Mathematics* (J. Satsuma, S. Oishi, and M. Sugihara, eds.), pp. 512-515, Asakura Publishing Co., 2013 (in Japanese).

"Mysteries around graph Laplacian eigenvalue 4" (with Y. Nakatsukasa and E. Woei), *Linear Algebra and its Applications*, vol. 438, no. 8, pp. 3231-3246, 2013.

"Earth Mover's Distance based Local Discriminant Basis" (with B. Marchand), in *Multiscale Signal Analysis and Modeling* (X. Shen and A. I. Zayed, eds.), Lecture Notes in Electrical Engineering, Chap.12, pp. 275-294, Springer, 2013.

"Existence theorem and minimal cardinality of UEP framelets and MEP bi-framelets" (with Z. Zhang), *Applied and Computational Harmonic Analysis*, vol. 34, no. 2, pp. 297-307, 2013.

"On the phase transition phenomenon of graph Laplacian eigenfunctions on trees" (with E. Woei), RIMS Kôkyûroku, vol. 1743, pp. 77-90, 2011.

"On Slepian series expansion for digitized signals" (with X. Shen),
submitted for publication, 2010.

"Signal ensemble classification using low-dimensional embeddings and Earth Mover's Distance" (with L. Lieu), in *Wavelets and Multiscale Analysis: Theory and Applications* (J. Cohen and A. I. Zayed, eds.), Chap.11, pp. 227-256, Birkhäuser, 2011.

"Harmonic wavelet transform and image approximation" (with Z. Zhang),
*Journal of Mathematical Imaging and Vision*, vol. 38, no. 1, pp. 14-34, 2010.

"Ring-like structures of frequency domains of wavelets" (with Z. Zhang), *Applied and Computational Harmonic Analysis*, vol. 29, no. 1, pp. 18-29, 2010.

"The polynomial-Fourier transform with minimum mean square error for noisy data" (with Y. Wang), *Journal of Computational and Applied Mathematics*, vol. 234, no. 5, pp. 1586-1610, 2010.

"On an efficient sparse representation of objects of general shape via continuous extension and wavelet approximation" (with Z. Zhang), *International Journal of Wavelets, Multiresolution, and Information Processing*, vol. 8, no. 2, pp. 253-269, 2010.

"A method of sequentially predicting DCT coefficients using gradient information of an input signal and its application to image compression" (with K. Ashizawa, J. Ogawa, and K. Yamatani), *Urban Science Studies*, vol. 14, pp. 63-70, 2009 (in Japanese).

"Signal classification by matching node connectivities" (with L. Lieu), *Proc. 15th IEEE Statistical Signal Processing Workshop*, pp. 81-84, 2009.

"Analysis of neuronal dendrite patterns using eigenvalues of graph Laplacians" (with E. Woei),
*Japan SIAM Letters*, vol. 1, pp. 13-16, 2009. Invited Paper.

"Constructions of periodic wavelet frames using extension principles" (with Z. Zhang), *Applied and Computational Harmonic Analysis*, vol. 27, no. 1, pp. 12-23, 2009.

"Simultaneous segmentation, compression, and denoising of signals using polyharmonic local sine transform and minimum description length criterion" (with E. Woei), submitted for publication, 2008.

"Data analysis and representation on a general domain using eigenfunctions of Laplacian," *Applied and Computational Harmonic Analysis*, vol. 25, no. 1, pp. 68-97, 2008.

"PHLST5: A practical and improved version of polyharmonic local sine transform" (with J. Zhao and Y. Wang), *Journal of Mathematical Imaging and Vision*, vol. 30, no.1, pp. 23-41, 2008.

"An approximation formula in Hilbert space" (with Z. Zhang), in *Recent Advances in Computational Sciences* (P. Jorgensen, X. Shen, C.-W. Shu, and N. Yan, eds.), pp. 218-227, World Scientific, 2008.

"Classification of objects in synthetic aperture sonar images" (with B. Marchand and H. Xiao), *Proc. 14th IEEE Statistical Signal Processing Workshop*, pp. 433-437, 2007.

"Automated discrimination of shapes in high dimensions" (with L. Lieu), in *Wavelets XII* (D. Van De Ville, V. K. Goyal, and M. Papadakis, eds.), Proc. SPIE 6701, Paper #67011V, 2007.

"High dimensional data compression via PHLCT" (with Z. Zhang), in *Wavelets XII* (D. Van De Ville, V. K. Goyal, and M. Papadakis, eds.), Proc. SPIE 6701, Paper #670127, 2007.

"The method of hierarchical multi-neighbor predictors and residual orthogonal transforms and its application to image compression" (with K. Ashizawa and K. Yamatani), *Transactions of Japan Society for Industrial and Applied Mathematics*, vol. 17, no. 3, pp. 239-257, 2007 (in Japanese).

"Improvement of DCT-based compression algorithms using Poisson's equation" (with K. Yamatani), *IEEE Trans. Image Proc.*, vol. 15, no. 12, pp. 3672-3689, 2006.

"The polyharmonic local sine transform: A new tool for local image analysis and synthesis without edge effect" (with J.-F. Remy), *Applied and Computational Harmonic Analysis*, vol. 20, no. 1, pp. 41-73, 2006.

"Geometric harmonics as a statistical image processing tool for images defined on irregularly-shaped domains" in *Proceedings of 13th IEEE Statistical Signal Processing Workshop*, pp. 425-430, 2005.

"Simultaneous segmentation, compression, and denoising using polyharmonic local sine transform and minimum description length criterion" (with E. Woei), in *Proc. 13th IEEE Statistical Signal Processing Workshop*, pp. 315-320, 2005.

"Using edge information in time-frequency representations for chirp parameter estimation" (with N. Bennett), *Applied and Computational Harmonic Analysis*, vol. 18, no. 2, pp. 186-197, 2005.

"The generalized spike process, sparsity, and statistical independence," in
*Modern Signal Processing* (D. Rockmore and D. Healy, Jr., eds.), MSRI Publications Vol. 46, pp. 317-340, Cambridge University Press, 2004.

"Sparsity vs. statistical independence in adaptive signal representations: A case study of the spike process" (with B. Benichou), in *Beyond Wavelets* (G. V. Welland ed.), Studies in Computational Mathematics, Vol. 10, Chap.9, pp. 225-257, Academic Press, 2003.

"A new local sine transform without overlaps: A combination of computational harmonic analysis and PDE" (with J.-F. Remy), in *Wavelets X* (M. A. Unser, A. Aldroubi, and A. F. Laine, eds.), Proc. SPIE 5207, pp. 495-506, 2003.

"
Discriminant feature extraction using empirical probability density estimation and a local basis library" (with R. R. Coifman, F. B. Geshwind, and F. Warner), *Pattern Recognition*, vol. 35, pp. 2841-2852, 2002.

"The continuous boundary local Fourier transform" (with B. M. Larson), in *Wavelet Applications in Signal and Image Processing IX* (A. F. Laine, M. A. Unser, and A. Aldroubi, eds.), Proc. SPIE 4478, pp. 415-426, 2001.

"Image approximation and modeling via least statistically-dependent bases," *Pattern Recognition*, vol. 34, pp. 1765-1784, 2001.

"Edgeworth approximations of the Kullback-Leibler distance towards problems in image analysis," (with J.-J. Lin and R. A. Levine), submitted for publication, 2001.

"An iterative nonlinear Gaussianization algorithm for image simulation and synthesis" (with J.-J. Lin and R. A. Levine), submitted for publication, 2001.

"Wavelet despiking of fractographs" (with J.-M. Aubry), in *Wavelet Applications in Signal and Image Processing VIII* (A. Aldroubi, A. F. Laine, and M. A. Unser, eds.), Proc. SPIE 4119, pp. 853-860, 2000.

"Sparsity vs. statistical independence from a best-basis viewpoint" (with B. M. Larson and B. Benichou), in *Wavelet Applications in Signal and Image Processing VIII* (A. Aldroubi, A. F. Laine, and M. A. Unser, eds.), Proc. SPIE 4119, pp. 474-486, 2000. Invited Paper.

"An iterative nonlinear Gaussianization algorithm for resampling dependent components" (with J.-J. Lin and R. A. Levine), in *Proc. 2nd International Workshop on Independent Component Analysis and Blind Signal Separation*, pp. 245-250, 2000.

"Edgeworth expansions of the Kullback-Leibler information," (with J.-J. Lin and R. A. Levine), submitted for publication, 1999.

"The local Fourier dictionary: a natural tool for data analysis," in *Wavelet Applications in Signal and Image Processing VII* (M. A. Unser, A. Aldroubi, and A. F. Laine, eds.), Proc. SPIE 3813, pp. 610-624, 1999. Invited paper.

"A method to detect and characterize ellipses using the Hough transform," (with N. Bennett and R. Burridge), *IEEE Trans. Pattern Anal. Machine Intell.*, vol. 21, no. 7, pp. 652-657, 1999.

"The least statistically-dependent basis and its applications," in *Proceedings of 32nd Asilomar Conference on Signals, Systems & Computers*, pp. 732-736, 1998.

"Least statistically-dependent basis and its application to image modeling," in *Wavelet Applications in Signal and Image Processing VI* (A. F. Laine, M. A. Unser, and A. Aldroubi, eds.), Proc. SPIE 3458, pp. 24-37, 1998.
"Extraction of geological information from acoustic well-logging waveforms using time-frequency wavelets" (with R. R. Coifman), *Geophysics*, vol. 62, no. 6, pp. 1921-1930,
1997.
"Classification
of geophysical acoustic waveforms and extraction of geological information
using time-frequency atoms," in *1996 Proc. Computing Section of Amer.
Statist. Assoc.*, pp. 322-327, 1997.
"Improved discriminant bases using empirical probability density estimation" (with
R. R. Coifman), in *1996 Proc. Computing Section of Amer. Statist. Assoc.*, pp. 312-321, 1997.
"On local feature extraction for signal classification" (with R. R. Coifman),
in *Applied Analysis* (O. Mahrenholtz and R. Mennicken, eds.), in *Zeitschrift für Angewandte Mathematik und Mechanik*, vol. 76, no. S2, pp. 453-456,
Akademie-Verlag, Berlin, 1996
"The local Karhunen-Loeve bases" (with R. R. Coifman), in *Proc. IEEE International Symposium on Time-Frequency and Time-Scale Analysis*, pp. 129-132, 1996.
"Local discriminant bases and their applications" (with R. R. Coifman), *J. Mathematical Imaging and Vision*, vol. 5, no. 4, pp. 337-358, 1995, Invited paper.
"On local orthonormal bases for classification and regression" (with R. R. Coifman), in *Proc. 1995 International Conference on Acoustics, Speech, and Signal
Processing*, IEEE Signal Processing Society, May 1995, Detroit, MI.
"Selection of best bases for classification and regression" (with R. R. Coifman), in *Proc.1994 IEEE-IMS Workshop on Information Theory and Statistics*, p.51, IEEE-IMS, Oct. 1994, Alexandria, VA.
"Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum description length criterion," in *Wavelets in Geophysics* (E. Foufoula-Georgiou and P. Kumar, eds.), chap.XI, pp. 299-324, Academic Press, San Diego, CA, 1994.
"Local discriminant bases" (with R. R. Coifman), in *Wavelet Applications in Signal and Image Processing II* (A.F.Laine and M.A.Unser, eds.), Proc. SPIE 2303, pp. 2-14, Jul. 1994, San Diego, CA.
"Constructions of local orthonormal bases for classification and regression" (with R. R. Coifman), *Comptes Rendus Acad. Sci. Paris, Serie I *, vol. 319, pp. 191-196, Jul. 1994.
"Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum description length criterion," in *Wavelet Applications *(H. H. Szu, ed.), Proc. SPIE 2242, pp. 224-235, Apr. 1994, Orlando, FL.
"Multiresolution representations using the auto-correlation functions of compactly supported wavelets" (with G. Beylkin), *IEEE Trans. Signal Processing*, vol. 41, no. 12, pp. 3584-3590, 1993; Erratum: vol. 45, no. 3, p.768, 1997.
"Multiresolution representations using the auto-correlation
functions of wavelets" (with G. Beylkin), in *Progress in Wavelet Analysis
and Applications *(Y. Meyer and S. Roques, eds.), pp. 721-726, Editions
Frontieres, B.P.33, 91192 Gif-sur-Yvette Cedex, France, 1993.
"Signal/noise separation using the adaptive waveform library"
(with R. R. Coifman, F. Majid), in *Proc. the Eighth Workshop on Image and Multidimensional Signal Processing*, pp. 136-137, IEEE Signal Processing Society, Sep. 1993, Cannes, France.
"Wavelets, their autocorrelation functions, and multiresolution
representations of signals," (with G. Beylkin), in *Intelligent Robots and
Computer Vision XI: Biological, Neural Net, and 3-D Methods* (D.P.Casasent,
ed.), Proc. SPIE 1826, pp. 39-50, Nov. 1992, Boston, MA.
"Multiresolution representations using the auto-correlation functions of compactly supported wavelets" (with G. Beylkin), in *Proc. 1992 International Conference on Acoustics, Speech, and Signal Processing*,vol. 4, pp. 381-384, IEEE Signal Processing Society, Mar. 1992, San Francisco, CA.
"Cross well tomography using curved rays and constraints"
(with K. Hsu), in *Proc. the Seventh Workshop on Image and Multidimensional
Signal Processing*, Paper 6.6, IEEE Signal Processing Society, Sep. 1991,
Lake Placid, NY.
"Generalized *E*-filter and its application to edge detection" (with M. A. Cunningham), *IEEE Trans. Pattern Anal. Machine Intell.*, vol. 12, no. 8, pp. 814-817, 1990.
"Superresolution of noisy band-limited data by data adaptive regularization and its application to seismic trace inversion" in *Proc. 1990 International Conference on Acoustics, Speech, and Signal Processing*, vol. 3, pp. 1237-1240, IEEE Signal Processing Society, Apr. 1990, Albuquerque, NM.
"On the behavior of pulses on the parallel active lines"
(in Japanese), *Proc. the IECE Workshop on Nonlinear Problems*, the Institute of Electronics and Communication Engineers of Japan, Sep. 1984, Tokyo, Japan.

#
Naoki's Unpublished Manuscripts, Reports, and Theses (partial list)

"Local
Feature Extraction and Its Applications Using a Library of Bases," Ph.D. Thesis
(Advisor: Prof. Ronald R. Coifman), Department of Mathematics, Yale University,
Dec. 1994.
"Multiresolution representations using the auto-correlation functions of compactly supported wavelets" (with G. Beylkin), Research Note, Schlumberger-Doll Research, Aug. 1991.
"On the behavior of pulses on the parallel active lines,"
M.Eng. Thesis (Advisor: Prof. Jin-ichi Nagumo), Department of Mathematical
Engineering and Information Physics, University of Tokyo, Japan, Mar. 1984.
"Dynamical pattern formation and computer graphics," B.Eng. Thesis
(Advisor: Prof. Jin-ichi Nagumo), Department of Mathematical Engineering
and Information Physics, University of Tokyo, Mar. 1982.

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