I. Cohen, S. Raz, and D. Malah, "Shift invariant wavelet packet bases," in Proc. IEEE Int. Conf. on Acoust., Speech and Signal Proc. --- ICASSP '95, pp. 1081--1084, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....number of vectors of averages and differences while at the same time halving the length of each of them. For all scales j, 1 # j # L) and shifts i, 1 # i # N 1) tables are computed of size jx(i 1) which give direct access to the required coefficients. N.B. The work of Cohen, Malah and Raz [8] is similar. Utilising the wavelet packet decomposition (WPD) approach, they used a cost function to estimate the best wavelet basis within each level and at each node of the decomposition. The resultant transformation has been proven to be shift invariant; thus the process and decision ....

Israel Cohen, Shalom Raz and David Malah, "Shift Invariant Wavelet Packet Bases", Proceedings of the 20th IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP-95, Detroit, Michigan, 1995. pp. 1081-1084.

....have been proposed recently to introduce shift invariance into the framework of wavelet transforms. An early approach was to look at the extrema only of the wavelet transform modulus [9] Several authors suggested the introduction of a cost function in order to come up with a unique best basis [2, 4, 7]. A cost function that figures prominently is the entropy cost function used in [3] Note that the best basis of a structure might change if it is embedded into a larger structure. Filter oriented approaches have been introduced in [5] and [14] Most approaches cited above use a notion of shift ....

I. Cohen, S. Raz, D. Malah, "Shift Invariant Wavelet Packet Bases", ICASSP-95, Detroit 1995.

....of basis that have different time space and frequency scale characteristics. Due to the inherent hierarchical structure of the wavelet transforms, fast algorithms that expand signals onto those basis, and efficient methods that find the best basis within the huge set, exist and are practical [9, 6, 13, 12, 5, 4, 10, 3, 2]. One of the main ingredients in the wavelets transform is the downsampling at each scale. Although the downsampling reduces the output data rate and results in compact representation, it also introduces one artifact shift variance. The wavelet transform of a signal and the wavelet transform of ....

I. Cohen, S. Raz, and D. Malah. Shift invariant wavelet packet bases. In IEEE Proc. Int. Conf. Acoust., Speech, Signal Processing, volume 4, pages 1080--1084, Detroit, MI, 1995. IEEE.

....The algorithm has a structure similar to the best wavelet packets algorithm, and the computational complexity of remains O(N log N ) Going one step further, we have proposed an algorithm to find 3 the best wavelet packets and best shift jointly. Similar algorithms were independently proposed in [14, 8], and were shown to be advantageous as an unknown transient detector. Another well known disadvantage of the discrete wavelet transform is that the transform does not change with time. Sudden change in the signal causes many large wavelet coefficients across several scales. Although those large ....

....to 2D is described in [52] 3.4 Best Shift Wavelet Packet Transform 3.4.1 Basic Idea We can combine the ideas of the best wavelet packet transform and the best shift wavelet transform, and jointly find the best shift and the best wavelet packet. Similar ideas were independently proposed in [14, 8], however, the algorithm in [14] is suboptimal compared with the algorithm we describe here. The basic idea is to further split the highpass band and keep both the even and odd down samples, i.e. iterate the building block in Figure 3.7 on all the output branches. The resulting two level complete ....

I. Cohen, S. Raz, and D. Malah. Shift invariant wavelet packet bases. In Proc. Int. Conf. Acoust., Speech, Signal Processing, volume 4, pages 1080--1084, Detroit, MI, 1995. IEEE. 115

....measured by some metric) is significantly influenced by the alignment of the input signal with respect to the basis vectors. Thus, wavelet expansions may not perform well in certain applications. Recent work has focused on overcoming the effects of signal translation in wavelet expansions [3] [5] by efficiently computing wavelet bases among all time shifts and using a binary tree search algorithm to find the overall best basis with respect to some cost function. In addition to time sensitivity, however, the This work was supported in part by the the Office of Naval Research under the ....

I. Cohen, S. Raz, and D. Malah, "Shift invariant wavelet packet bases," in Proc. IEEE Int. Conf. on Acoust., Speech and Signal Proc. --- ICASSP '95, pp. 1081--1084, 1995.

....coefficients. The waveforms of the library are well localized in the time frequency plane, and organized in a binary tree structure facilitating efficient search algorithms for the best basis. In particular we focus on a shift invariant decomposition in an extended library of wavelet packets [12]. The resultant best basis representa tion is preferable to the standard wavelet packet decompo sition (WPD) 13] due to its desirable properties. Namely, shift invariance, lower information cost and improved time frequency resolution [14] The interference terms in the Wignet domain are ....

....basis can be implemented. A serious drawback of the wavelet packet decomposition (WPD) and local cosine decomposition (LCD) 13] is the lack of shift invariance. Hence ve elnploy lnodified versions vhich induce shift invariance, lover inforlnation cost and ilnproved tilne frequency resolution [12, 16, 17]. Let us specifically consider the shift mvariat wavelet packet decompositio (SIWPD) 12, 14] The library of bases is extended by introducing an additional degree of freedoln that adjusts the tilne localization of the basis functions. This degree of freedoln is practically incorporated into the ....

[Article contains additional citation context not shown here]

I. Cohen, S. Raz and D. Malah, "Shift invariant wavelet packet bases", Proc. ICASSP-95, Detroit, Michigan, 8 12 May 1995, pp. 1081 1084.

.... limiting conditions on the scaling function [57, 3, 4] Recently, several authors proposed independently to extend the library of bases, in which the best representations are searched for, by introducing additional degrees of freedom that adjust the time localization of the basis functions [47, 11, 12, 23, 36]. It was proved that the proposed modifications of the wavelet transform and wavelet packet decomposition lead to orthonormal best basis representations which are shift invariant and characterized by lower information costs. The principal idea is to adapt the down sampling when expanding each ....

....of signals, which are identical to within a time shift, their respective time frequency representations are identical to within the same time shift. One way to achieve shift invariance is to adjust the time localization of the basis functions, which are chosen for representing an analyzed signal [47, 11, 36]. That is, when the signal is translated in time by v, a new best basis is selected whose elements are also translated by v compared to the former best basis. Consequently, the expansion coefficients, that are now associated with translated basis functions, stay unchanged and the time frequency ....

[Article contains additional citation context not shown here]

I. Cohen, S. Raz and D. Malah, "Shift invariant wavelet packet bases", Proc. of the 20th IEEE pp. 1081 1084.

....join neighboring basis functions, invariably degrades the energy concentration and may artificially split a given signal component into several frequency bands. In this paper, we propose an adaptive suppression of interference terms using the shift invariant wavelet packet decomposition (SIWPD) [6,9]. A prescribed signal is expanded on its best SIWPD basis, and subsequently transformed into the Wigner domain. The interference terms are controlled by adaptively thresholding the cross WD of interactive basis functions according to their distance and amplitudes in an idealized time frequency ....

.... Furthermore, the time frequency tilings, produced by the best basis expansions, do not generally conform to standard time frequency energy distributions [9] Hence we employ modified versions which induce shift invariance, lower information cost and improved time frequency resolution [6 8]. Let us specifically consider the shift invariant wavelet packet decomposition (SIWPD) 6,9] The library of bases is extended by introducing an additional degree of freedom that adjusts the time localization of the basis functions. This degree of freedom is practically incorporated into the ....

[Article contains additional citation context not shown here]

I. Cohen, S. Raz, D. Malah, Shift invariant wavelet packet bases, in: Proc. 20th IEEE Internat. Conf. on Acoustics, Speech and Signal Processing, ICASSP-95, Detroit, Michigan, 8---12 May 1995, pp. 1081---1084.

....resulting representations are non unique and involve approximate signal reconstructions. Another approach is to extend the library of bases, in which the best representations are searched for, by introducing an additional degree of freedom that adjusts the time localization of the basis functions [8, 9, 10, 11]. In case of wavelet transform or wavelet packet decomposition, the additional degree of freedom is possibly an adaptive even odd down sampling. That is, following the low pass and high pass filtering, when expanding a parent node, retain either all the odd samples or all the even samples, ....

....all the odd samples or all the even samples, according to the choice which minimizes the cost function. This modification of the wavelet transform and wavelet packet decomposition leads to orthonormal bestbasis representations which are shift invariant and characterized by lower information costs [9]. In this work a similar approach is applied to smooth local trigonometric bases. We modify the LCD of Coifman and Wickerhauser by incorporating into the best basis search algorithm two additional degrees of freedom that increase the adaptability of the best basis. These degrees of freedom are ....

I. Cohen, S. Raz and D. Malah, "Shift invari- ant wavelet packet bases", Proc. ICASSP-95, pp. 1081 1084, May 1995.

....representations resulting from 2# di erent shift options, where # is the number of nodes in the best expansion tree, and choose that representation (shift option) which minimizes the entropy. This procedure is sub optimal compared with the shiftinvariant wavelet packet decomposition (SIWPD) [5,6], since the expansion tree is determined by the averaged entropy. Additionally, the shift options in step (iii) are examined one by one, whereas the SIWPD not only provides a recursive selection method for the optimal shift, but also o ers an inherent trade o between the computational complexity ....

....N designates the wavelet packets at the nest resolution level (l 0) which are relevant to analyzing the given signal. The extended library is larger than the standard wavelet packet library by a square power, but is still structured into a tree con guration which supports fast search algorithms [5]. The tree is depicted in Fig. 1. Each node in the tree is indexed by the triplet (l,n,m) and represents the subspace Span#B l #. 6) Since there are two alternatives for decomposing into two orthogonal subspaces, l #### # ## #; l 3#m,m#2# #, 7) upon expanding a ....

I. Cohen, S. Raz, D. Malah, Shift invariant wavelet packet bases, in: Proc. of the 20th IEEE Internat. Conf. Acoust. Speech Signal Process. ICASSP-95, Detroit, Michigan, 8}12 May 1995, pp. 1081}1084.

....et al. 5] are sensitive to the initial phase of the signal. Shift invariant multiresolution representations that exist are either non orthogonal, non unique [6] or entail high oversampling rates [7, 8] Recently we have developed an orthonormal shift in variant wavelet packet decomposition [9]. In this work, similar principles are applied to smooth local trigonometric bases. We introduce a best basis search algorithm, namely shift invariant adapted polarity local trigonometric decom position (SIAP LTD) that leads to an orthonormal shift invariant representation. The ....

I. Cohen, S. Raz and D. Malah, "Shift invariant wavelet packet bases", Proc. 20th ICASSP, May 1995.

....the shift invariant best basis decompositions. Finally, in Chapter 6 we conclude with a summary and discussion on future research directions. We would like to note that Chapters 2 and 3 and part of Chapter 4 are the detailed and expanded version of our published materials. Chapter 2 is based on [27, 28], Chapter 3 is based on [29, 30, 31, 32] and part of Chapter 4 is based on [31, 33] Additional manuscripts [34, 35, 36, 37, 38] based on Chapters 4 and 5, are about to be published. 1.4 Background A natural framework for the understanding of wavelet bases, and for the construction of new ....

.... [53] Consequently, the coe#cients of a delayed signal are not time shifted version of those of the original signal, and the cost of the expansion (as measured by some information cost functional) is significantly influenced by the alignment of the input signal with respect to the basis functions [27]. Thus, wavelet expansions, as well as generalizations proposed by Herley et al. 67, 68] may not perform well in statistical signal processing applications, such as detection or parameter estimation of signals with unknown arrival time. This problem of wavelet transforms, namely their ....

[Article contains additional citation context not shown here]

I. Cohen, S. Raz and D. Malah, "Shift invariant wavelet packet bases", Proc. of the 20th IEEE Int. Conf. on Acoustics, Speech and Signal Processing, ICASSP-95, Detroit, Michigan, 8--12 May 1995, pp. 1081--1084.

.... limiting conditions on the scaling function [49, 1, 2] Recently, several authors proposed independently to extend the library of bases, in which the best representations are searched for, by introducing additional degrees of freedom that adjust the time localization of the basis functions [40, 8, 12, 24, 33, 14]. It was proved that the proposed modifications of the wavelet transform and wavelet packet decomposition lead to orthonormal best basis representations which are shift invariant and characterized by lower information costs. The principal idea is to adapt the down sampling when expanding each ....

....the down sampling when expanding each parent node. That is, following the low pass and high pass filtering, when expanding a parent node, retain either all the odd samples or all the even samples, according to the choice which minimizes the cost function. In this work, which is summarized in [8], we generate a shifted wavelet packet (SWP) library and introduce a shift iva iat tavelet packet decompositio (SIWPD) algorithm for a best basis selection with respect to n dditive cost function (e.g. entropy) We prove that the proposed lgorithm leds to best bsis representation that is both ....

[Article contains additional citation context not shown here]

I. Cohen, S. Raz and D. Malah, "Shift invariant wavelet packet bases", Proc. of the 20th IEEE Int. Conf. on Acoustics, Speech and Signal Processing, Detroit, Michigan, $ 12 May 1995, pp. 1081 1084.

....coefficients. The waveforms of the library are well localized in the time frequency plane, and organized in a binary tree structure facilitating efficient search algorithms for the best basis. In particular we focus on a shift invariant decomposition in an extended library of wavelet packets [12]. The resultant best basis representation is preferable to the standard wavelet packet decomposition (WPD) 13] due to its desirable properties. Namely, shift invariance, lower information cost and improved timefrequency resolution [14] The interference terms in the Wigner domain are controlled ....

....the best basis can be implemented. A serious drawback of the wavelet packet decomposition (WPD) and local cosine decomposition (LCD) 13] is the lack of shift invariance. Hence we employ modified versions which induce shift invariance, lower information cost and improved time frequency resolution [12, 16, 17]. Let us specifically consider the shift invariant wavelet packet decomposition (SIWPD) 12, 14] The library of bases is extended by introducing an additional degree of freedom that adjusts the time localization of the basis functions. This degree of freedom is practically incorporated into the ....

[Article contains additional citation context not shown here]

I. Cohen, S. Raz and D. Malah, "Shift invariant wavelet packet bases", Proc. ICASSP-95, Detroit, Michigan, 8-- 12 May 1995, pp. 1081--1084.

....resulting representations are non unique and involve approximate signal reconstructions. Another approach is to extend the library of bases, in which the best representations are searched for, by introducing an additional degree of freedom that adjusts the time localization of the basis functions [8, 9, 10, 11]. In case of wavelet transform or wavelet packet decomposition, the additional degree of freedom is possibly an adaptive even odd down sampling. That is, following the low pass and high pass filtering, when expanding a parent node, retain either all the odd samples or all the even samples, ....

....all the odd samples or all the even samples, according to the choice which minimizes the cost function. This modification of the wavelet transform and wavelet packet decomposition leads to orthonormal bestbasis representations which are shift invariant and characterized by lower information costs [9]. In this work a similar approach is applied to smooth local trigonometric bases. We modify the LCD of Coifman and Wickerhauser by incorporating into the best basis search algorithm two additional degrees of freedom that increase the adaptability of the best basis. These degrees of freedom are ....

I. Cohen, S. Raz and D. Malah, "Shift invariant wavelet packet bases", Proc. ICASSP-95, pp. 1081--1084, May 1995.

....representations resulting from 2 different shiftoptions, where is the number of nodes in the best expansion tree, and choose that representation (shift option) which minimizes the entropy. This procedure is sub optimal compared with the ShiftInvariant Wavelet Packet Decomposition (SIWPD) [5, 6], since the expansion tree is determined by the averaged entropy. Additionally, the shift options in step (iii) are examined one by one, whereas the SIWPD not only provides a recursive selection method for the optimal shift, but also offers an inherent trade off between the computational ....

....the wavelet packets at the finest resolution level ( 0) which are relevant to analyzing the given signal. The extended library is larger than the standard wavelet packet library by a square power, but is still structured into a tree configuration which supports fast search algorithms [5]. The tree is depicted in Fig. 1. Each node in the tree is indexed by the triplet ( n; m) and represents the subspace U ;n;m = Span fB ;n;m g : 6) Since there are two alternatives for decomposing U ;n;m into two orthogonal subspaces: U ;n;m = U Gamma1;2n;m c Phi U Gamma1;2n 1;m c ; m c ....

I. Cohen, S. Raz and D. Malah, "Shift invariant wavelet packet bases", Proc. of the 20th IEEE Int. Conf. on Acoustics, Speech and Signal Processing, ICASSP-95, Detroit, Michigan, 8--12 May 1995, pp. 1081--1084.

....join neighboring basis functions, invariably degrades the energy concentration and may artificially split a given signal component into several frequency bands. In this paper, we propose an adaptive suppression of interference terms using the Shift Invariant Wavelet Packet Decomposition (SIWPD) [6, 9]. A prescribed signal is expanded on its best SIWPD basis, and subsequently transformed into the Wigner domain. The interference terms are controlled by adaptively thresholding the cross WD of interactive basis functions according to their distance and amplitudes in an idealized time frequency ....

....functions. Furthermore, the time frequency tilings, produced by the best basis expansions, do not generally conform to standard time frequency energy distributions [9] Hence we employ modified versions which induce shift invariance, lower information cost and improved time frequency resolution [6, 8, 7]. Let us specifically consider the shift invariant wavelet packet decomposition (SIWPD) 6, 9] The library of bases is extended by introducing an additional degree of freedom that adjusts the time localization of the basis functions. This degree of freedom is practically incorporated into the ....

[Article contains additional citation context not shown here]

I. Cohen, S. Raz and D. Malah, "Shift invariant wavelet packet bases", Proc. of the 20th IEEE Int. Conf. on Acoustics, Speech and Signal Processing, ICASSP-95, Detroit, Michigan, 8--12 May 1995, pp. 1081--1084.

No context found.

I. Cohen, S. Raz and D. Malah, "Shift invariant wavelet packet bases", Proc. 20th ICASSP, May 1995.

.... limiting conditions on the scaling function [49, 1, 2] Recently, several authors proposed independently to extend the library of bases, in which the best representations are searched for, by introducing additional degrees of freedom that adjust the time localization of the basis functions [40, 8, 12, 24, 33, 14]. It was proved that the proposed modifications of the wavelet transform and wavelet packet decomposition lead to orthonormal best basis representations which are shift invariant and characterized by lower information costs. The principal idea is to adapt the down sampling when expanding each ....

....the down sampling when expanding each parent node. That is, following the low pass and high pass filtering, when expanding a parent node, retain either all the odd samples or all the even samples, according to the choice which minimizes the cost function. In this work, which is summarized in [8], we generate a shifted wavelet packet (SWP) library and introduce a shift invariant wavelet packet decomposition (SIWPD) algorithm for a best basis selection with respect to an additive cost function (e.g. entropy) We prove that the proposed algorithm leads to a best basis representation that ....

[Article contains additional citation context not shown here]

I. Cohen, S. Raz and D. Malah, "Shift invariant wavelet packet bases", Proc. of the 20th IEEE Int. Conf. on Acoustics, Speech and Signal Processing, Detroit, Michigan, 8--12 May 1995, pp. 1081--1084.

.... limiting conditions on the scaling function [57, 3, 4] Recently, several authors proposed independently to extend the library of bases, in which the best representations are searched for, by introducing additional degrees of freedom that adjust the time localization of the basis functions [47, 11, 12, 23, 36]. It was proved that the proposed modifications of the wavelet transform and wavelet packet decomposition lead to orthonormal bestbasis representations which are shift invariant and characterized by lower information costs. The principal idea is to adapt the down sampling when expanding each ....

....of signals, which are identical to within a time shift, their respective time frequency representations are identical to within the same time shift. One way to achieve shift invariance is to adjust the time localization of the basis functions, which are chosen for representing an analyzed signal [47, 11, 36]. That is, when the signal is translated in time by , a new best basis is selected whose elements are also translated by compared to the former best basis. Consequently, the expansion coefficients, that are now associated with translated basis functions, stay unchanged and the time frequency ....

[Article contains additional citation context not shown here]

I. Cohen, S. Raz and D. Malah, "Shift invariant wavelet packet bases", Proc. of the 20th IEEE Int. Conf. on Acoustics, Speech and Signal Processing, Detroit, Michigan, 8--12 May 1995, pp. 1081--1084.

No context found.

I. Cohen, S. Raz, and D. Malah, "Shift invariant wavelet packet bases," in Proc. IEEE Int. Conf. on Acoust., Speech and Signal Proc. --- ICASSP '95, pp. 1081--1084, 1995.

No context found.

I. Cohen, S. Raz, and D. Malah, "Shift-invariant wavelet packet bases," in Proc. ICASSP--95, (Detroit, MI), pp. 1081--1084, 1995.

No context found.

I. Cohen, S. Raz, and D. Malah, "Shift-invariant wavelet packet bases," in Proc. ICASSP, Detroit, MI, 1995, pp. 1081--1084.

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