S. del Marco, J. Weiss, and K. Jager. Wavepacket-based transient signal detector using a translation invariant wavelet transform. In Wavelet Applications in Signal and Image Processing, volume 2242, pages 154--165, San Diego, CA, July 1994. SPIE.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....this proach the retainment of shift invariance, necessitates an oversized library containing the basis functions and all their shifted versions. The obvious drawbacks of matching pursuit are the rather high complexity level as well as the non orthogonality of the expansion. In another approach [7], shift invariance is achieved by an adaptive translation of subbands. This translation, merely determined by one level decomposition, leads to a sub optimal representation, which is a specia case in the context of the present work. In this work we generate a shifted wavelet packet library a.nd ....

....on that wlue which minimizes the cost function . Since, t ech level, the tree expansion is restricted to de d levels, the complexity is now O[N2a(L d 2) In the extreme cse, d = 1, the complexity, O(2NL) is simil to that ssocited with WPD, nd the representa tion merges with that proposed in [7]. Clearly, the lrger d d L, the lger the complexity, however, the determined best bsis is of higher quMity; nmely, characterized by lower information cost . 5. CONCLUSION A library of orthonormal Shifted Wavelet Packets is defined and a search algorithm leading to a Shift Invariant Wavelet ....

S. P. Del Marco, J. Weiss and K. Jaglet, "Wavepacket- based transient signal detector using a translation invariant wavelet transform", Proc. SPlE 2242, pp. 792- 802 (1994)

.... resolution levels (L log 2 N) and d is the maximum depth of a subtree used at a given parent node to determine the shift mode of its children (1 L) In the extreme case d = 1, the complexity, O(NL) is similar to that associated with WPD, and the representation merges with that proposed in [57]. As a rule, the larger d and L, the larger the complexity, however, the determined best basis is of a higher quality; namely, characterized by a lower information cost. For d = L and for an identical number of resolution levels, SIWPD leads necessarily to an information cost that is lower than ....

....is now O[N2 d 2) More specifically, the algorithm requires rN[2 d 2) 2] real multiplications, where r is the length of the filters. In the extreme case, d = 1, the complexity, O(2NL) resembles that associated with WPD, and the representation merges with that proposed in [57]. As a rule, the larger d and L, the larger the complexity, however, the determined best basis is of a higher quality; namely, characterized by a lower information cost. 2.5.1 Example To demonstrate the trade o# between information cost and complexity we refer to Figs. 2.11 2.13. These figures ....

S. Del Marco, J. Weiss and K. Jagler, "Wavepacket-based transient signal detector using a translation invariant wavelet transform", Proc. SPIE, Vol. 2242, 1994, pp. 792-- 802.

.... 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 ....

.... resolution levels (L log 2 N) and d is the maximum depth of a subtree used at a given parent node to determine the shift mode of its children (1 d L) In the extreme case d = 1, the complexity, O(NL) is similar to that associated with WPD, and the representation merges with that proposed in [24]. As a rule, the larger d and L, the larger the complexity, however, the determined best basis is of a higher quality; namely, characterized by a lower information cost. For d = L and for an identical number of resolution levels, SIWPD leads necessarily to an information cost that is lower than ....

[Article contains additional citation context not shown here]

S. P. Del Marco, J. Weiss and K. Jaglet, ;;Wavepacket-based transient signal detector using a translation invariant wavelet transform", Proc. SPIE, Vol. 2242, 1994, pp. 792 802.

....with the level number, it is, in the general case, useless to go deeper than the 6 th or 7 th level. Best basis selection for WPT and CPT are presented and tested with different information cost functions and other interesting variations in [9] Here, the method used is a shift invariant WPT [6, 10], with a 6th level decomposition and the additive pseudoentropy information cost function I c (s) For the experiment, the signal is another humpback whale vocalization (frequency modulated type) corrupted with both shipping and snapping shrimp noise of equal energy. No pink noise was added as ....

J. Del Marco, S.and Weiss and K. Jagler, "Wavepacket-based transient signal detector using a translation invariant wavelet transform," in Wavelet Applications, no. 2242 in SPIE Proceedings.

.... 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 ....

.... resolution levels (L log 2 N) and d is the maximum depth of a subtree used at a given parent node to determine the shift mode of its children (1 d L) In the extreme case d = 1, the complexity, O(NL) is similar to that associated with WPD, and the representation merges with that proposed in [24]. As a rule, the larger d and L, the larger the complexity, however, the determined best basis is of a higher quality; namely, characterized by a lower information cost. For d = L and for an identical number of resolution levels, SIWPD leads necessarily to an information cost that is lower than or ....

[Article contains additional citation context not shown here]

S. P. Del Marco, J. Weiss and K. Jagler, "Wavepacket-based transient signal detector using a translation invariant wavelet transform", Proc. SPIE, Vol. 2242, 1994, pp. 792--802.

....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 ....

S. del Marco, J. Weiss, and K. Jager. Wavepacket-based transient signal detector using a translation invariant wavelet transform. In Wavelet Applications in Signal and Image Processing, volume 2242, pages 154--165, San Diego, CA, July 1994. SPIE.

....necessitates an oversized library containing the basis functions and all their shifted versions. The obvious drawbacks of matching pursuit are the rather high complexity level as well as the To appear in Proc. 20th ICASSP, May 1995. non orthogonality of the expansion. In another approach [7], shift invariance is achieved by an adaptive translation of subbands. This translation, merely determined by one level decomposition, leads to a sub optimal representation, which is a special case in the context of the present work. In this work we generate a shifted wavelet packet library and ....

....the cost function M. Since, at each level, the tree expansion is restricted to d d levels, the complexity is now O[N2 d (L Gamma d 2) In the extreme case, d = 1, the complexity, O(2NL) is similar to that associated with WPD, and the representation merges with that proposed in [7]. Clearly, the larger d and L, the larger the complexity, however, the determined best basis is of a higher quality; namely, characterized by a lower information cost . 5. CONCLUSION A library of orthonormal Shifted Wavelet Packets is defined and a search algorithm leading to a Shift ....

S. P. Del Marco, J. Weiss and K. Jagler, "Wavepacketbased transient signal detector using a translation invariant wavelet transform", Proc. SPIE 2242, pp. 792802 (1994)

....One well known disadvantage of the discrete wavelet transform (DWT) is the lack of shift invariance. The reason is that there are many legitimate DWTs for different shifted versions of the same signal. Looking at the problem from the positive side, we [38] independently of other researchers [52, 14], proposed an algorithm to find the best shifted version of DWTs for a given input signal. 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 ....

....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 ....

[Article contains additional citation context not shown here]

S. del Marco, J. Weiss, and K. Jager. Wavepacket-based transient signal detector using a translation invariant wavelet transform. In Wavelet Applications in Signal and Image Processing, volume 2242, pages 154--165, San Diego, CA, July 1994. SPIE.

....account. If n = 1 , the new sequences d 11 and c 11 will be precisely the sequences that were discarded in the downsampling step of the transform of the original (unshifted) signal. Hence, to get both the odd and the even branches, it is necessary to low pass filter and high pass filter only once [5] . c 0 c 0 z z n n z k z k 1n d 1n c H G 2 2 2 2 H G z (2k n) Figure 2: Effect of Shifting the Input Sequence by = 2k n. Figure (3) shows the full tree of costs, where Dmk and Cmk are the costs of sequences dmk and c mk . C is the cost of the input sequence. The tree shows the ....

Del Marco, S., et al. "Wavepacket-based transient signal detector using a translation invariant wavelet transform, " Proc. of the SPIE vol.2242, Wavelet Applications 1994, p. 792-802.

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S. del Marco, J. Weiss, and K. Jager. Wavepacket-based transient signal detector using a translation invariant wavelet transform. In Wavelet Applications in Signal and Image Processing, volume 2242, pages 154--165, San Diego, CA, July 1994. SPIE.

No context found.

S. del Marco, J. Weiss, and K. Jager. Wavepacket-based transient signal detector using a translation invariant wavelet transform. In Wavelet Applications in Signal and Image Processing, volume 2242, pages 154--165, San Diego, CA, July 1994. SPIE.

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