Ten Lectures on Wavelets

Matching pursuits with time-frequency dictionaries

Mallat, S., & Zhang, Z. (1993) · IEEE Transactions on Signal Processing · doi:10.1109/78.258082 · Cited by 9,023

Ideal Spatial Adaptation by Wavelet Shrinkage

Donoho, D. L., & Johnstone, I. M. (1994) · Biometrika · doi:10.1093/biomet/81.3.425 · Cited by 8,730

Atomic Decomposition by Basis Pursuit

Chen, S. S., Donoho, D. L., & Saunders, M. A. (1998) · SIAM Journal on Scientific Computing · doi:10.1137/s1064827596304010 · Cited by 6,734

Content-based image retrieval at the end of the early years

Smeulders, A. W. M., Worring, M., Santini, S., Gupta, A., & Jain, R. (2000) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.895972 · Cited by 6,050

Atomic Decomposition by Basis Pursuit

Chen, S. S., Donoho, D. L., & Saunders, M. A. (2001) · SIAM Review · doi:10.1137/s003614450037906x · Cited by 5,030

Adapting to Unknown Smoothness via Wavelet Shrinkage

Donoho, D. L., & Johnstone, I. M. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476626 · Cited by 4,577

Characterization of signals from multiscale edges

Mallat, S., & Zhong, S. (1992) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.142909 · Cited by 3,191

Turbulence, Coherent Structures, Dynamical Systems and Symmetry

Holmes, P. J., Lumley, J. L., & Berkooz, G. (1996) · Cambridge University Press eBooks · doi:10.1017/cbo9780511622700 · Cited by 3,152

Adaptive wavelet thresholding for image denoising and compression

Chang, S.-F., Yu, B., & Vetterli, M. (2000) · IEEE Transactions on Image Processing · doi:10.1109/83.862633 · Cited by 2,927

ABINIT: First-principles approach to material and nanosystem properties

Gonze, X., Amadon, B., Anglade, P.-M., Beuken, J.-M., François Bottin, A., Boulanger, P., Bruneval, F., Caliste, D., Caracas, R., Côté, M., et al. (2009) · Computer Physics Communications · doi:10.1016/j.cpc.2009.07.007 · Cited by 2,723

Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool

Daubechies, I. C., Lu, J., & Wu, H. (2010) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2010.08.002 · Cited by 2,496

The dual-tree complex wavelet transform

Selesnick, I., Baraniuk, R. G., & Kingsbury, N. G. (2005) · IEEE Signal Processing Magazine · doi:10.1109/msp.2005.1550194 · Cited by 2,474

Bayesian compressive sensing

Ji, S., Xue, Y., & Carin, L. (2008) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2007.914345 · Cited by 2,406

Anisotropic diffusion in image processing

Weickert, J. (1998) · Cited by 2,230

ADVANCED SPECTRAL METHODS FOR CLIMATIC TIME SERIES

Ghil, M., Allen, M. R., Dettinger, M. D., Ide, K., Kondrashov, D., MANN, M. E., Robertson, A. W., Saunders, A., Tian, Y. Z., Váradi, F., et al. (2002) · Reviews of Geophysics · doi:10.1029/2000rg000092 · Cited by 2,209

SIMPLIcity: semantics-sensitive integrated matching for picture libraries

Wang, J. Z., Li, J., & Wiederhold, G. C. M. (2001) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.955109 · Cited by 2,196

Wavelets on graphs via spectral graph theory

Hammond, D. K., Vandergheynst, P., & Gribonval, R. (2010) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2010.04.005 · Cited by 2,173

The Nonsubsampled Contourlet Transform: Theory, Design, and Applications

da Cunha, A. L., Zhou, J., & Do, M. N. (2006) · IEEE Transactions on Image Processing · doi:10.1109/tip.2006.877507 · Cited by 2,035

Deep Learning for Image Super-Resolution: A Survey

Wang, Z., Chen, J., & Hoi, S. C. H. (2020) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2020.2982166 · Cited by 2,113

Factoring wavelet transforms into lifting steps

Daubechies, I. C., & Sweldens, W. (2005) · Springer eBooks · doi:10.1007/bfb0011095 · Cited by 2,011

Translation-Invariant De-Noising

Coifman, R. R., & Donoho, D. L. (1995) · Lecture notes in statistics · doi:10.1007/978-1-4612-2544-7_9 · Cited by 1,943

Nonlinear black-box modeling in system identification: a unified overview

Sjoberg, J. S., Zhang, Q., Lennart Ljung, A., Benveniste, A., Delyon, B., Glorennec, P. Y., Hjalmarsson, H., & Juditsky, A. (1995) · Automatica · doi:10.1016/0005-1098(95)00120-8 · Cited by 1,968

Uncertainty principles and ideal atomic decomposition

Donoho, D. L., & Huo, X. (2001) · IEEE Transactions on Information Theory · doi:10.1109/18.959265 · Cited by 1,907

Scale issues in hydrological modelling: A review

Blöschl, G., & Sivapalan, M. (1995) · Hydrological Processes · doi:10.1002/hyp.3360090305 · Cited by 1,855

Despiking Acoustic Doppler Velocimeter Data

Goring, D. G., & Nikora, V. (2002) · Journal of Hydraulic Engineering · doi:10.1061/(asce)0733-9429(2002)128:1(117 · Cited by 1,708

Multifractality in human heartbeat dynamics

Ivanov, P. C., Amaral, L. A. N., Goldberger, A. L., Havlin, S., Rosenblum, M., Struzik, Z. R., & Stanley, H. E. (1999) · Nature · doi:10.1038/20924 · Cited by 1,690

Wavelet-based statistical signal processing using hidden Markov models

Crouse, M. S., Nowak, R. D., & Baraniuk, R. G. (1998) · IEEE Transactions on Signal Processing · doi:10.1109/78.668544 · Cited by 1,631

Splines: a perfect fit for signal and image processing

Unser, M. A. (1999) · IEEE Signal Processing Magazine · doi:10.1109/79.799930 · Cited by 1,627

Blind Separation of Speech Mixtures via Time-Frequency Masking

Yılmaz, Ö., & Rickard, S. (2004) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2004.828896 · Cited by 1,463

A wavelet-based image fusion tutorial

Pájares, G., & García, J. M. D. L. C. (2004) · Pattern Recognition · doi:10.1016/j.patcog.2004.03.010 · Cited by 1,368

Multiple description coding: compression meets the network

Goyal, V. K. (2001) · IEEE Signal Processing Magazine · doi:10.1109/79.952806 · Cited by 1,344

Texture classification and segmentation using wavelet frames

Unser, M. A. (1995) · IEEE Transactions on Image Processing · doi:10.1109/83.469936 · Cited by 1,321

Dictionaries for Sparse Representation Modeling

Rubinstein, R., Bruckstein, A. M., & Elad, M. (2010) · Proceedings of the IEEE · doi:10.1109/jproc.2010.2040551 · Cited by 1,318

A Two-Step Framework for Constructing Blind Image Quality Indices

Moorthy, A. K., & Bovik, A. C. (2010) · IEEE Signal Processing Letters · doi:10.1109/lsp.2010.2043888 · Cited by 1,196

Regularization Networks and Support Vector Machines

Evgeniou, T., Pontil, M., & Poggio, T. (2000) · Advances in Computational Mathematics · doi:10.1023/a:1018946025316 · Cited by 1,201

Mathematical Models for Local Nontexture Inpaintings

Shen, J., & Chan, T. F.-C. (2002) · SIAM Journal on Applied Mathematics · doi:10.1137/s0036139900368844 · Cited by 1,189

Highly sensitive feature detection for high resolution LC/MS

Tautenhahn, R., Böttcher, C., & Neumann, S. (2008) · BMC Bioinformatics · doi:10.1186/1471-2105-9-504 · Cited by 1,175

Adaptive Greedy Approximations

Davis, G. M., Mallat, S., & Avellaneda, M. (1997) · Constructive Approximation · doi:10.1007/bf02678430 · Cited by 1,154

Analysis of EEG records in an epileptic patient using wavelet transform

Adeli, H., Zhou, Z., & Dadmehr, N. (2003) · Journal of Neuroscience Methods · doi:10.1016/s0165-0270(02)00340-0 · Cited by 1,152

The Stationary Wavelet Transform and some Statistical Applications

Nason, G. P., & Silverman, B. W. (1995) · Lecture notes in statistics · doi:10.1007/978-1-4612-2544-7_17 · Cited by 1,138

Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance

Do, M. N., & Vetterli, M. (2002) · IEEE Transactions on Image Processing · doi:10.1109/83.982822 · Cited by 1,134

Studying Aesthetics in Photographic Images Using a Computational Approach

Datta, R., Joshi, D., Li, J., & Wang, J. Z. (2006) · Lecture notes in computer science · doi:10.1007/11744078_23 · Cited by 1,133

Multiresolution-based image fusion with additive wavelet decomposition

Núñez, J., Otazu, X., Fors, O., Prades, A., Palà, V., & Arbiol, R. (1999) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/36.763274 · Cited by 1,125

Wavelet Transforms That Map Integers to Integers

Calderbank, A. R., Daubechies, I. C., Sweldens, W., & Yeo, B.-L. (1998) · Applied and Computational Harmonic Analysis · doi:10.1006/acha.1997.0238 · Cited by 1,090

Automatic linguistic indexing of pictures by a statistical modeling approach

Li, J., & Wang, J. Z. (2003) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2003.1227984 · Cited by 1,087

The steerable pyramid: a flexible architecture for multi-scale derivative computation

Simoncelli, E. P., & Freeman, W. T. (2002) · Proceedings - International Conference on Image Processing · doi:10.1109/icip.1995.537667 · Cited by 1,077

Imaging via Compressive Sampling

Romberg, J. K. (2008) · IEEE Signal Processing Magazine · doi:10.1109/msp.2007.914729 · Cited by 1,030

What Are the Main Drivers of the Bitcoin Price? Evidence from Wavelet Coherence Analysis

Krištoufek, L. (2015) · PLoS ONE · doi:10.1371/journal.pone.0123923 · Cited by 1,008

Multi-level Wavelet-CNN for Image Restoration

Liu, P., Zhang, H., Zhang, K., Lin, L., & Zuo, W. (2018) · IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) · doi:10.1109/cvprw.2018.00121 · Cited by 998

Recent advances in time–frequency analysis methods for machinery fault diagnosis: A review with application examples

Feng, Z., Liang, M., & Chu, F. (2013) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2013.01.017 · Cited by 998

On Early Stopping in Gradient Descent Learning

Yao, Y., Rosasco, L., & Caponnetto, A. (2007) · Constructive Approximation · doi:10.1007/s00365-006-0663-2 · Cited by 990

Data Mining: Concepts and Techniques (2nd edition)

Han, J., & Kamber, M. (2006) · Cited by 968

The uncertainty principle: A mathematical survey

Folland, G. B., & Sitaram, A. (1997) · Journal of Fourier Analysis and Applications · doi:10.1007/bf02649110 · Cited by 971

Wavelet analysis of long-range-dependent traffic

Abry, P., & Veitch, D. N. (1998) · IEEE Transactions on Information Theory · doi:10.1109/18.650984 · Cited by 952

Travelling waves and spatial hierarchies in measles epidemics

Grenfell, B. T., Bjørnstad, O. N., & Kappey, J. (2001) · Nature · doi:10.1038/414716a · Cited by 952

Grassmannian frames with applications to coding and communication

Strohmer, T., & Heath, R. W. (2003) · Applied and Computational Harmonic Analysis · doi:10.1016/s1063-5203(03)00023-x · Cited by 920

Introduction to Multifractal Detrended Fluctuation Analysis in Matlab

Ihlen, E. A. F. (2012) · Frontiers in Physiology · doi:10.3389/fphys.2012.00141 · Cited by 915

Wavelet transforms and the ECG: a review

Addison, P. S. (2005) · Physiological Measurement · doi:10.1088/0967-3334/26/5/r01 · Cited by 908

Spatially adaptive wavelet thresholding with context modeling for image denoising

Chang, S., Yu, B., & Vetterli, M. (2000) · IEEE Transactions on Image Processing · doi:10.1109/83.862630 · Cited by 887

Affective image classification using features inspired by psychology and art theory

Machajdik, J., & Hanbury, A. (2010) · ACM International Conference on Multimedia (ACM MM) · doi:10.1145/1873951.1873965 · Cited by 873

Context-driven fusion of high spatial and spectral resolution images based on oversampled multiresolution analysis

Aiazzi, B., Alparone, L., Baronti, S., & Garzelli, A. (2002) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2002.803623 · Cited by 854

Study and comparison of various image edge detection techniques

Chandrakar, N., & Bhonsle, D. (2012) · International Journal of Managment, IT and Engineering · Cited by 852

Introduction of sensor spectral response into image fusion methods. Application to wavelet-based methods

Otazu, X., González-Audícana, M., Fors, O., & Núñez, J. (2005) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2005.856106 · Cited by 848

Meshfree and particle methods and their applications

Li, S., & Liu, W. K. (2002) · Applied Mechanics Reviews · doi:10.1115/1.1431547 · Cited by 861

hp-VPINNs: Variational physics-informed neural networks with domain decomposition

Kharazmi, E., Zhang, Z., & Karniadakis, G. E. (2020) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2020.113547 · Cited by 840

Extending the Linear Model with R

Faraway, J. J. (2016) · Chapman & Hall/CRC eBooks · doi:10.1201/9781315382722 · Cited by 857

Wavelet entropy: a new tool for analysis of short duration brain electrical signals

Rosso, O. A., Blanco, S., Yordanova, J., Kolev, V., Figliola, A., Schürmann, M., & Başar, E. (2001) · Journal of Neuroscience Methods · doi:10.1016/s0165-0270(00)00356-3 · Cited by 823

A theory of regularity structures

Hairer, M. (2014) · Inventiones mathematicae · doi:10.1007/s00222-014-0505-4 · Cited by 817

A general framework for multiresolution image fusion: from pixels to regions

Piella, G. (2003) · Information Fusion · doi:10.1016/s1566-2535(03)00046-0 · Cited by 801

PyWavelets: A Python package for wavelet analysis

Lee, G. R., Gommers, R., Waselewski, F., Wohlfahrt, K., & O'Leary, A. (2019) · The Journal of Open Source Software · doi:10.21105/joss.01237 · Cited by 780

Climate Signal Detection Using Wavelet Transform: How to Make a Time Series Sing

Lau, K.-M., & Weng, H. (1995) · Bulletin of the American Meteorological Society · doi:10.1175/1520-0477(1995)076 · Cited by 778

Heterogeneous Multiscale Methods: A Review

Weinan, E., Engquist, B., Li, X., Ren, W., & Vanden‐Eijnden, E. (2007) · Communications in Computational Physics · doi:10.4208/cicp.2007.v2.p367 · Cited by 776

Wavelets, Approximation, and Statistical Applications

Härdle, W. K., Kerkyacharian, G., Picard, D., & Tsybakov, A. B. (1998) · Lecture notes in statistics · doi:10.1007/978-1-4612-2222-4 · Cited by 761

Ambulatory system for human motion analysis using a kinematic sensor: monitoring of daily physical activity in the elderly

Najafi, B., Aminian, K., Paraschiv-Ionescu, A., Loew, F., Büla, C., & Robert, P. A. (2003) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2003.812189 · Cited by 760

Block Compressed Sensing of Natural Images

Gan, L. (2007) · IEEE International Conference on Digital Signal Processing (DSP) · doi:10.1109/icdsp.2007.4288604 · Cited by 759

Improved peak detection in mass spectrum by incorporating continuous wavelet transform-based pattern matching

Du, P., Kibbe, W. A., & Lin, S. M. (2006) · Bioinformatics · doi:10.1093/bioinformatics/btl355 · Cited by 759

Time–frequency feature representation using energy concentration: An overview of recent advances

Sejdić, E., Djurović, I., & Jiang, J. (2008) · Digital Signal Processing · doi:10.1016/j.dsp.2007.12.004 · Cited by 756

Multiresolution analysis for surfaces of arbitrary topological type

Lounsbery, M., DeRose, T., & Warren, J. D. (1997) · ACM Transactions on Graphics · doi:10.1145/237748.237750 · Cited by 755

Perceptual coding of digital audio

Painter, T., & Spanias, A. (2000) · Proceedings of the IEEE · doi:10.1109/5.842996 · Cited by 754

Framelets: MRA-based constructions of wavelet frames

Daubechies, I. C., Han, B., Ron, A., & Shen, Z. (2003) · Applied and Computational Harmonic Analysis · doi:10.1016/s1063-5203(02)00511-0 · Cited by 734

Wavelet analysis of ecological time series

Cazelles, B., Chávez, M., Berteaux, D., Ménard, F., Vik, J. O., Jenouvrier, S., & Stenseth, N. C. (2008) · Oecologia · doi:10.1007/s00442-008-0993-2 · Cited by 734

Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage

Chambolle, A., Vore, R. A. D., Lee, N.-Y., & Lucier, B. J. (1998) · IEEE Transactions on Image Processing · doi:10.1109/83.661182 · Cited by 733

A categorization of multiscale-decomposition-based image fusion schemes with a performance study for a digital camera application

Zhang, Z., & Blum, R. S. (1999) · Proceedings of the IEEE · doi:10.1109/5.775414 · Cited by 723

THE CONTINUOUS WAVELET TRANSFORM: MOVING BEYOND UNI‐ AND BIVARIATE ANALYSIS

Aguiar‐Conraria, L., & Soares, M. J. (2013) · Journal of Economic Surveys · doi:10.1111/joes.12012 · Cited by 722

Wavelet neural networks for function learning

Zhang, J., Walter, G. G., Miao, Y., & Lee, W. (1995) · IEEE Transactions on Signal Processing · doi:10.1109/78.388860 · Cited by 721

Event Detection in Twitter

Weng, J., & Lee, B. (2021) · Proceedings of the International AAAI Conference on Web and Social Media · doi:10.1609/icwsm.v5i1.14102 · Cited by 719

Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces

Aldroubi, A., & Gröchenig, K. (2001) · SIAM Review · doi:10.1137/s0036144501386986 · Cited by 716

The finite ridgelet transform for image representation

Do, M. N., & Vetterli, M. (2003) · IEEE Transactions on Image Processing · doi:10.1109/tip.2002.806252 · Cited by 710

A wavelet-based continuous classification scheme for multifunction myoelectric control

Englehart, K., Hudgin, B., & Parker, P. A. (2001) · IEEE Transactions on Biomedical Engineering · doi:10.1109/10.914793 · Cited by 697

Bearing fault diagnosis based on wavelet transform and fuzzy inference

Lou, X., & Loparo, K. A. (2003) · Mechanical Systems and Signal Processing · doi:10.1016/s0888-3270(03)00077-3 · Cited by 692

Optimally Sparse Multidimensional Representation Using Shearlets

Guo, K., & Demetrio Labate, A. (2007) · SIAM Journal on Mathematical Analysis · doi:10.1137/060649781 · Cited by 687

A Wavelet-Chaos Methodology for Analysis of EEGs and EEG Subbands to Detect Seizure and Epilepsy

Adeli, H., Ghosh‐Dastidar, S., & Dadmehr, N. (2007) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2006.886855 · Cited by 686

Wavelet analysis of oscillations in the peripheral blood circulation measured by laser Doppler technique

Stefanovska, A., Bračič, M., & Kvernmo, H. D. (1999) · IEEE Transactions on Biomedical Engineering · doi:10.1109/10.790500 · Cited by 695

Affine Systems inL2(Rd): The Analysis of the Analysis Operator

Ron, A., & Shen, Z. (1997) · Journal of Functional Analysis · doi:10.1006/jfan.1996.3079 · Cited by 682

Wavelet Transform With Tunable Q-Factor

Selesnick, I. (2011) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2011.2143711 · Cited by 678

Error estimates and condition numbers for radial basis function interpolation

Schaback, R. (1995) · Advances in Computational Mathematics · doi:10.1007/bf02432002 · Cited by 670

A chronology of interpolation: from ancient astronomy to modern signal and image processing

Meijering, E. H. W. (2002) · Proceedings of the IEEE · doi:10.1109/5.993400 · Cited by 665

ON INSTANTANEOUS FREQUENCY

Huang, N. E., Wu, Z., LONG, S. R., Arnold, K. C., Chen, X., & Blank, K. (2009) · Advances in Adaptive Data Analysis · doi:10.1142/s1793536909000096 · Cited by 663

Interactive multi-resolution modeling on arbitrary meshes

Kobbelt, L. P., Campagna, S., Vorsatz, J., & Seidel, H. (1998) · ACM SIGGRAPH Conference (SIGGRAPH) · doi:10.1145/280814.280831 · Cited by 661

Filters, Random Fields and Maximum Entropy (FRAME): Towards a Unified Theory for Texture Modeling

Zhu, S. C., Wu, Y., & Mumford, D. B. (1998) · International Journal of Computer Vision · doi:10.1023/a:1007925832420 · Cited by 659

Wavelets: the mathematical background

Cohen, A., & Kovačević, J. (1996) · Proceedings of the IEEE · doi:10.1109/5.488697 · Cited by 309

Orthonormal bases of compactly supported wavelets

Daubechies, I. C. (1988) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160410705 · Cited by 8,143

Wavelets and allied topics

Jain, P., Mhaskar, H. N., & Krishna, M. C. (2001) · CERN Document Server (European Organization for Nuclear Research) · Cited by 5

Orthonormal Bases of Wavelets with Finite Support — Connection with Discrete Filters

Daubechies, I. C. (1990) · Inverse problems and theoretical imaging · doi:10.1007/978-3-642-75988-8_3 · Cited by 53

Orthonormal Bases of Compactly Supported Wavelets II. Variations on a Theme

Daubechies, I. C. (1993) · SIAM Journal on Mathematical Analysis · doi:10.1137/0524031 · Cited by 394