#
Naoki's Selected Publications

"The scattering transform network with generalized Morse wavelets and its application to music genre classification," (with W. H. Chak and D. Weber), submitted for publication, 2022.

"Monogenic wavelet scattering network for texture image classification," (with W. H. Chak), submitted for publication, 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.

Please email
me if you have any comments or questions!

Go back to
Naoki's home page