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Bibliography
Mallat, S. and Hwang, W. L., Singularity detection and processing with wavelets, IEEE Trans. Inf. Theory, Vol. 38, No. 2, pp. 617–643, 1992.
Strickland, R. N. and Hahn, H. I., Wavelet transform matched filters for the detection and classification of microcalcifications in mammography, In: Proceedings of the International Conference on Image Processing, Washington, D.C., Vol. 1, pp. 422–425, 1995.
Grossman, A. and Morlet, J., Decomposition of Hardy functions into square integrable wavelets of constant shape, SIAM J. Math. Anal., Vol. 15, No. 4, pp. 723–736, 1984.
Haar, A., Zur Theorie der Orthogonalen Funktionensysteme, Math. Annal., Vol. 69, pp. 331–371, 1910.
Mallat, S., A theory for multiresolution signal decomposition: The wavelet representation IEEE Trans. Pattern Anal. Mach. Intell., Vol. 11, No. 7, pp. 674–693, 1989.
Daubechies, I., Orthonormal bases of compactly supported wavelets, Commun. Pure Appl. Math., Vol. 41, No. 7, pp. 909–996, 1988.
Unser, M., Aldroubi, A., and Laine, A., IEEE transactions on medical imaging: Special issue on wavelets in medical imaging, Vol. 22, No. 3, 2003.
Weaver, J. B., Yansun, X., Healy, D. M., and Cromwell, L. D., Filtering noise from images with wavelet transforms Magn. Reson. Med., Vol. 21, No. 2, pp. 288–295, 1991.
Unser, M. and Aldroubi, A., A review of wavelets in biomedical applications Proceedings of the IEEE, Vol. 84, No. 4, pp. 626–638, 1996.
Laine, A., Wavelets in spatial processing of biomedical images, Ann. Rev. Biomed. Eng., Vol. 2, pp. 511–550, 2000.
Aldroubi, A. and Unser, M., Wavelets in Medicine and Biology, CRC Press, Boca Raton, FL, 1996.
Jain, A. K., Fundamentals of Digital Image Processing, Prentice-Hall, Englewood Cliffs, NJ, 1989.
Papoulis, A., The Fourier Integral and its Applications, McGraw-Hill, New York, NY, 1987.
Mallat, S., A Wavelet Tour of Signal Processing, Academic Press, San Diego, CA, 1998.
Daubechies, I., Ten Lectures on Wavelets, Siam, Philadelphia, PA, 1992.
Mallat, S. and Zhong, S., Characterization of signals from multi-scale edges, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 14, No. 7, pp. 710–732, 1992.
Holschneider, M., Kronland-Martinet, K., Morlet, J., and Tchamitchian, P., Wavelets, Time Frequency Methods and Phase Space, Springer-Verlag, Berlin, 1989.
Shensa, M., The discrete wavelet transform: Wedding the a trous and mallat algorithms, IEEE Trans. Signal Process., Vol. 40, No. 10, pp. 2464–2482, 1992.
Koren, I. and Laine, A., A discrete dyadic wavelet transform for multidimensional feature analysis, In: Time Frequency and Wavelets in Biomedical Signal Processing, IEEE Press Series in Biomedical Engineering, M. Akay, Ed., IEEE Press, Piscataway, NJ, pp. 425–448, 1998.
Feichtinger, H. and Strohmer, T., eds, Gabor Analysis and Algorithms: Theory and Applications, Birkhäuser, Boston, MA, 1998.
Wickerhauser, M. V., Adapted Wavelet Analysis from Theory to Software, Wellesley, Boston, MA, 1993.
Meyer, F. and Coifman, R., Brushlets: A tool for directional image analysis and image compression, Appl. Comput. harmonic Anal., Vol. 4, pp. 147–187, 1997.
Gabor, D., Theory of communication, J. IEE, Vol. 93, pp. 429–457, 1946.
Bastiaans, M., A sampling theorem for the complex spectrogram and Gabor’s expansion of a signal in Gaussian elementary signals, Opt. Eng., Vol. 20, No. 4, pp. 594–598, 1981.
Porat, M. and Zeevi, Y., The generalized Gabor scheme of image representation in biological and machine vision, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 10, No. 4, pp. 452–468, 1988.
Hubel, D. and Wiesel, T., Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex, J. Physiol., Vol. 160, pp. 106–154, 1962.
Daugman, J., Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression, IEEE Trans. Acoust., Speech, Signal Process., Vol. 36, No. 7, pp. 1169–1179, 1988.
Porat, M. and Zeevi, Y., Localized texture processing in vision: Analysis and synthesis in the Gaborian space, IEEETrans. Biomed. Eng., Vol. 36, No. 1, pp. 115–129, 1989.
Coifman, R. R., Meyer, Y., and Wickerhauser, M. V., Wavelet Analysis and signal processing, In: Wavelets and Their Applications, B. Ruskai, Ed., Jones and Barlett, Boston, pp. 153–178, 1992.
Coifman, R. R. and Woog, L. J., Adapted waveform analysis, wavelet packets, and local cosine libraries as a tool for image processing, In: Investigative and Trial Image Processing, San Diego, CA, Vol. 2567, 1995.
Malvar, H., Lapped transforms for efficient transform/subband coding, IEEE Trans. Acoust. Sign. Speech Process., Vol. 38, pp. 969–978, 1990.
Donoho, D. L. and Johnstone, I. M., Ideal de-noising in an orthonormal basis chosen from a library of bases, Statistics Department, Stanford University, Technical Report, 1994.
Donoho, D., De-noising by soft-thresholding, IEEE Trans. Inf. Theory, Vol. 41, No. 3, pp. 613–627, 1995.
Gao, H. and Bruce, A., Waveshrink with firm shrinkage, Statist. Sinica, Vol. 7, pp. 855–874, 1997.
Laine, A., Fan, J., and Yang, W., Wavelets for contrast enhancement of digital mammography, IEEE Eng. Med. Biol. (September), pp. 536–550, 1995.
Koren, I., Laine, A., and Taylor, F., Image fusion using steerable dyadic wavelet transform, In: Proceedings of the International Conference on Image Processing, Washington, D.C., pp. 232–235, 1995.
Laine, A., Fan, J., and Schuler, S., A framework for contrast enhancement by dyadic wavelet analysis, In: Digital Mammography, A. Gale, S. Astley, D. Dance, and A. Cairns, Eds., Elsevier, Amsterdam, 1994.
Laine, A., Schuler, S., Fan, J., and Huda, W., Mammographic feature enhancement by multi-scale analysis, IEEE Trans. Med. Imaging, Vol. 13, No. 4, pp. 725–740, 1994.
Fan, J. and Laine, A., multi-scale contrast enhancement and de-noising in digital radiographs, In: Wavelets in Medicine and Biology, A. Aldroubi and M. Unser, Eds., CRC Press, Boca Raton FL, pp. 163–189, 1996.
Coifman, R. and Donoho, D., Translation-invariant de-noising, In: Wavelets and Statistics, A. Antoniadis and G. Oppenheim, Eds., Springer-Verlag, New York, NY, 1995.
Donoho, D. and Johnstone, I., Ideal spatial adaptation via wavelet shrinkage, Biometrika, Vol. 81, pp. 425–455, 1994.
Stein, C., Estimation of the mean of a multivariate normal distribution, Ann. Stat., Vol. 9, pp. 1135–1151, 1981.
Donoho, D., Nonlinear solution of linear inverse problems by wavelet-vaguelette decompositions, J. Appl. Comput. Harmonic Anal., Vol. 2, No. 2, pp. 101–126, 1995.
Chang, S., Yu, B., and Vetterli, M., Spatially adaptive wavelet thresholding with context modeling for image de-noising, IEEE Trans. Image Process., Vol. 9, No. 9, pp. 1522–1531, 2000.
Donoho, D. and Johnstone, I., Adapting to unknown smoothness via wavelet shrinkage, J. Am. Stat. Assoc., Vol. 90, No. 432, pp. 1200–1224, 1995.
Koren, I., A Multi-Scale Spline Derivative-Based Transform for Image Fusion and Enhancement, Ph.D. Thesis, Electrical Engineering, University of Florida, 1996.
Kalifa, J., Laine, A., and Esser, P., Regularization in tomographic reconstruction using thresholding estimators, IEEE Trans. Med. Imaging, Vol. 22, No. 3, pp. 351–359, 2003.
Selesnick, I., The slantlet transform, IEEE Trans. Signal Process., Vol. 47, No. 5, pp. 1304–1313, 1999.
Candes, E. and Donoho, D., Curvelets—a surprisingly effective nonadaptive representation for objects with edges, In: Curve and Surface Fitting: Saint-Malo 1999, A. Cohen, C. Rabut, and L. Schumaker, Eds., Vanderbilt University Press, Nashville, TN, 1999.
Starck, J., Candes, E., and Donoho, D., The curvelet transform for image de-noising, IEEE Trans. Image Process., Vol. 11, No. 6, pp. 670–684, 2002.
Candes, E. and Donoho, D., Ridgelets: The key to higher-dimensional intermittency?, Phil. Trans. R. Soc. A, Vol. 357, pp. 2495–2509, 1999.
Liebling, M., Blu, T., and Unser, M., Fresnelets: New Multiresolution Wavelet Bases for Digital Holography, IEEE Trans. Image Process., Vol. 12, No. 1, pp. 29–43, 2003.
Gao, H., Wavelet shrinkage de-noising using the non-negative Garrote, J. Comput. Graph. Stat., Vol. 7, pp. 469–488, 1998.
Antoniadis, A. and Fan, J., Regularization of wavelet approximations, J. Am. Stat. Assoc., Vol. 96, No. 455, pp. 939–967, 2001.
Nason, G., Wavelet shrinkage using cross-validation, J. R. Stat. Soc., Vol. 58, pp. 463–479, 1996.
Weyrich, N. and Warhola, G., De-noising using wavelets and cross-validation, NATA Adv. Study Inst., Vol. 454, pp. 523–532, 1995.
Jansen, M., Malfait, M., and Bultheel, A., Generalised cross-validation for wavelet thresholding, Signal Process., Vol. 56, pp. 33–44, 1997.
Ogden, R. T. and Parzen, E., Change-point approach to data analytic wavelet thresholding, Stat. Comput., Vol. 6, pp. 93–99, 1996.
Angelini, E., Laine, A., Takuma, S., Holmes, J., and Homma, S., LV volume quantification via spatio-temporal analysis of real-time 3D echocardiography, IEEE Trans. Med. Imaging, Vol. 20, pp. 457–469, 2001.
Jin, Y., Angelini, E., Esser, P., and Laine, A., De-noising SPECT/PET images using cross-scale regularization, In: Proceedings of the Sixth International Conference on Medical Image Computing and Computer Assisted Interventions (MICCAI 2003), Montreal, Canada, Vol. 2879, No. 2, pp. 32–40, 2003.
Mulet-Parada, M. and Noble, J. A., 2D+T acoustic boundary detection in echocardiography, In: Medical Image Computing and Computer-Assisted Intervention-MICCAI’98, Cambridge, MA, pp. 806–813, 1998.
Chen, C., Lu, H., and Han, K., A textural approach based on Gabor functions for texture edge detection in ultrasound images, Ultrasound Med. Biol., Vol. 27, No. 4, pp. 515–534, 2001.
McLachlan, G. J. and Krishnan, T., The EM Algorithm and Extensions, Wiley & Sons, Inc., New York, 1997.
Shepp, L. and Vardi, V., Maximum likelihood reconstruction for emission computed tomography, IEEE Trans. Med. Imaging, Vol. 1, pp. 113–122, 1982.
Farquhar, T. H., Chatziioannou, A., Chinn, G., Dahlbom, M., and Hoffman, E. J., An investigation of filter choice for filtered back-projection reconstruction in PET, IEEE Trans. Nucl. Sci., Vol. 45(3 Part 2), pp. 1133–1137, 1998.
Hudson, H. and Larkin, R., Accelerated image reconstruction using ordered subsets of projection data, IEEE Trans. Med. Imaging, Vol. 13, No. 4, pp. 601–609, 1994.
Freeman, W. and Adelson, E., The design and use of steerable filters, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 13, pp. 891–906, 1991.
Babaud, J., Witkin, A., Baudin, M., and Duba, R., Uniqueness of the Gaussian kernel for scale-space filtering, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 8, pp. 26–33, 1986.
Julez, B., A Theory of preattentive texture discrimination based on first-order statistics of textons, Biol. Cybern., Vol. 41, pp. 131–138, 1981.
Watson, A., Barlow, H., and Robson, J., What dose the eye see best?, Nature, Vol. 302, pp. 419–422, 1983.
Beck, J., Sutter, A., and Ivry, R., Spatial frequency channels and perceptual grouping in texture segregation, Comput. Vis., Graph. Image Process., Vol. 37, pp. 299–325, 1987.
Daugman, J., Image analysis by local 2-D spectral signatures, J. Opt. Soc. Am. A, Vol. 2, pp. 74, 1985.
Unser, M., Texture classification and segmentation using wavelet frames, IEEE Trans. Image Process., Vol. 4, No. 11, pp. 1549–1560, 1995.
Laine, A. and Fan, J., Texture classification by wavelet packet signatures, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 15, No. 11, pp. 1186–1191, 1993.
Laine, A. and Fan, J., Frame representation for texture segmentation, IEEE Trans. Image Process., Vol. 5, No. 5, pp. 771–780, 1996.
Hsin, H. and Li, C., An experiment on texture segmentation using modulated wavelets, IEEE Trans. Syst., Man Cybern., Vol. 28, No. 5, pp. 720–725, 1998.
Wang, J., Multiwavelet packet transform with application to texture segmentation, Electron. Lett., Vol. 38, No. 18, pp. 1021–1023, 2002.
Acharyya, M. and Kundu, M., Document image segmentation using wavelet scale-space features, IEEE Trans. Circuits Syst. Video Technol., Vol. 12, No. 12, pp. 1117–1127, 2002.
Wang, J., Li, J., Gray, R., and Wiederhold, G., Unsupervised multiresolution segmentation for images with low depth of field, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 23, No. 1, pp. 85–90, 2001.
Etemad, K., Doermann, D., and Chellappa, R., Multi-scale segmentation of unstructured document pages using soft decision integration, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 19, No. 1, pp. 92–96, 1997.
Porter, R. and Canagarajah, N., A robust automatic clustering scheme for image segmentation using wavelets, IEEE Trans. Image Process., Vol. 5, No. 4, pp. 662–665, 1996.
Zhang, J., Wang, D., and Tran, Q., A wavelet-based multiresolution statistical model for texture, IEEE Trans. Image Process., Vol. 7, No. 11, pp. 1621–1627, 1998.
Choi, H. and Baraniuk, R., Multis-cale image segmentation using wavelet-domain hidden markov models, IEEE Trans. Image Process., Vol. 10, No. 9, pp. 1309–1321, 2001.
Li, J. and Gray, R., Context-based multi-scale classification of document images using wavelet coefficient distributions, IEEE Trans. Image Process., Vol. 9, No. 9, pp. 1604–1616, 2000.
Charalampidis, D. and Kasparis, T., Wavelet-based rotational invariant roughness features for texture classification and segmentation, IEEE Trans. Image Process., Vol. 11, No. 8, pp. 825–837, 2002.
Chan, T. F. and Vese, L. A., Active controus without edges, IEEE Trans. Image Process., Vol. 10, No. 2, pp. 266–277, 2001.
Yezzi, A., Tsai, A., and Willsky, A., A statistical approach to image segmentation for biomodal and trimodal imagery, ICCV, pp. 898–903, 1999.
Canny, J., A computational approach to edge detection, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 8, No. 6, pp. 679–698, 1986.
Aydin, T., Yemez, Y., Anarim, E., and Sankur, B., Multi-directional and multi-scale edge detection via M-band wavelet Transform, IEEE Trans. Image Process., Vol. 5, No. 9, pp. 1370–1377, 1996.
Laine, A. F., Huda, W., Chen, D., and Harris, J. G., Local enhancement of masses using continuous scale representations, J. Math. Imaging Vis., Vol. 7, No. 1, 1997.
Laine, A., and Zong, X., Border indentification of echocardiograms via multi-scale edge detection and shape modeling, In: IEEE International Conference on Image Processing, Lausanne, Switzerland, pp. 287–290, 1996.
Koren, I., Laine, A. F., Fan, J., and Taylor, F. J., Edge detection in echocardiographic image sequences by 3-D multiscale analysis, IEEE International Conference on Image Processing, Vol. 1, No. 1, pp. 288–292, 1994.
Dima, A., Scholz, M., and Obermayer, K., Automatic segmentation and skeletonization of neurons from confocal microscopy images based on the 3-D wavelet transform, IEEE Trans. Image Process., Vol. 11, No. 7, pp. 790–801, 2002.
Wilson, R., Calway, A., and Pearson, R., A generalized wavelet transform for Fourier analysis: The multiresolution Fourier transform and its application to image and audio signal analysis, IEEE Trans. Inf. Theory, Vol. 38, No. 2, pp. 674–690, 1992.
Yoshida, H., Katsuragawa, S., Amit, Y., and Doi, K., Wavelet snake for classification of nodules and false positives in digital chest radiographs, In: IEEE EMBS Annual Conference, Chicago, IL, pp. 509–512, 1997.
deRivaz, P. and Kingsbury, N., Fast Segmentation using level set curves of complex wavelet surfaces, In: IEEE International Conference on Image Processing, Vol. 3, pp. 29–32, 2000.
Wu, H., Liu, J., and Chui, C., A wavelet frame based image force model for active contouring algorithms, IEEE Trans. Image Process., Vol. 9, No. 11, pp. 1983–1988, 2000.
Sun, H., Haynor, D., and Kim, Y., Semiautomatic video object segmentation using VSnakes, IEEE Trans. Circuits Syst. Video Technol., Vol. 13, No. 1, pp. 75–82, 2003.
Neves, S., daSilva, E., and Mendonca, G., Wavelet-watershed automatic infrared image segmentation method, IEEE Electron. Lett., Vol. 39, No. 12, pp. 903–904, 2003.
Bello, M., A combined Markov random field and wave-packet transform-based approach for image segmentation, IEEE Trans. Image Process., Vol. 3, No. 6, pp. 834–846, 1994.
Davatzikos, C., Tao, X., and Shen, D., Hierarchical active shape models using the wavelet transform, IEEE Trans. Med. Imaging, Vol. 22, No. 3, pp. 414–423, 2003.
Strickland, R. N. and Hahn, H. I., Wavelet transforms for detecting microcalcifications in mammograms, IEEE Trans. Med. Imaging, Vol. 15, No. 2, pp. 218–229, 1996.
Zhang, X. and Desai, M., Segmentation of bright targets using wavelets and adaptive thresholding, IEEE Trans. Image Process., Vol. 10, No. 7, pp. 1020–1030, 2001.
Allen, R., Kamangar, F., and Stokely, E., Laplacian and orthogonal wavelet pyramid decompositions in coarse-to-fine registration, IEEE Trans. Signal Process., Vol. 41, No. 12, pp. 3536–3541, 1993.
Unser, M., Thevenaz, P., Lee, C., and Ruttimann, U., Registration and statistical analysis of PET images using the wavelet transform, IEEE Eng. Med. Biol. (September/October), pp. 603–611, 1995.
McGuire, M. and Stone, H., Techniques for multiresolution image registration in the presence of occlusions, IEEE Trans. Geosci. Remote Sensing, Vol. 38, No. 3, pp. 1476–1479, 2000.
Zheng, Q. and Chellappa, R., Acomputational vision approach to image registration, IEEE Trans. Image Process., Vol. 2, No. 3, pp. 311–325, 1993.
Moigne, J., Campbell, W., and Cromp, R., Automated parallel image registration technique based on the correlation of wavelet features, IEEE Trans. Geosci. Remote Sensing, Vol. 40, No. 8, pp. 1849–1864, 2002.
Dinov, I., Mega, M., Thompson, P., Woods, R., Sumners, D., Sowell, E., and Toga, A., Quantitative comparison and analysis of brain image registration using frequency-adaptive wavelet shrinkage, IEEE Trans. Inf. Technol. Biomed., Vol. 6, No. 1, pp. 73–85, 2002.
Unser, M. and Blu, T., Mathematical properties of the JPEG2000 wavelet filters, IEEE Trans. Image Process., Vol. 12, No. 9, pp. 1080–1090, 2003.
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Jin, Y., Angelini, E., Laine, A. (2005). Wavelets in Medical Image Processing: Denoising, Segmentation, and Registration. In: Suri, J.S., Wilson, D.L., Laxminarayan, S. (eds) Handbook of Biomedical Image Analysis. International Topics in Biomedical Engineering. Springer, Boston, MA. https://doi.org/10.1007/0-306-48551-6_6
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