Ten Lectures on Wavelets

Fourier–Bessel series expansion based empirical wavelet transform for analysis of non-stationary signals

Bhattacharyya, A., Singh, L. K., & Pachori, R. B. (2018) · Digital Signal Processing · doi:10.1016/j.dsp.2018.02.020 · Cited by 207

Frames for operators

Găvruţa, L. (2011) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2011.07.006 · Cited by 206

The $S$-Transform From a Wavelet Point of View

Ventosa, S., Simon, C., Schimmel, M., Dañobeitia, J. J., & Lázaro, A. M. (2008) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2008.917029 · Cited by 206

Efficient solution of Poisson’s equation with free boundary conditions

Genovese, L., Deutsch, T., Neelov, A., Goedecker, S., & Beylkin, G. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2335442 · Cited by 205

Detecting Epileptic Seizures in Long-term Human EEG: A New Approach to Automatic Online and Real-Time Detection and Classification of Polymorphic Seizure Patterns

Meier, R., Dittrich, H., Schulze‐Bonhage, A., & Aertsen, A. (2008) · Journal of Clinical Neurophysiology · doi:10.1097/wnp.0b013e3181775993 · Cited by 205

Time-frequency misfit and goodness-of-fit criteria for quantitative comparison of time signals

Kristeková, M., Kristek, J., & Moczo, P. (2009) · Geophysical Journal International · doi:10.1111/j.1365-246x.2009.04177.x · Cited by 205

Dynamics of a neural system with a multiscale architecture

Breakspear, M. J., & Stam, C. J. (2005) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2005.1643 · Cited by 205

Adaptive hypothesis testing using wavelets

Spokoiny, V. G. (1996) · The Annals of Statistics · doi:10.1214/aos/1032181163 · Cited by 205

Compactly Supported Tight Frames Associated with Refinable Functions

Chui, C. K., & He, W. (2000) · Applied and Computational Harmonic Analysis · doi:10.1006/acha.2000.0301 · Cited by 205

Short-term load forecasting by wavelet transform and evolutionary extreme learning machine

Song, L., Wang, P., & Goel, L. (2015) · Electric Power Systems Research · doi:10.1016/j.epsr.2015.01.002 · Cited by 204

Fully adaptive multiresolution finite volume schemes for conservation laws

Cohen, A. K., Kaber, S. M., Müller, S., & Postel, M. (2001) · Mathematics of Computation · doi:10.1090/s0025-5718-01-01391-6 · Cited by 204

An expert system based on S-transform and neural network for automatic classification of power quality disturbances

Uyar, M., Yıldırım, S., & Gençoğlu, M. T. (2008) · Expert Systems with Applications · doi:10.1016/j.eswa.2008.07.030 · Cited by 203

EEG analysis using wavelet-based information tools

Rosso, O. A., Martin, M. T., Figliola, A., Keller, K., & Plastino, A. (2006) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2005.10.009 · Cited by 204

Wavelets on the 2-Sphere: A Group-Theoretical Approach

Antoine, J.-P., & Vandergheynst, P. (1999) · Applied and Computational Harmonic Analysis · doi:10.1006/acha.1999.0272 · Cited by 203

Damage detection using the Lipschitz exponent estimated by the wavelet transform: applications to vibration modes of a beam

Hong, J., Kim, Y. Y., Lee, H. C., & Lee, Y. W. (2002) · International Journal of Solids and Structures · doi:10.1016/s0020-7683(01)00279-7 · Cited by 202

On Dual Wavelet Tight Frames

Han, B. (1997) · Applied and Computational Harmonic Analysis · doi:10.1006/acha.1997.0217 · Cited by 202

Adaptive perceptual color-texture image segmentation

Chen, J., Pappas, T. N., Mojsilović, A., & Rogowitz, B. E. (2005) · IEEE Transactions on Image Processing · doi:10.1109/tip.2005.852204 · Cited by 204

Multiscale contrast enhancement for radiographies: Laplacian pyramid versus fast wavelet transform

Dippel, S., Stahl, M., Wiemker, R., & Blaffert, T. (2002) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2002.1000258 · Cited by 202

Quantum signal processing

Eldar, Y. C., & Oppenheim, A. V. (2002) · IEEE Signal Processing Magazine · doi:10.1109/msp.2002.1043298 · Cited by 201

Scaling properties of foreign exchange volatility

Ramazan Gençay, A., Selçuk∥, F., & Whitcher, B. J. (2001) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(00)00456-8 · Cited by 201

A method for spike sorting and detection based on wavelet packets and Shannon's mutual information

Hulata, E., Segev, R., & Ben‐Jacob, E. (2002) · Journal of Neuroscience Methods · doi:10.1016/s0165-0270(02)00032-8 · Cited by 201

The analysis of foreign exchange data using waveform dictionaries

Ramsey, J. B., & Zhang, Z. (1997) · Journal of Empirical Finance · doi:10.1016/s0927-5398(96)00013-8 · Cited by 200

Linearized Bregman Iterations for Frame-Based Image Deblurring

Jian-feng Cai, A., Osher, S., & Shen, Z. (2009) · SIAM Journal on Imaging Sciences · doi:10.1137/080733371 · Cited by 200

Stability Properties of Graph Neural Networks

Gama, F., Bruna, J., & Ribeiro, A. (2020) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2020.3026980 · Cited by 219

An Invitation to Compressive Sensing

Foucart, S., & Rauhut, H. (2013) · Applied and numerical harmonic analysis · doi:10.1007/978-0-8176-4948-7_1 · Cited by 199

Automatic fault feature extraction of mechanical anomaly on induction motor bearing using ensemble super-wavelet transform

He, W., Zi, Y., Chen, B., Wu, F. C., & He, Z. (2014) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2014.09.007 · Cited by 199

Financial forecasting using ANFIS networks with Quantum-behaved Particle Swarm Optimization

Bagheri, A., Peyhani, H. M., & Akbari, M. (2014) · Expert Systems with Applications · doi:10.1016/j.eswa.2014.04.003 · Cited by 199

Dynamics of Particles and Fields

Martin, B. (1999) · Advances in imaging and electron physics · doi:10.1016/s1076-5670(08)70227-1 · Cited by 199

A new intensity‐scale approach for the verification of spatial precipitation forecasts

Casati, B., Ross, G., & Stephenson, D. B. (2004) · Meteorological Applications · doi:10.1017/s1350482704001239 · Cited by 198

Multidimensional Directional Filter Banks and Surfacelets

Lu, Y. M., & Do, M. N. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.891785 · Cited by 198

Adaptive Weights Smoothing with Applications to Image Restoration

Polzehl, J., & Spokoiny, V. G. (2000) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00235 · Cited by 198

Gated Graph Recurrent Neural Networks

Ruiz, L., Gama, F., & Ribeiro, A. (2020) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2020.3033962 · Cited by 214

Structural damage identification using damping: a compendium of uses and features

Cao, M. S., Sha, G. G., Gao, Y. F., & Ostachowicz, W. (2017) · Smart Materials and Structures · doi:10.1088/1361-665x/aa550a · Cited by 196

Wavelet analysis of stock returns and aggregate economic activity

Gallegati, M. (2007) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2007.07.019 · Cited by 196

A wavelet-based damage detection algorithm based on bridge acceleration response to a vehicle

Hester, D., & González, A. (2011) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2011.06.007 · Cited by 196

A study on compactly supported orthogonal vector-valued wavelets and wavelet packets

Chen, Q., & Cheng, Z. (2006) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2006.03.097 · Cited by 196

Real-time computerized annotation of pictures

Li, J., & Wang, J. Z. (2006) · ACM International Conference on Multimedia (ACM MM) · doi:10.1145/1180639.1180841 · Cited by 196

Thermistor at a Distance: Unobtrusive Measurement of Breathing

Fei, J., & Pavlidis, I. (2010) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2009.2032415 · Cited by 201

Multiscale MAP filtering of SAR images

Foucher, S., Bénié, G. B., & Boucher, J.-M. (2001) · IEEE Transactions on Image Processing · doi:10.1109/83.892442 · Cited by 196

A wavelet analysis of mean and volatility spillovers between oil and BRICS stock markets

Boubaker, H., & Raza, S. A. (2017) · Energy Economics · doi:10.1016/j.eneco.2017.01.026 · Cited by 196

Volume data and wavelet transforms

Muraki, S. (1993) · IEEE Computer Graphics and Applications · doi:10.1109/38.219451 · Cited by 196

The Statistical Analysis of Functional MRI Data

Lazar, N. A. (2008) · Statistics in the health sciences · doi:10.1007/978-0-387-78191-4 · Cited by 197

Modeling drivers’ speech under stress

Fernandez, R., & Picard, R. W. (2003) · Speech Communication · doi:10.1016/s0167-6393(02)00080-8 · Cited by 195

Motor Imagery EEG Signals Decoding by Multivariate Empirical Wavelet Transform-Based Framework for Robust Brain–Computer Interfaces

Sadiq, M. T., Yu, X., Yuan, Z., Fan, Z., Rehman, A. U., Ullah, I., Li, G., & Xiao, G. (2019) · IEEE Access · doi:10.1109/access.2019.2956018 · Cited by 195

Iterative Incremental Clustering of Time Series

Lin, J., Vlachos, M., Keogh, E., & Gunopulos, D. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-24741-8_8 · Cited by 194

Anisotropic Hardy spaces and wavelets

Bownik, M. (2003) · Memoirs of the American Mathematical Society · doi:10.1090/memo/0781 · Cited by 194

Sampling with Arbitrary Sampling and Reconstruction Spaces and Oblique Dual Frame Vectors

Eldar, Y. C. (2003) · Journal of Fourier Analysis and Applications · doi:10.1007/s00041-003-0004-2 · Cited by 194

An additive approach to transform-domain information hiding and optimum detection structure

Cheng, Q. S., & Huang, T. S. (2001) · IEEE Transactions on Multimedia · doi:10.1109/6046.944472 · Cited by 194

Decadal Scale Patterns in Beach Oscillation and Rotation Narrabeen Beach, Australia—Time Series, PCA and Wavelet Analysis

Short, A. D., & Trembanis, A. C. (2004) · Journal of Coastal Research · doi:10.2112/1551-5036(2004)020[0523:dspibo]2.0.co;2 · Cited by 193

Localization of Frames, Banach Frames, and the Invertibility of the Frame Operator

Gr�chenig, K. (2004) · Journal of Fourier Analysis and Applications · doi:10.1007/s00041-004-8007-1 · Cited by 193

Multivariate denoising using wavelets and principal component analysis

Aminghafari, M., Chèze, N., & Poggi, J. (2005) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2004.12.010 · Cited by 192

Structural damage identification using static test data and changes in frequencies

Wang, X., Hu, N., Fukunaga, H., & Yao, Z. (2001) · Engineering Structures · doi:10.1016/s0141-0296(00)00086-9 · Cited by 192

Automatic reduction of hyperspectral imagery using wavelet spectral analysis

Kaewpijit, S., Moigne, J. L., & El-Ghazawi, T. A. (2003) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2003.810712 · Cited by 192

Systematic risk and timescales

̧ay, R. G., ̧uk, F. S., & Whitcher, B. J. (2003) · Quantitative Finance · doi:10.1088/1469-7688/3/2/305 · Cited by 192

Oil price and exchange rates: A wavelet based analysis for India

Tiwari, A. K., Dar, A. B., & Bhanja, N. (2013) · Economic Modelling · doi:10.1016/j.econmod.2012.11.043 · Cited by 192

A Review on Deep Learning in Medical Image Reconstruction

Zhang, H., & Dong, B. (2020) · Journal of the Operations Research Society of China · doi:10.1007/s40305-019-00287-4 · Cited by 196

A study on water quality prediction by a hybrid CNN-LSTM model with attention mechanism

Yang, Y., Xiong, Q., Wu, C., Zou, Q., Yu, Y., Yi, H., & Gao, M. (2021) · Environmental Science and Pollution Research · doi:10.1007/s11356-021-14687-8 · Cited by 196

Emerging applications of multirate signal processing and wavelets in digital communications

Wornell, G. W. (1996) · Proceedings of the IEEE · doi:10.1109/5.488701 · Cited by 192

Current signature analysis of induction motor mechanical faults by wavelet packet decomposition

Ye, Z., Wu, B., & Sadeghian, A. (2003) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2003.819682 · Cited by 191

Time frequency relationship between energy consumption, economic growth and environmental degradation in the United States: Evidence from transportation sector

Raza, S. A., Shah, N., & Sharif, A. (2019) · Energy · doi:10.1016/j.energy.2019.01.077 · Cited by 190

Detection of Edges in Spectral Data

Gelb, A., & Tadmor, E. (1999) · Applied and Computational Harmonic Analysis · doi:10.1006/acha.1999.0262 · Cited by 190

The superposition principle and cavity ring-down spectroscopy

Lehmann, K. K., & Romanini, D. (1996) · The Journal of Chemical Physics · doi:10.1063/1.472955 · Cited by 190

Compressed modes for variational problems in mathematics and physics

Ozoliņš, V., Lai, R., Caflisch, R. E., & Osher, S. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1318679110 · Cited by 189

Asymmetric and time-varying linkages between carbon emissions, globalization, natural resources and financial development in China

Ling, G., Razzaq, A., Guo, Y., Fatima, T., & Shahzad, F. (2021) · Environment Development and Sustainability · doi:10.1007/s10668-021-01724-2 · Cited by 189

Time Frequency Analysis of Dispersive Waves by Means of Wavelet Transform

KISHIMOTO, K., INOUE, H., Hamada, M., & SHIBUYA, T. (1995) · Journal of Applied Mechanics · doi:10.1115/1.2896009 · Cited by 189

Robust Image Watermarking Based on Multiband Wavelets and Empirical Mode Decomposition

Bi, N., Sun, Q., Huang, D., Yang, Z., & Huang, J. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.901206 · Cited by 188

Image-Quality-Based Adaptive Face Recognition

Sellahewa, H., & Jassim, S. (2010) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2009.2037989 · Cited by 188

The co-movement between oil and clean energy stocks: A wavelet-based analysis of horizon associations

Maghyereh, A., Awartani, B. M. A., & Abdoh, H. (2018) · Energy · doi:10.1016/j.energy.2018.12.039 · Cited by 188

PLS regression on wavelet compressed NIR spectra

Trygg, J., & Wold, S. (1998) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(98)00013-6 · Cited by 188

Vibration-based structural damage identification using wavelet transform

Bayissa, W. L., Haritos, N., & Thelandersson, S. (2007) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2007.11.001 · Cited by 188

SLEX Analysis of Multivariate Nonstationary Time Series

Ombao, H., von Sachs, R., & Guo, W. (2005) · Journal of the American Statistical Association · doi:10.1198/016214504000001448 · Cited by 187

Applications of the synchrosqueezing transform in seismic time-frequency analysis

Herrera, R. H., Han, J., & van der Baan, M. (2014) · Geophysics · doi:10.1190/geo2013-0204.1 · Cited by 187

Forecasting of the daily meteorological pollution using wavelets and support vector machine

Osowski, S., & Garanty, K. (2006) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2006.10.008 · Cited by 186

A SVM-based pipeline leakage detection and pre-warning system

Qu, Z., Feng, H., Zeng, Z., Zhuge, J., & Jin, S. (2009) · Measurement · doi:10.1016/j.measurement.2009.12.022 · Cited by 186

Traveling-Wave-Based Fault-Location Technique for Transmission Grids Via Wide-Area Synchronized Voltage Measurements

Korkali, M., Lev-Ari, H., & Abur, A. (2011) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2011.2176351 · Cited by 186

A review of numerical methods for nonlinear partial differential equations

Tadmor, E. (2012) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-2012-01379-4 · Cited by 195

Maximal Overlap Wavelet Statistical Analysis With Application to Atmospheric Turbulence

Cornish, C. R., Bretherton, C. S., & Percival, D. B. (2006) · Boundary-Layer Meteorology · doi:10.1007/s10546-005-9011-y · Cited by 186

Approximation of functions over redundant dictionaries using coherence

Gilbert, A. C., Muthukrishnan, S., & Strauss, M. J. (2003) · doi:10.5555/644108.644149 · Cited by 185

Multiresolution Flux Decomposition

Howell, J., & Mahrt, L. J. (1997) · Boundary-Layer Meteorology · doi:10.1023/a:1000210427798 · Cited by 185

Multiresolution Wavelet Analysis of Heartbeat Intervals Discriminates Healthy Patients from Those with Cardiac Pathology

Stefan Thurner, A., Feurstein, M., & Teich, M. C. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.1544 · Cited by 185

A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfaces

Arnéodo, A., Decoster, N., & Roux, S. G. (2000) · The European Physical Journal B · doi:10.1007/s100510051161 · Cited by 185

An Integrated Index for the Identification of Focal Electroencephalogram Signals Using Discrete Wavelet Transform and Entropy Measures

Sharma, R. K., Pachori, R. B., & Acharya, U. R. (2015) · Entropy · doi:10.3390/e17085218 · Cited by 184

Proximal Thresholding Algorithm for Minimization over Orthonormal Bases

Combettes, P. L., & Pesquet, J.-C. (2007) · SIAM Journal on Optimization · doi:10.1137/060669498 · Cited by 184

Wavelet basis functions in biomedical signal processing

Rafiee, J., Reif, J., Prause, N., & Schoen, M. P. (2010) · Expert Systems with Applications · doi:10.1016/j.eswa.2010.11.050 · Cited by 184

A survey and evaluation of promising approaches for automatic image-based defect detection of bridge structures

Jahanshahi, M. R., Kelly, J. S., Masri, S. F., & Sukhatme, G. S. (2008) · Structure and Infrastructure Engineering · doi:10.1080/15732470801945930 · Cited by 190

Wavelet methods in numerical analysis

Cohen, A. K. (2000) · Handbook of numerical analysis · doi:10.1016/s1570-8659(00)07004-6 · Cited by 184

Advances in multiple scale kernel particle methods

Liu, W. K., Chen, Y., Chang, C. T., & Belytschko, T. (1996) · Computational Mechanics · doi:10.1007/bf00350529 · Cited by 184

Sparse microwave imaging: Principles and applications

Zhang, B., Hong, W., & Wu, Y. (2012) · Science China Information Sciences · doi:10.1007/s11432-012-4633-4 · Cited by 185

Estimating the Parameters of a Fractional Brownian Motion by Discrete Variations of its Sample Paths

Coeurjolly, J. (2001) · Statistical Inference for Stochastic Processes · doi:10.1023/a:1017507306245 · Cited by 183

Wavelet spectra compared to Fourier spectra

Perrier, V., Philipovitch, T., & Basdevant, C. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531340 · Cited by 183

Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization

Izuki, M. (2010) · Analysis Mathematica · doi:10.1007/s10476-010-0102-8 · Cited by 182

Statistical techniques for online anomaly detection in data centers

Wang, C., Viswanathan, K., Lakshminarayan, C. K., Talwar, V., Satterfield, W., & Schwan, K. (2011) · IFIP/IEEE International Symposium on Integrated Network Management (IM) · doi:10.1109/inm.2011.5990537 · Cited by 182

Sequence-based modeling of deep learning with LSTM and GRU networks for structural damage detection of floating offshore wind turbine blades

Choe, D., Kim, H.-C., & Kim, M. (2021) · Renewable Energy · doi:10.1016/j.renene.2021.04.025 · Cited by 187

Practical statistics for astronomers

(2004) · Choice Reviews Online · doi:10.5860/choice.41-5965 · Cited by 182

On the continuous wavelet transforms applied to discrete vibrational data for detecting open cracks in damaged beams

Gentile, A., & Messina, A. (2003) · International Journal of Solids and Structures · doi:10.1016/s0020-7683(02)00548-6 · Cited by 181

Studying Digital Imagery of Ancient Paintings by Mixtures of Stochastic Models

Li, J., & Wang, J. Z. (2004) · IEEE Transactions on Image Processing · doi:10.1109/tip.2003.821349 · Cited by 181

Reproducing kernel hierarchical partition of unity, Part I?formulation and theory

Li, S., & Liu, W. K. (1999) · International Journal for Numerical Methods in Engineering · doi:10.1002/(sici)1097-0207(19990530)45:3 · Cited by 181

Generalized cross validation for wavelet thresholding

Jansen, M., Malfait, M. J., & Bultheel, A. (1997) · Signal Processing · doi:10.1016/s0165-1684(97)83621-3 · Cited by 181

The Discrete Wavelet Transform in S

Nason, G. P., & Silverman, B. W. (1994) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.1994.10474637 · Cited by 181

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