J. Kovacevic and W. Sweldens, "Wavelet families of increasing order in arbitrary dimensions," IEEE Transactions on Image Processing, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....grids. An early example of quincunx downsampling and upsampling (in multigrid context) can be found in [2] Early examples of quincunx downsampling in connection with 2 channel multidimensional filter banks can be found in [13, 14] The lifting scheme has been invented by Sweldens [10, 11] In [6, 15, 16, 17] the lifting scheme is used with quincunx downsampling to develop non separable wavelets on a rectangular grid. An educational and introductory approach to the lifting scheme (in 1D) can be found in [5] LISQ can do the following for you. This toolbox performs the wavelet decomposition of a ....

....(downsampling) of discrete di#erential operators. Also in multigrid context, the ordering is used in the so called red black relaxation because of its decoupling properties in the case of standard five point discretization. The lifting scheme As extensive literature exists on this topic, e.g. [1, 5, 6, 10, 11, 12, 15, 16, 17]) we confine ourselves to a basic recapitulation. We consider a n dimensional signal s j j )as a function s j : S j R where S n , n N. We transform s j 1 into a coarser, approximating, signal s j 1 and a detail signal d j 1 such that S j 1 # S j (downsampling) and S j = S j 1 D j 1 , ....

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J. Kovacevic and W. Sweldens, Wavelet families of increasing order in arbitrary dimensions, IEEE Trans. Imag. Proc., 9(3), 480--496, 2000.

....filters H and G can be computed by H##n# H##n # ## G##n# G##n # ## # # P #n# #U #n# # # U #n# # ; 2.1) H##n# H##n # ## # G##n# # G##n # ## # # #UP#n# U#n# #P #n# # # ; 2.2) where P and U denote the filter sequences of the operators # and # respectively. In [12] Kovacevic and Sweldens showed that we can always use lifting schemes with N primal vanishing moments and # N dual vanishing moments #N # N# by taking for # a Neville filter of order N with a shift and for # half the adjoint of a Neville filter of order N and shift , see [17] Example ....

....consists of M channels, where M denotes the absolute value of the determinant of the dilation matrix, that is used in the corresponding discrete wavelet transform. In each channel the signal is translated along one of the M coset representatives from the unit cell of the corresponding lattice, see [12]. The signal in the first channel is then used for predicting the data in all other channels by using M # # possible different prediction operators # # ; #### . Thereafter the first channel is updated using update operators # # ; #### on the M # # other channels. Let us consider an ....

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J. Kovacevic and W. Sweldens, "Wavelet families of increasing order in arbitrary dimensions", IEEE Trans. Imag. Proc., 9(3), 480--496, 2000.

....we work mainly in the discrete setting and therefore need not calculate some integrals with refinable functions being integrands. Finally, the algorithms proposed in this paper can be easily implemented. We note that, for any positive integers N and N with N N , Kovacevic and Sweldens [23] constructed an interpolatory mask a satisfying sum rules of order N and its dual mask a d satisfying sum rules of order N . Recently, when a is an interpolatory mask, an algorithm for constructing dual masks which satisfy sum rules of any given order is proposed in Han [13] When OE is a ....

J. Kovacevic and W. Sweldens, Wavelet families of increasing order in arbitrary dimensions, preprint (1997).

....and non zero elements for only one row (k th row) above the diagonal. Also, the reversibility is preserved even when using the transposed matrix, L [k] t (z) or U [k] t (z) Note that an alternative for lossless M channel ltering system can be obtained by extending the integer lifting [2,10]. Since the proposed ORT has a ltering e ect on only the k th output, it can be regarded as a trivial transform. However, if a cascaded version of the ORT is employed, it is possible to develop useful M channel lter banks for lossless image compression. As a simple approach, we consider M M ....

J. Kovacevic and W. Sweldens, Wavelet Families of Increasing Order in Arbitrary Dimensions, Submitted to IEEE Trans. Image Process. (December 1997). Available http ://cm.bell-labs.com/who/wim/papers/mdlift.ps.gz

....rests with its authors. This research is also supported by the Flemish Information Technology Action Program ( Vlaams Actieprogramma Informatietechnologie ) project number ITA 950244. Note After finishing this work, we learned that Kovacevic and Sweldens have completed a similar construction [6]. ....

J. Kovacevic and W. Sweldens. Wavelet families of increasing order in arbitrary dimensions. Technical report, Bell Laboratories, Lucent Technologies, 1997.

....has many, conflicting, faces. For example, in the construction of compactly supported bivariate interpolatory subdivision schemes, as well as in the related construction of certain orthogonal and biorthogonal refinable functions (see e.g. DGL] DDD] CD] CS] RiS1 2] JRS] HL] HJ] [KS], BW] one expects to have a relatively large mask, hence one has to cope with the sheer size of the problem. In contrast, in the theory of wavelet frames, and in the subsequent constructions of tight wavelet frames and bi frames, cf. RS2 5] and in particular [GR] good wavelet systems (e.g. ....

J. Kovacevic and W. Sweldens, Wavelet families increasing order in arbitrary dimensions, (1997) preprint.

.... Donoho s interpolating wavelet theory [12] Harten has described a kind of piecewise biorthogonal wavelet construction method [17] Swelden independently develops this method as the wellknown lifting scheme [56] which can be regarded as a special case of the Neville filters considered in [27]. The lifting scheme enables one to construct custom designed biorthogonal wavelet transforms by just assuming a single low pass filter (a smooth operation) without iterations. Theoretically, the interpolating wavelet theory is closely related to the finite element technique in the numerical ....

J. Kovacevic, W. Swelden, "Wavelet families of increasing order in arbitrary dimensions," Submitted to IEEE Trans. Image Processing, 1997.

....of Radar Signal Processing, Xi an 710071, China (e mail: zhbao rsp.xidian.edu.cn) Lagrange Wavelets for Signal Processing Zhuoer Shi, G. W. Wei, Donald J. Kouri, David K. Hoffman and Zheng Bao 2 I. INTRODUCTION The theory of interpolating wavelets has attracted much attention recently [1, 9, 11, 12, 13, 20, 21, 22, 29, 30, 33, 34, 35, 36, 37, 45, 46]. It possesses the attractive characteristic that the wavelet coefficients are obtained from the direct linear combinations of discrete samples rather than from the traditional inner product integrals. Mathematically, various interpolating wavelets can be formulated in a biorthogonal setting. ....

....wavelets can be formulated in a biorthogonal setting. Harten has described a kind of piecewise biorthogonal wavelet construction [13] Swelden independently has developed essentially this method into the lifting scheme [37] which can be regarded as a special case of the Neville filters [21]. Unlike the previous method for constructing biorthogonal wavelets, which relies on explicit solution of coupled algebraic equations [5, 6, 7] the lifting scheme enables one to construct a customdesigned biorthogonal wavelet transforms assuming only a single low pass filter without iterations. ....

J. Kovacevic, W. Swelden, "Wavelet families of increasing order in arbitrary dimensions," Submitted to IEEE Trans. Image Processing, 1997.

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J. Kovacevic and W. Sweldens, "Wavelet families of increasing order in arbitrary dimensions," IEEE Transactions on Image Processing, 1999.

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J. Kovacevic and W. Sweldens, "Wavelet families of increasing order in arbitrary dimensions," IEEE Trans. on IP, 1999.

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J. Kovacevic and W. Sweldens, "Wavelet families of increasing order in arbitrary dimensions," IEEE Trans. on IP, 1999.

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J. Kovacevic and W. Sweldens. Wavelet families of increasing order in arbitrary dimensions. IEEE Transactions on Image Processing, 9(3):480--496, 1999.

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J. Kovacevic and W. Sweldens. Wavelet families of increasing order in arbitrary dimensions. IEEE Trans. Image Proc., 9(3):480--496, March 2000.

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