Complex Wavelets for Shift Invariant Analysis and Filtering of Signals

By N. Kingsbury. 2001

1,901 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Media Technology

View Paper: https://www.semanticscholar.org/paper/9af641990d47fa01a3c90602645d93299d06ba22

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Citations in the corpus

The double-density dual-tree DWT (2004, methodology): “…filters of short support satis- fying 1) the perfect reconstruction conditions (5)–(8); 2) the Hilbert pair relations (4) or, equivalently, (15) and (16), which should be nearly satisfied; 3) zero moment conditions for , where are specified; 4) lowpass zeros at , where the factor should divide…”
Bivariate shrinkage with local variance estimation (2002, methodology): “DigitalObjectIdentifier 10.1109/LSP.2002.806054 both the orthogonal wavelet transform and the dual-tree complex wavelet transform (CWT) [7], [8], and some comparisons with the best available wavelet-based image-denoising results will be given in order to illustrate the effectiveness of the system.”
Face Recognition Under Varying Illumination Using Gradientfaces (2009, background): “However, the authors in [24] show that there are no illumination invariants, the illumination invariant obtained by the above-mentioned methods is at best insensitive to illumination.”
Image processing for artist identification (2008, methodology): “To jumpstart the development of such methods, the Van Gogh and Kröller-Müller Museums in The Netherlands graciously agreed to make a data set of 101 high-resolution gray-scale scans [C. Richard Johnson, Jr., Ella Hendriks, Igor J. Berezhnoy, Eugene Brevdo, Shannon M. Hughes, Ingrid Daubechies, Jia…”
Sparse directional image representations using the discrete shearlet transform (2008, background): “They include several schemes of “directional wavelets” (such as [1,3]), contourlets [12,31], complex wavelets [25,34] brushlets [9], ridgelets [6], curvelets [7], bandelets [29] and shearlets [20,18], introduced by the authors and their collaborators.”
Dictionaries for Sparse Representation Modeling (2010, background): “The complex wavelet transform [65], [66] is an oriented and near-translation-invariant high-dimensional extension of the wavelet transform, achieved through the utilization of two mother wavelets satisfying a specific relationship between them.”
Iterative Thresholding for Sparse Approximations (2008, background): “For example if all M dimensional subsets of elements from {φi} are linearly independent, but there exist a subset of size M + 1 in which the elements are dependent, then the spark of Φ is M + 1.”
The dual-tree complex wavelet transform (2005, methodology): “Examples include steerable pyramids [41, 96], directional filter banks and pyramids [10, 31], curvelets [15, 100], and directional wavelet transforms based on complex filter banks [36,39,55,57].”
The Curvelet Transform (2010, background): “Observe that the Fourier transformed elements of the wavelet basis have the form c ^ j , k 1 j 2 5 2 2 j /2 e 2 i 2 2 j j k c ^ 1 2 2 j j 2 , i.e., dilation by 2 j in space domain corresponds to dilation by 2 2 j in frequency domain, and the translation corresponds to a phase shift.”
PHOTOMETRIC SUPERNOVA CLASSIFICATION WITH MACHINE LEARNING (2016, methodology): “Alternative wavelet constructions that achieve better translation- and scale-invariance could be considered (e.g. Kingsbury 2001; Lo et al. 2009; Xiong et al. 2000) but a detailed optimization of the wavelet transform used was not performed, highlighting the robustness of our approach.”
Wavelets for fault diagnosis of rotary machines: A review with applications (2014, background): “This means a small shift in the input signal will cause large variations in energy distribution of the wavelet coefficients at different scales [159].”
Restoration of Poissonian Images Using Alternating Direction Optimization (2010, neutral): “Yet another example of a redundant Parseval frame is provided by complex wavelets, with the corresponding direct and inverse transforms having O ( n ) cost [24], [34].”