D. Wei, J. Tian, R. O. Wells, Jr., and C. S. Burrus, "A new class of biorthogonal wavelet systems for image transform coding," IEEE Trans. Image Processing, to be published.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... 2 band, biorthogonal, symmetric, 6 10 Transform 3 in [57] MIT97 MIT 9 7 Transform 2 band, biorthogonal, symmetric, interpolating, 9 7, 4,2) Section 4 (Item 3) in [45] BCW3 Biorthogonal Coifman Transform (Order 3) 2 band, biorthogonal, symmetric, interpolating, 13 7, 4,4) Table 3. 1 in [52] [58] V4 Vaidyanathan 4 Band Transform 4 band, orthogonal, symmetric Table II in [44] A4 Alkin 4 Band Transform 4 band, orthogonal, symmetric Table II in [5] At this point, we note that the V4 transform has highly discontinuous synthesis scaling and 4. Reversible Embedded Image Compression 79 ....

D. Wei, J. Tian, R. O. Wells, and C. S. Burrus. A new class of biorthogonal wavelet systems for image transform coding. Technical report, Computational Mathematics Laboratory, Rice University, October 1995. Technical Report CML TR 95-14.

.... M ANY families of wavelet systems have been constructed in the last decade, for instance, orthonormal Daubechies wavelets [1] orthonormal coiflets [2] biorthogonal spline wavelets (BSW s) 3] semiorthogonal spline wavelets [4] 5] and general biorthogonal Coifman wavelets (GBCW s) 6] [7]. Most families of wavelet bases are indexed by the number of vanishing moments of the wavelet or, equivalently, the number of zeros at of the transfer function of the associated lowpass filter. For instance, if the synthesis wavelet and the analysis wavelet in a biorthogonal wavelet system have ....

.... In this paper, we systematically study the asymptotic convergence (at least in the pointwise sense) of the dual finite impulse response (FIR) filters associated with two families of biorthogonal wavelets the BSW systems and the GBCW systems which have been successfully applied to image coding [7], 20] 21] To the best of our knowledge, this has not By Gibbs like phenomenon, we mean any overshoot and or oscillating behavior in the asymptotic approximation of an ideal HBLP magnitude response, including the ordinary Gibbs phenomenon. 1053 587X 98 10.00 1998 IEEE been reported in the ....

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D. Wei, J. Tian, R. O. Wells, Jr., and C. S. Burrus, "A new class of biorthogonal wavelet systems for image transform coding," IEEE Trans. Image Processing, to be published.

....to propose an approach for the design of realvalued, compactly supported, and orthonormal wavelets with negligible phase distortion on their corresponding FB s. Imposing a certain number of vanishing moments on wavelets and or scaling functions has been one criterion used to design wavelets [2] [7]. We say that a function has the first vanishing moments (or zero moments) centered at if (1) for . Most families of wavelets are indexed by the number of vanishing moments for wavelets, which also represents the number of zeros at of the frequency response of their associated FB s [2] 8] ....

....other than the biggest two) A more careful inspection reveals that they are surprisingly similar to the filters of some biorthogonal spline wavelets, referred to as in [4, Table 6. 1] In fact, they may be regarded as the filters of the general biorthogonal Coifman wavelets with the same orders [7], i.e. the same numbers of vanishing moments on wavelets. We list the filter coefficients of these generalized coiflets and their corresponding biorthogonal wavelets in Table IV. They are very similar to each other except that the filters of the generalized coiflets have longer supports (or ....

D. Wei, J. Tian, R. O. Wells, Jr., and C. S. Burrus, "A new class of biorthogonal wavelet systems for image transform coding," IEEE Trans. Image Processing, vol. 7, pp. 1000--1013, July 1998.

....Searching for high performance wavelets for image coding has been an active research area. The 9 7tapped FB constructed in [2] has been the most widely used one in the image coding community. Recently, some even length FBs having good compression capability have been discovered [3] 4] In [5], a general class of biorthogonal coiflet systems was constructed. The resulting FBs have odd lengths. Those of even orders were shown to be symmetric and have comparable compression performance to the 9 7tapped FB. However, those of odd orders are neither symmetric nor antisymmetric and not ....

....be symmetric and have comparable compression performance to the 9 7tapped FB. However, those of odd orders are neither symmetric nor antisymmetric and not suitable for image coding. In fact, this is because the zero centered moment conditions imposed on scaling functions conflict with antisymmetry [5]. In this work, we design antisymmetric biorthogonal coiflet systems. The key in our design is to impose 1 2 centered moment conditions instead of zero centered ones on scaling functions. The resulting FBs have even lengths and are linear phase. The results in [5] indicates that the vanishing ....

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D. Wei, J. Tian, R. O. Wells, Jr., and C. S. Burrus, "A new class of biorthogonal wavelet systems for image transform coding," IEEE Trans. Image Processing, vol. 7, pp. 1000--1013, July 1998.

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D. Wei, J. Tian, R. O. Wells, Jr., and C. S. Burrus, \A new class of biorthogonal wavelet systems for image transform coding," IEEE Trans. on Image Processing, vol. 7, pp. 1000-1013, Jul. 1998.

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