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Topic: Wavelet transform

	ipedia.com: Wavelet Article (Site not responding. Last check: 2007-10-21)
		Wavelet transforms are now being adopted for a vast number of different applications, often replacing the conventional Fourier transform in many applications.
		All wavelet transforms may be considered to be forms of time-frequency representation and are, therefore, related to the subject of harmonic analysis.
		The wavelets forming a CWT are subject to Heisenberg's uncertainty principle and, equivalently, discrete wavelet bases may be considered in the context of other forms of uncertainty principle.
	www.ipedia.com /wavelet.html (321 words)

	Discrete Wavelet Transform for Audio Compression
		Wavelets are a family of basis function for the space of square integrable functions.
		The wavelet transform is performed on the residual using edge-prediction and noise modeling.
		Wavelet coefficients in the lower frequency bands are encoded using 2 schemes, 8-bit log PCM and the 3 level Max-Lloyd quantizer.
	is.rice.edu /~welsh/elec431/wavelets.html (984 words)

	WaveletWadingPool.html
		By directly applying the wavelet transform, the paper hopes to show the reader how some simple wavelets work, by way of introduction to the heavier mathematics that are justified by these initial attempts.
		We can apply this transform once to the image, and create four smaller "images", one which is the averages of the pixels, and is the coefficients of the low resolution space, and the other three which are the wavelet coefficients that allow us to reconstruct the image.
		This seems justifiable since two wavelet vectors that are not orthogonal that are both quantized introduce more error in the direction that they are not orthogonal, possibly exceeding the threshold for error that we are trying to control during the quantization step.
	www.cgl.uwaterloo.ca /~anicolao/wadingpool/WaveletWadingPool.html (2076 words)

	Wavelet Transform Software Package (Site not responding. Last check: 2007-10-21)
		Wavelet Timer is a benchmarking program for evaluating the feasibility of using the wavelet transform for video signals.
		The wavelet transform is a mathematical transform similar to the commonly known Fourier transform.
		The two transforms investigated for this project are the Haar 4-2 wavelet transform, which is considered to be the simplest wavelet basis, and the Integer 5-3 wavelet transform, which is optimized for hardware implementations.
	norum.homeunix.net /~carl/wavelet (660 words)

	Programmers Heaven -> Discreet-Wavelet-Transform (Site not responding. Last check: 2007-10-21)
		The purpose of the Wavelet Transform (WT) is to separate a signal into its frequency components.
		Changing the scale of the wavelet changes the frequency band that is analyzed and the position of the wavelet changes the time frame analyzed.
		g is the wavelet filter, h the scaling filter, x the input signal and yh the wavelet coefficients and yl the lowpass filtered signal to be used in the next iteration.
	www.programmersheaven.com /d/click.aspx?ID=A13100&Rss=True (1280 words)

	A Really Friendly Guide To Wavelets
		In (1) the wavelet transform is calculated by continuously shifting a continuously scalable function over a signal and calculating the correlation between the two.
		This is a disadvantage of discrete wavelets: the resulting wavelet transform is no longer shift invariant, which means that the wavelet transforms of a signal and of a time-shifted version of the same signal are not simply shifted versions of each other.
		The first number is the number of vanishing moments of the analyzing wavelet (the wavelet that decomposes a signal) and the second number is the number of vanishing moments of the synthesizing wavelet (the wavelet that reconstructs the signal).
	perso.wanadoo.fr /polyvalens/clemens/wavelets/wavelets.html (5926 words)

	The Wavelet Packet Transform
		The wavelet function used to construct the wavelet packet tree in Figure 1 is a version of the Haar wavelet that I refer to as the Haar classic wavelet function.
		In the wavelet literature the result of the wavelet packet transform is sometimes referred to as a wavelet packet table.
		Templates allow the wavelet transform algorithms to be expressed in generic form, allowing the wavelet transform to be applied to these containers.
	www.bearcave.com /misl/misl_tech/wavelets/packet (2686 words)

	The Daubechies D4 Wavelet Transform
		The beginning of the data sequence repeats folling the end of the sequence (in the case of the forward transform) and the end of the data wraps around to the beginning (in the case of the inverse transform).
		One of the elegant features of Lifting Scheme versions of the wavelet transform is the fact that the inverse transform is a mirror of the forward transform, which addition and subtraction operations interchanged.
		The final scaling value in the Daubechies D4 transform is not the average of the data set (the average of the data set is 25.9375), as it is in the case of the Haar transform.
	www.bearcave.com /misl/misl_tech/wavelets/daubechies (1837 words)

	Wavelet Software at Brooklyn Poly
		The wavelet transform provides a multiresolution representation using a set of analyzing functions that are dilations and translations of a few functions (wavelets).
		The dual-tree complex wavelet transform overcomes these limitations - it is nearly shift-invariant and is oriented in 2D [Kin-2002].
		The 2D dual-tree wavelet transform produces six subbands at each scale, each of which are strongly oriented at distinct angles.
	taco.poly.edu /WaveletSoftware (362 words)

	The Fast Lifting Wavelet Transform
		Usually a signal transform is used to transform a signal to a different domain, perform some operation on the transformed signal and inverse transform it, back to the original domain.
		the wavelet transform is orthogonal, otherwise it is biorthogonal.
		Due to the infinite variety of wavelets it is possible to design a transform which maximally exploits the properties of a specific wavelet[8], and of course this has been done.
	perso.wanadoo.fr /polyvalens/clemens/lifting/lifting.html (5432 words)

	Wave:Wavelets 3
		One condition of the wavelet transform is that the average of the wavelet itself must be zero.
		However, it is much simpler to use the fact that the wavelet transform is the convolution between the two functions x and Psi, and to carry out the wavelet transform in Fourier space using the Fast Fourier Transform (FFT).
		The result is that signals in the wavelet transform at one end of the time series will get wrapped around to the other end.
	paos.colorado.edu /research/wavelets/wavelet3.html (639 words)

	THE WAVELET TUTORIAL PART I by ROBI POLIKAR (Site not responding. Last check: 2007-10-21)
		The wavelet transform is a relatively new concept (about 10 years old), but yet there are quite a few articles and books written on them.
		Hilbert transform, short-time Fourier transform (more about this later), Wigner distributions, the Radon Transform, and of course our featured transformation, the wavelet transform, constitute only a small portion of a huge list of transforms that are available at engineer's and mathematician's disposal.
		Wavelet transform is capable of providing the time and frequency information simultaneously, hence giving a time-frequency representation of the signal.
	users.rowan.edu /~polikar/WAVELETS/WTpart1.html (3223 words)

	The Wavelet Transform for Filtering Financial Data Streams (Site not responding. Last check: 2007-10-21)
		The preprocessing methods were the à trous wavelet transform, and a variant on this which departed from wavelet transform properties and which we term the time-based à trous multiscale method.
		The Haar wavelet transform was first described in the early years of this century and is described in almost every text on the wavelet transform.
		Our new wavelet transform combines the Haar wavelet transform, which is based on a particular well-specified pattern of averages and differences, with the so-called à trous ("with holes") transform.
	strule.cs.qub.ac.uk /~gzheng/financial-engineering/finpapermay99.html (3517 words)

	Wavelet Transform
		DWT is the discrete variant of the wavelet transform.
		Wavelet transform represents a valid alternative to the cosine transform used in standard JPEG.
		The DWT of images is a transform based on the tree structure with D levels that can be implemented by using an appropriate bank of filters.
	www.jpeg.org /.demo/FAQJpeg2k/wavelet-transform.htm (388 words)

	The Haar wavelet transform
		The nice thing is that wavelets are localized since they only live on part of the interval of the data, as opposed to the trigonometric functions used in Fourier analysis which live on the entire interval of the data.
		While it is very important to keep in mind that the wavelet transform can be described by a unitary matrix, it is not efficient to perform the transformation by multiplying the matrix to a vector.
		A vector which is the Haar transformation of the vector you gave as input corresponding to the level you gave as an input.
	amath.colorado.edu /courses/4720/2000Spr/Labs/Haar/haar.html (2455 words)

	The Wavelet Transform (Site not responding. Last check: 2007-10-21)
		Like the discrete Fourier transform, the discrete wavelet transform (DWT) is a linear operation that defines a forward and inverse relationship between the time-domain and the frequency-domain, also called the wavelet domain.
		For example, the inverse wavelet transform, when viewed as a matrix operator, is simply the transpose of the forward transform.
		Most of the usefulness of wavelets relies on the fact that wavelet transforms can usefully be severely truncated-that is, they can be effectively turned into sparse expressions.
	idlastro.gsfc.nasa.gov /idl_html_help/signal13.html (166 words)

	Structure Detection in Low Intensity X-Ray Images using the Wavelet Transform Applied to Galaxy Cluster Cores Analysis (Site not responding. Last check: 2007-10-21)
		The key point is that the wavelet transform is able to discriminate structures as a function of scale, and thus is well suited to detect small scale structures embedded within larger scale features.
		In the case of the à trous wavelet transform algorithm, the reconstruction is obtained by a simple addition of the wavelet scales and the last smoothed array.
		The use of the adjoint wavelet transform operator (Bijaoui et Rué, 1995) instead of the simple coaddition of the wavelet scale for the reconstruction suppresses the artifacts which may appear around objects.
	ecf.hq.eso.org /adass/adassVII/starckjl.html (1788 words)

	Light Field Compression using Wavelet Transform and Vector Quantization
		Wavelet transform followed by vector quantization is very useful for compressing light fields.
		Because wavelet bases have compact supports, we can swap in different resolutions of subbands for light field slabs during rendering based on the orientations of the slabs and the viewing parameters.
		Haar wavelet is generally not a good idea in applying to image compression but it seems to work pretty well for compressing light fields.
	graphics.stanford.edu /~liyiwei/project/ee372/report.html (1784 words)

	The Daubechies wavelet transform
		The goal with this lab is to design a Daubechies wavelet transform and use it to compress and de-noise one dimensional signals and images.
		Note that this is not only for performing a one level wavelet decomposition, but for performing the full wavelet transformation.
		A vector which is the wavelet transformation of the vector you gave as input corresponding to the level you gave as an input.
	amath.colorado.edu /courses/4720/2000Spr/Labs/DB/db.html (1234 words)

	The Wavelet Digest :: View topic - Question: A Trous Wavelet Transform
		I use the a trous wavelet transform for extracting cloud features from satellite images.
		I would like to improve the performance of the a trous transform for cloud edges and in general, for linear features.
		The a trous wavelet transform is implemented with the B3-spline filter {1/16, 1/4, 3/8, 1/4, 1/16} since it has an excellent interpolating property.
	www.wavelet.org /phpBB2/viewtopic.php?t=5345&view=next (132 words)

	The fast wavelet transform (Site not responding. Last check: 2007-10-21)
		Wavelet basis functions are recursively computed from previous iterations.
		Figure 1: Wavelet decomposition and reconstruction of a 1-D seismic trace.
		One can make an overall estimate of the relative frequency distribution in a signal by viewing a plot of the coefficients, but the intervals are not as smooth as a Fourier transform.
	sepwww.stanford.edu /public/docs/sep65/rick2/paper_html/node2.html (273 words)

	Discrete Periodic Wavelet Transform (Site not responding. Last check: 2007-10-21)
		In the papers below the discrete wavelet transform (DWT) is extended to functions on the discrete circle to create a fast and complete discrete periodic wavelet transform (DPWT).
		It is proven that the same filter coefficients used with the DWT may be used with the DPWT to create an orthonormal basis of discrete periodic wavelets.
		The illustration shows examples of elements of a periodic wavelet basis for length 128 sequences.
	www.inversioninc.com /wavelet.html (237 words)

	Wavelet Image Compression Construction Kit
		The coder is not the most sophisticated--it's a simple transform coder--but each individual piece of the transform coder has been chosen for high performance.
		The current transform routine should be fairly straightforward to extend to perfom wavelet packet decompositions.
		The wavelet transform implements symmetrized boundaries and works for images of (more or less) arbitrary sizes, as long as the aspect ratio is less than 2:1 (the aspect ratio limitation should be straightforward to eliminate, but I haven't gotten around to it).
	www.geoffdavis.net /dartmouth/wavelet/wavelet.html (1180 words)

	The Wavelet Seismic Inversion Lab (Site not responding. Last check: 2007-10-21)
		Characterizing the irregularity of measurements by means of the wavelet transform by Joes Staal
		Wavelet Compression of Seismic Data by E. Magani, et al.
		Application of the wavelet transform to time-frequency filtering, multiples removal and lower crust frequency studies: 54th Mtg.
	timna.mines.edu /~zmeng/waveletlab/waveletlab.html (386 words)

	Mehr zu "Haar-Wavelet" bei Metando (Site not responding. Last check: 2007-10-21)
		The disadvantage of the Haar wavelet is that it is not continuous and..
		The Haar wavelet is also the simplest possible wavelet.....2×2 Haar matrix that is associated with the Haar wavelet is..
		The Haar wavelet is the first known wavelet and was.....2×2 Haar matrix that is associated..the Haar wavelet is..
	www.metando.de /search_Haar-Wavelet_0.html (489 words)

	The Discrete Periodic Wavelet Transform in 1D -- from Mathematica Information Center
		This version of the FWT called the discrete periodic wavelet transform (DPWT) was developed by N. Getz in 1992 (Memo.
		The DPWT requires no data padding and the filter coefficients representing the wavelet basis system are adaptively modified to have the same length of a data set, if that data set is shorter than the array of filter coefficients.
		As a result of these improvements, the DPWT is invertible to as many number of decomposition levels as possible (L if the length of the data is 2^L).
	library.wolfram.com /infocenter/MathSource/447 (218 words)

	Some Recent Papers of F. Murtagh
		F. Murtagh, The Haar wavelet transform of a dendrogram - I.
		The Haar wavelet transform of a dendrogram - II.
		M. Nibouche, A. Bouridane, F. Murtagh and O. Nibouche, FPGA-based discrete wavelet transforms system, in G. Brebner and R. Woods, Eds., Field-Programmable Logic and Applications, LNCS 2147, Springer-Verlag, 2001, pp.
	www.cs.rhul.ac.uk /home/fionn/papers (1113 words)

	Geoff Davis's Home Page
		We examine the central issues of invertibility, stability, artifacts, and frequency-domain characteristics in the construction of non-linear analogs of the wavelet transform.
		We describe a new type of non-linearity for use in constructing non-linear transforms: a set of linear predictors that are chosen adaptively using a non-linear selection function.
		We motivate the use of the wavelet transform in coding using rate-distortion considerations as well as approximation-theoretic considerations.
	www.geoffdavis.net (1452 words)

	Digital Image Watermarking in the Wavelet Transform Domain
		Many image transforms have been considered, most prominent among them is the discrete cosine transform (DCT) which has also been favored in the early image and video coding standards.
		The wavelet transform [Daubechies92a] has a number of advantages [Xia98a,Lumini00a] over other transforms such as the DCT that can be exploited for both, image compression and watermarking applications.
		First, we propose using wavelet filter parametrization as a means to improve the security of many previously proposed algorithms and demonstrate that our concept of secret key-dependent wavelet filters can be easily employed as a security framework.
	www.cosy.sbg.ac.at /~pmeerw/Watermarking/MasterThesis (872 words)

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