A wavelet tree on the string "abracadabra". At each node the symbols of the string are projected onto two partitions of the alphabet, and a bitvector denotes to which partition each symbol belongs. Note that only the bitvectors are stored; the strings in the nodes are only for illustratory purposes.
The Wavelet Tree is a succinct data structure to store strings in compressed space. It generalizes the and operations defined on bitvectors to arbitrary alphabets.
Originally introduced to represent compressed suffix arrays,[1] it has found application in several contexts.[2][3] The tree is defined by recursively partitioning the alphabet into pairs of subsets; the leaves correspond to individual symbols of the alphabet, and at each node a bitvector stores whether a symbol of the string belongs to one subset or the other.
The name derives from an analogy with the wavelet transform for signals, which recursively decomposes a signal into low-frequency and high-frequency components.
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The WaveletTree is a succinct data structure to store strings in compressed space. It generalizes the r a n k q {\displaystyle \mathbf {rank} _{q}} and...
analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key...
wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet....
subband tree structuring (SB-TS), also called wavelet packet decomposition (WPD; sometimes known as just wavelet packets or subband tree), is a wavelet transform...
Embedded zerotrees of wavelet transforms (EZW) is a lossy image compression algorithm. At low bit rates, i.e. high compression ratios, most of the coefficients...
in hierarchical trees (SPIHT) is an image compression algorithm that exploits the inherent similarities across the subbands in a wavelet decomposition of...
Wavelets are often used to analyse piece-wise smooth signals. Wavelet coefficients can efficiently represent a signal which has led to data compression...
complex wavelet transform (CWT) is a complex-valued extension to the standard discrete wavelet transform (DWT). It is a two-dimensional wavelet transform...
function by high-order contexts, and compressing each partition with a wavelettree. The space usage is extremely competitive in practice with other state-of-the-art...
Euclidean space. Diffusion wavelets are an extension of classical wavelet theory from harmonic analysis. Unlike classical wavelets whose basis functions are...
Proceedings, Part IV. Chen, Chen; et al. (2012). "Compressive Sensing MRI with WaveletTree Sparsity". Proceedings of the 26th Annual Conference on Neural Information...
Roques, Sylvie (1993). Progress in wavelet analysis and applications: proceedings of the International Conference "Wavelets and Applications", Toulouse, France...
implementation of some succinct data structures like bit vectors and wavelettrees. The population count of a bitstring is often needed in cryptography...
JPEG format, JPEG 2000 instead uses discrete wavelet transform (DWT) algorithms. It uses the CDF 9/7 wavelet transform (developed by Ingrid Daubechies in...
Retrieved 2013-04-16. "Diary of an x264 Developer » the problems with wavelets". Archived from the original on 2014-01-29. Retrieved 2014-02-06. "Description...
as Daubechies wavelet filters. NJIT Symposia on Subbands and Wavelets 1990, 1992, 1994, 1997. Mohlenkamp, M. J. A Tutorial on Wavelets and Their Applications...
to the wavelet-based contourlet transform is that the wavelet-based contourlet packets are similar to the wavelet packets which allows quad-tree decomposition...
single survival tree is to build many survival trees, where each tree is constructed using a sample of the data, and average the trees to predict survival...
Roques, Sylvie (1993). Progress in wavelet analysis and applications: proceedings of the International Conference "Wavelets and Applications," Toulouse, France...
Tian and Wugang Zhao) for introducing a new type of tree structure named TSA-tree, based on wavelets. His other work includes the Clustered AGgregation...
than CADRG and no color loss) ECW – Enhanced Compressed Wavelet (from ERDAS). A compressed wavelet format, often lossy. Esri grid – proprietary binary raster...
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