4.10.1 Wavelet Representations

Chapter Contents (Back)
Wavelets. Representation, Wavelets. Wavelet transformations are generated by a smoothing filter and a wavelet filter. Different wavelet filters can be applied. One interpretation is that the wavelet transform is the same as applying quadrature mirror filters. The wavelet provides both time and frequency information. (Or in images space and frequency.) For general wavelet information see: Wavelet.Org:
WWW Link.
See also Wavelets for Watermarks.
See also Shearlet Based Restoration, Noise, Compressive Sensing.

Grosssmann, A., and Morlet, J.,
Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape,
SIAM_Math(15), 1984, pp. 723-736. The mathmatical introduction of wavelets. Later adopted by computer vision. BibRef 8400

Pentland, A.P.[Alex P.],
Interpolation Using Wavelet Bases,
PAMI(16), No. 4, April 1994, pp. 410-414.
IEEE DOI BibRef 9404
Earlier:
Surface Interpolation Using Wavelets,
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Springer DOI BibRef
And:
Spatial and Temporal Surface Interpolation Using Wavelet Bases,
SPIE(1570), 1991, pp. 43-62. Surface Reconstruction. Regularization. BibRef

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And: Corrections: IP(4), No. 9, September 1995, pp. 1340. BibRef

Haddad, Z.S., Simanca, S.R.,
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Hessnielsen, N., Wickerhauser, M.V.,
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BibRef

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BibRef
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Wavelet decomposition of binary finite images,
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IEEE DOI 9411
BibRef

Mohanty, K.K.,
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Watson, G.H., Watson, S.K.,
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Wu, B.F., Su, Y.L.,
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Scheunders, P.,
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Scheunders, P.,
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Segman, J.[Joseph], Zeevi, Y.Y.,
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Sagiv, C.[Chen], Sochen, N.A.[Nir A.], Zeevi, Y.Y.[Yehoshua Y.],
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Earlier:
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Springer DOI 0505
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Ferdman, Y.[Yossi], Sagiv, C.[Chen], Sochen, N.A.[Nir A.],
Full Affine Wavelets Are Scale-Space with a Twist,
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BibRef

Zhu, H.X.[Hui-Xia], Ritter, G.X.,
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Peyrin, F., Zaim, M., Goutte, R.,
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Antoine, J.P., Carrette, P., Murenzi, R., Piette, B.,
Image analysis with 2-D continuous wavelet transform,
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And: Correction. SP(35), No. 1, 1994, pp. 93. BibRef

Jansen, M., Bultheel, A.,
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A Nonlinear Contour Preserving Transform for Geometrical Image Compression,
IMVIP07(143-149).
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Normal multiresolution mesh, Image compression, Piecewise smooth, Wavelets BibRef

Crouse, M.S., Nowak, R.D., Baraniuk, R.G.,
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TSP(46), No. 4, April 1998, pp. 886-902. 9804
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Nowak, R.D., Baraniuk, R.G.,
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Romberg, J.K.[Justin K.], Choi, H.H.[Hyeok-Ho], Baraniuk, R.G.[Richard G.],
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Bayesian Wavelet-Domain Image Modeling using Hidden Markov Trees,
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Romberg, J.K.[Justin K.], Choi, H.H.[Hyeok-Ho], Baraniuk, R.G.[Richard G.],
Multiscale Edge Grammars for Complex Wavelet Transforms,
ICIP01(I: 614-617).
IEEE DOI 0108
BibRef
Earlier:
Multiscale Classification Using Complex Wavelets and Hidden Markov Tree Models,
ICIP00(Vol II: 371-374).
IEEE DOI 0008
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Choi, H.H.[Hyeok-Ho], Baraniuk, R.G.[Richard G.],
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IP(10), No. 9, September 2001, pp. 1309-1321.
IEEE DOI 0108
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Baraniuk, R.G.,
Wavelet soft-thresholding of time-frequency representations,
ICIP94(I: 71-74).
IEEE DOI 9411
BibRef

Berkner, K., Wells, Jr., R.O.,
A New Hierarchical Scheme for Approximating the Continuous Wavelet Transform with Applications to Edge Detection,
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IEEE Top Reference. BibRef 9908

Aldroubi, A.[Akram], Eden, M.[Murray], and Unser, M.[Michael],
Discrete Spline Filters for Multiresolutions and Wavelets of L2,
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Unser, M.[Michael],
Vanishing moments and the approximation power of wavelet expansions,
ICIP96(I: 629-632).
IEEE DOI BibRef 9600

Unser, M.,
Multigrid adaptive image processing,
ICIP95(I: 49-52).
IEEE DOI 9510
BibRef

Blu, T., and Unser, M.,
Quantitative L2 Error Analysis for Interpolation Methods and Wavelet Expansions,
ICIP97(I: 663-666).
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Luisier, F., Blu, T.,
SURE-LET Multichannel Image Denoising: Interscale Orthonormal Wavelet Thresholding,
IP(17), No. 4, April 2008, pp. 482-492.
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BibRef

Luisier, F., Blu, T., Unser, M.,
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Sure-Based Wavelet Thresholding Integrating Inter-Scale Dependencies,
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IEEE DOI 0610
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Blu, T., Luisier, F.,
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Tafti, P.D.[Pouya Dehghani], van de Ville, D., Unser, M.[Michael],
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Unser, M., Sage, D., van de Ville, D.,
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Unser, M.[Michael], van de Ville, D.[Dimitri],
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Higher-order riesz transforms and steerable wavelet frames,
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van de Ville, D.[Dimitri], Unser, M.[Michael],
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Hung, K.C.,
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Curve Representations. BibRef

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Tang, Y.Y., Yang, L., Liu, J.,
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IEEE Top Reference. 0004
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He, W., Lai, M.J.,
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Liew, A.W.C., Law, N.F.,
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Chang, S.G., Yu, B., Vetterli, M.,
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Chang, S.G., Yu, B.[Bin], Vetterli, M.,
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IEEE DOI 9810
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Chang, S.G., Yu, B.[Bin], Vetterli, M.,
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IP(9), No. 9, September 2000, pp. 1532-1546.
IEEE DOI 0008
BibRef
Earlier:
Multiple copy image denoising via wavelet thresholding,
ICIP98(I: 545-549).
IEEE DOI 9810
BibRef
Earlier:
Image Denoising via Lossy Compression and Wavelet Thresholding,
ICIP97(I: 604-607).
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Chang, S.G., and Vetterli, M.,
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ICIP01(I: 622-625).
IEEE DOI 0108
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ICIP01(II: 21-24).
IEEE DOI 0108
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Earlier:
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IEEE DOI 0008
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Earlier:
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Simoncelli, E.P., and Olshausen, B.A.,
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Wavelet-based 2-d multichannel signal estimation,
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Atkinson, I.C.[Ian C.], Kamalabadi, F.[Farzad],
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Alnasser, M., Foroosh, H.,
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Andreopoulos, Y.,
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Held, S., Storath, M., Massopust, P., Forster, B.,
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Mishiba, K.[Kazu], Ikehara, M.[Masaaki], Yoshitome, T.[Takeshi],
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IEICE(E96-D), No. 11, November 2013, pp. 2427-2436.
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Mishiba, K.[Kazu], Yoshitome, T.[Takeshi],
Image resizing with SIFT feature preservation,
ICIP13(991-995)
IEEE DOI 1402
Bidirectional control BibRef

Mishiba, K.[Kazu], Ikehara, M.[Masaaki],
Seam carving in wavelet transform domain,
ICIP11(1497-1500).
IEEE DOI 1201
BibRef

Ward, J.P.[John Paul], Chaudhury, K.N.[Kunal Narayan], Unser, M.[Michael],
Decay Properties of Riesz Transforms and Steerable Wavelets,
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Ward, J.P.[John Paul], Pad, P., Unser, M.[Michael],
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SPLetters(22), No. 11, November 2015, pp. 1918-1921.
IEEE DOI 1509
signal representation BibRef

Pad, P., Uhlmann, V., Unser, M.,
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IP(25), No. 5, May 2016, pp. 2275-2287.
IEEE DOI 1604
Algorithm design and analysis BibRef

Easley, G.R.[Glenn R.], Labate, D.[Demetrio], Patel, V.M.[Vishal M.],
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Traoré, A.[Albekaye], Carré, P.[Philippe], Olivier, C.[Christian],
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SP:IC(36), No. 1, 2015, pp. 127-139.
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Earlier:
Reduced-reference metric based on the quaternionic wavelet coefficients modeling by information criteria,
ICIP14(526-530)
IEEE DOI 1502
Quaternionic Wavelet Transform. Degradation BibRef

Liang, J.Z.[Jiu-Zhen], Hou, Z.J.[Zhen-Jie], Chen, C.[Chen], Xu, X.X.[Xiu-Xiu],
Supervised bilateral two-dimensional locality preserving projection algorithm based on Gabor wavelet,
SIViP(10), No. 8, November 2016, pp. 1441-1448.
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Deng, G.,
Guided Wavelet Shrinkage for Edge-Aware Smoothing,
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IEEE DOI 1702
computational complexity BibRef

Li, H.H.[Hui-Hui], Zeng, Y.[Yan], Yang, N.[Ning],
Image reconstruction for compressed sensing based on joint sparse bases and adaptive sampling,
MVA(29), No. 1, January 2018, pp. 145-157.
Springer DOI 1801
2 sparse bases for representation. DCT and a double-density dual-tree complex wavelet transform were utilized as two different sparse bases. BibRef

Barina, D.[David], Kula, M.[Michal], Zemcik, P.[Pavel],
Parallel wavelet schemes for images,
RealTimeIP(16), No. 5, October 2019, pp. 1365-1381.
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Liu, X.[Xinwu],
Total generalized variation and wavelet frame-based adaptive image restoration algorithm,
VC(35), No. 12, December 2018, pp. 1883-1894.
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Sparse Wavelet Networks,
SPLetters(27), 2020, pp. 111-115.
IEEE DOI 2001
Wavelet network, sparse representation, non-convex regularization, system identification BibRef

Wu, F.Z.[Fu-Zhi], Wu, J.[Jiasong], Shu, H.Z.[Hua-Zhong], Carrault, G.[Guy], Senhadji, L.[Lotfi],
Spatial-Enhanced Multi-Level Wavelet Patching in Vision Transformers,
SPLetters(31), 2024, pp. 446-450.
IEEE DOI 2402
Wavelet domain, Transformers, Frequency-domain analysis, Discrete wavelet transforms, Convolution, Standards, low-level feature BibRef


Yin, J.H.[Ji-Hao], Gao, C.[Chao], Wang, Y.F.[Yi-Fei], Wang, Y.S.[Yi-Song],
Hyperspectral image classification using wavelet packet analysis and gray prediction model,
IASP10(322-326).
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Fernandes Mota, V.[Virginia], de Almeida Perez, E.[Eder], Knop de Castro, T.[Tassio], Chapiro, A.[Alexandre], Bernardes Vieira, M.[Marcelo],
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ICIP09(2165-2168).
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Motwani, M.C.[Mukesh C.], Motwani, R.C.[Rakhi C.], Harris, F.C.[Frederick C.],
Wavelet based fuzzy perceptual mask for images,
ICIP09(4261-4264).
IEEE DOI 0911
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Tang, G.J.[Gui-Ji], Ye, J.S.[Jin-Sheng], Zhang, R.P.[Rong-Pei], Hu, A.J.[Ai-Jun],
Harmonic wavelet packets method and its application to signal analysis of rotating machinery,
IASP09(108-113).
IEEE DOI 0904
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Cen, H.Y.[Hai-Yan], Bao, Y.[Yidan], Huang, M.[Min], He, Y.[Yong],
Time Series Analysis of Grey Forecasting Based on Wavelet Transform and Its Prediction Applications,
SSPR06(349-357).
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Deng, G.[Guang],
Signal Estimation Using Multiple-Wavelet Representations and Gaussian Models,
ICIP05(I: 453-456).
IEEE DOI 0512
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Fletcher, A.K., Goyal, V.K., Rainchandran, K.,
On multivariate estimation by thresholding,
ICIP03(I: 61-64).
IEEE DOI 0312
Threshold to eliminate noise in Wavelets. BibRef

Bastys, A.,
The Gibbs phenomenon bounds in wavelet approximations,
ICIP03(I: 1017-1020).
IEEE DOI 0312
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Ma, K., Tang, X.,
Discrete Wavelet Face Graph Matching,
ICIP01(II: 217-220).
IEEE DOI 0108
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Dragotti, P.L.[Pier Luigi],
Wavelet Transform Footprints: Catching Singularities for Compression and Denoising,
ICIP00(Vol II: 363-366).
IEEE DOI 0008
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Dragotti, P.L.[Pier Luigi], Vetterli, M.,
Footprints and Edgeprints for Image Denoising and Compression,
ICIP01(II: 237-240).
IEEE DOI 0108
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Dyadic Wavelet-based Nonlinear Conduction Equation: Theory and Applications,
ICIP00(Vol I: 880-883).
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Wei, D., Evans, B.L., and Bovik, A.C.,
Biorthogonal Quincunx Coifman Wavelets,
ICIP97(II: 246-249).
IEEE DOI
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Moni, S.,
A Tree Structured, Wavelet-Based Stochastic Process for Fast Image Processing,
ICIP97(II: 227-229).
IEEE DOI BibRef 9700

Cheung, K.W., and Po, L.M.,
Preprocessing for Discrete Multiwavelet Transform of Two-Dimensional Signals,
ICIP97(II: 350-353).
IEEE DOI BibRef 9700

Chao, J.J., and Lin, C.C.,
Sea Clutter Rejection in Radar Image Using Wavelets and Fractals,
ICIP97(II: 354-357).
IEEE DOI BibRef 9700

Rodenas, J.A., Cabarrocas, D., and Garello, R.,
Wavelet Transform of SAR Images for Internal Wave Detection and Orientation,
ICIP97(I: 841-844).
IEEE DOI 9710
BibRef

Monro, D.M., and Sherlock, B.G.,
Space-Frequency Balance in Biorthogonal Wavelets,
ICIP97(I: 624-627).
IEEE DOI 9710
BibRef

Krongold, B., Ramchandran, K., and Jones, D.,
Frequency-Shift-Invariant Orthonormal Wavelet Packet Representations,
ICIP97(I: 628-631).
IEEE DOI BibRef 9700

Strobel, N., Mitra, S.K., and Manjunath, B.S.,
Model-Based Detection and Correction of Corrupted Wavelet Coefficients,
ICIP97(I: 925-928).
IEEE DOI
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Ho, W., Chang, W.,
Wavelet Representation for Multigrid Computation in Surface Interpolation Problem,
ICPR96(I: 740-744).
IEEE DOI 9608
(National Chiao-Tung Univ., ROC) BibRef

Sarkar, S.[Sandip], Poor, H.V.[H. Vincent],
Multiband cyclic wavelet transforms,
ICIP96(I: 589-592).
IEEE DOI 9610
BibRef

Kautsky, J.[Jaroslav], Turcajová, R.[Radka],
Adaptive wavelets for signal analysis,
CAIP95(906-911).
Springer DOI 9509
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Watanabe, S., Akimoto, Y., Komatsu, T., Saito, T.,
A new stabilized zero-crossing representation in the wavelet transform domain and signal reconstruction,
ICIP95(I: 37-40).
IEEE DOI 9510
BibRef

Hall, R.W., Kucuk, S., and Hamdi, M.,
Wavelet Transform Embeddings in Mesh Architectures,
CVPR93(596-597).
IEEE DOI BibRef 9300

Chapter on Computational Vision, Regularization, Connectionist, Morphology, Scale-Space, Perceptual Grouping, Wavelets, Color, Sensors, Optical, Laser, Radar continues in
Wavelets, Surveys, Reviews, Overviews, Evaluations, General .


Last update:Apr 18, 2024 at 11:38:49