M. Vetterli and J. Kovacevic, Wavelets and Subband coding. Prentice Hall PTR, Engelwood Cliffs, New Jersey 07632, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and, in particular, make possible the lossless option maintaining the same algorithmic structure. Recently, a new framework for efficient computation of the DWT called Lifting Scheme (LS) has been developed by I. Daubethics and W. Sweldens [1] With respect to the classical filter bank structure [2], the LS has the great advantage of better computational efficiency in terms of number or multiplications and additions needed, moreover it enables a new method for filter design [3] To the best of our knowledge no architecture has been yet proposed for the LS implementation, although many VLSI ....

....of the first MAC. Then, next samples can be obtained at each clock cycle from subsequent MAC units. The filter coefficients silk] enter a shift register and the results of multiplication with samples din [k] are stored in the accumulators as follow: MAUl MAC2 MAC3 d, O] O d, dO ] 0 . [2] sd2] d. 21 8i[11 din[2] The latency introduced by each filtering core is taken into account by the programmable delay blocks, which are shift registers programmable according to the selected filter in order to delay din[j] or di, j] Fig. 1 points out that the lifting scheme processes two ....

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M. Vetterli, J. Kovaevid, Wavelets and subband coding, Prentice Hall PTR, Englewood Cliffs, New Jersey, 1995.

....and image processing, the discrete wavelet is closely related to filter banks. A typical 2 channel decomposition and reconstruction structure is given in Fig. 1. It is well known that the filter banks will provide perfect reconstruction (i.e. x = in Fig. 1) if they satisfy equations (3) and (4) [16]. Ho(z)Go(z) Hl(z)Gl(z) 2; 3) Ho( z)Go(z) Hl ( Z)Gl (z) 0. 4) A very important class of filter banks are orthonormal filter banks. For two channel, orthonor mal, FIR, real coefficient filter banks (T.O.F.R.FB. equations (3) and (4) are equivalent to equations (5) 6) and (7) 16] ....

....(4) 16] Ho(z)Go(z) Hl(z)Gl(z) 2; 3) Ho( z)Go(z) Hl ( Z)Gl (z) 0. 4) A very important class of filter banks are orthonormal filter banks. For two channel, orthonor mal, FIR, real coefficient filter banks (T.O.F.R.FB. equations (3) and (4) are equivalent to equations (5) 6) and (7)[16]. c0( c0( 1) 1) 2; Gl(z) z 2k lGo( Z 1) k Z; October 11, 2001 (5) 6) DRAFT x H o H H ,2 I = H G Fig. 1. 2 channel decomposition and reconstruction structure Hi(z) Gi(z 1) i E (0, 1) 7) Furthermore, it is easy to show that if we define P(z) Go(z)Go(z 1) then P(z) ....

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M. Vetterli, and J. Kovaevi, Wavelets and Subband Coding, Prentice-Hall PTR, 1995.

....exploit the coherence of the plenoptic function across different parameters (i.e. position, viewing angle, and time) A number of techniques have been developed for exploiting different kinds of coherence within various parameters of the plenoptic function. These include the DCT, wavelets [34], differential encoding, conditional replenishment, and motion compensation. In practice, these techniques constitute a toolbox from which specific representations can be formed. Some specific representations (e.g. JPEG [24] JPEG2000 [14] MPEG [12, 13] H.261 [33] etc. for still and moving ....

M. Vetterli and J. Kavacevic. Waveletes and Subband Coding. Prentice Hall PTR, 1995.

....rather to select the right signal and perform moment estimation only with them. Several criteria are used to make an intelligent selection of the signal. Work on frequency domain processing has been made by [CPT 94, Gos97, Gri98, CGME98, STMW99, WMWW99] Motivated by [AU96, Dau92, Teo98, VK95, BF94, Kai94, LMR98, Mey93, Koo93, Hol95, MTWW00] our purpose was to embed the ltering procedure into the known mathematical theory of wavelets. Why should wavelets be used in RWP signal processing In general, in case of removing contamination or denoising the experience shows that more than ....

M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice Hall PTR, New Jersey, 1995.

....Error Correction, Subband Wavelet Synthesis. Technical subject area Error Control Coding, Signal Processing for Communications. I. Introduction I N the area of image and video coding, subband decomposition and its special case, the discrete wavelet transform, are two popular techniques [1], 3] Most applications are based on the two channel scheme in which the original signal is split up into two subbands, each with half the size of the original. This process can be repeatedly applied to one or both subbands resulting in a tree structured splitting of a certain number of levels. ....

....of our aposteriori channel error correction method based on subband synthesis for the one dimensional case is described in detail. We use a simple example to show the effects we utilize for the correction. The filters used in the analysis synthesis stages of the two band decomposition are (e.g. [1]) h0 = 1; 3; 3; 1] h1 = Gamma1; Gamma3; 3; 1] g0 = Gamma1; 3; 3; Gamma1] and g1 = Gamma1; 3; Gamma3; 1] Consider the signal in Figure 1a. This signal may have an arbitrary form, but for simplicity, we have chosen a smooth signal with a mainly low pass characteristic, which is ....

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M. Vetterli and J. Kovacevi'c, Wavelets and Subband Coding, Prentice Hall PTR, 1995.

....expansion function B, which produces from h an approximation of x, i.e. y = B(h) The error is given by z = y Gamma x = B(A(x) Gamma x. The error image z usually has much lower entropy than the original image and can therefore be compressed considerably by a run length encoding scheme, cf. [1]. In order to yield higher compression ratios the error images are usually also quantized c = C(z) using scalar or vector quantization) giving a lossy image compression method. The compression ratio and the amount of loss can be controlled by the number of bits used to quantize the levels of the ....

Martin Vetterli and Jelena Kovacevic, Wavelets and Subband Coding, Prentice Hall PTR, 1995.

....wavelets. For compactly supported wavelets it is possible to give a fast implementation of the wavelet transform by convolution with the filter coefficients fh k g and fg k g. Since the filters are of short length we can compute the wavelet transform of a vector in R n with O(n) operations[34]. When we solve numerically the Galerkin equation (5.5) we are interested in computing the product of D j and a vector. Since D j is banded and explicitly known this is simply a product with a sparse matrix and thus requires O(2 j ) operations. The implementation details are similar to those in ....

M. Vetterli and J. Kovacevi'c. Wavelets and Subband Coding. Prentice Hall PTR, Englewood Cliffs, NJ, 1995.

....For compactly supported wavelets it is possible to give a fast implementation of the wavelet transform by convolution with the filter coefficients fh k g and fg k g. Since the filters are of short length we can compute the wavelet transform of a vector in R n with O(n log(n) operations[26]. When we solve numerically the discretized version of (2.6) we are interested in computing the product of D j and a vector. Since D j is banded and explicitly known this is simply a product with a sparse matrix and thus requires O(2 j ) operations. 5 Numerical Experiments 5.1 Experiments Here ....

M. Vetterli and J. Kovacevi'c. Wavelets and Subband Coding. Prentice Hall PTR, Englewood Cliffs, NJ, 1995.

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M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice Hall PTR, New Jersey, 1995.

....way. 3. SEPARABLE DIRECTIONAL TRANSFORM In this section, we concentrate on building some simple directional separable transforms. Among them, the simplest has four directions, namely f0 , 135 g. A one direction analysis leads to separation of an original image into two channels [8]. In the multi directional case, one directional analyses are applied direction by direction. Order is not important, since all combinations result in the same set of channels. For four directional analysis, application of horizontal, vertical and both 45 (or Gamma45 ) directional ....

M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice Hall PTR, New Jersey, 1995.

....above indicate that, in general, more complex methods of classification lead to better performance. Thus, there is also a trade off between computational complexity and classification gain. The complexity analysis of subband split, TCQ and rate allocation using Westerink s method can be found in [33], 18] and [8] respectively. It should be noted that the complexity of the ACTCQ decoder is only marginally higher than entropy coded uniform quantization. The additional complexity is due to keeping track of the trellis transitions. 8 Conclusions We have investigated various classification ....

Martin Vetterli and Jelena Kovacevi'c, Wavelets and subband coding, Prentice Hall PTR, Englewood Cliffs, New Jersey 1995.

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M. Vetterli and J. Kovacevic, Wavelets and Subband coding. Prentice Hall PTR, Engelwood Cliffs, New Jersey 07632, 1995.

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M. Vetterli and J. Kovacevic, Wavelets and Subband coding. Prentice Hall PTR, Engelwood Cliffs, New Jersey 07632.

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M. Vetterli and J. Kova#evi#, Wavelets and Subband Coding, Prentice Hall PTR, Englewood Clioes, NJ, 1995.

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M. Vetterli and J. Kovacevi'c, Wavelets and Subband Coding, Englewood Cliffs, NJ, Prentice Hall PTR, 1995.

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M. Vetterli and J. Kova#evi#, Wavelets and Subband Coding, Prentice Hall PTR, Englewood Clioes, NJ, 1995.

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