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WAVELET PACKETS IN WEIGHTED SOBOLEV SPACE

Yıl 2020, Cilt: 10 Sayı: 1, 138 - 149, 01.01.2020

R. Kumar M. Chauhan

Öz

We perform some splitting tricks over wavelets to construct basic wavelet packets in weighted Sobolev space. MRA based wavelet packet functions and their orthogonality at di erent levels in weighted Sobolev space are presented. Some examples of wavelet packets in weighted Sobolev space are given.

Anahtar Kelimeler

Wavelets wavelet packets multiresolution analysis weighted Sobolev space.

Kaynakça

  • Bastin, F. and Boigelot, C., (1998), Biorthogonal wavelets in Hm(R), J. Fourier Anal. Appl., 4, pp. –768.
  • Bastin, F. and Laubin, B., (1997), Compactly supported wavelets in Sobolev spaces of integer order
  • Appl. Comput. Harmon. Anal., 4, pp. 51–57. Bastin, F. and Laubin, B., (1997), Regular compactly supported wavelets in Sobolev spaces, Duke Math. J., 87, pp. 481–508.
  • Buzykanov, S., (2012), Enhancement of poor resolution text images in the weighted Sobolev space, in
  • Proceedings of the 19th International Conference on Systems, Signals and Image Processing (IWSSIP ), Vienna, Austria, April, pp. 536–539. Cohen, A. and Daubechies, I., (1993), On the instability of arbitrary biorthogonal wavelet packets
  • SIAM J. Math. Anal., 24, pp. 1340–1354.
  • Coifman, R. and Meyer, Y., Orthogonal wave packet bases, preprint. Coifman, R., Meyer, Y., Quake, S. and Wickerhauser, M. V., (1989), Signal Processing and compres- sion with wave packets, In: proceedings of the conference on wavelets, Marseilles: Spring.
  • Chui, C. R. and Li, C., (1993), Non-orthogonal wavelet packets, SIAM J. Math. Anal., 24, pp. 712–738.
  • Dayong, L. and Dengfeng, L., (2011), A characterization of orthonormal wavelet families in Sobolev spaces, Acta Math. Sci. Ser. B Engl. Ed., 31, pp. 1475–1488.
  • Ehler, M., (2010), The multiresolution structure of pairs of dual wavelet frames for a pair of Sobolev spaces, Jaen J. Approx, 2(2), pp. 193–214.
  • Han, B. and Shen, Z., (2009), Daul wavelet frames and rise bases in Sobolev spaces, Constr. Approx., , pp. 369–406.
  • Hern´andez, E. and Weiss, G., (1996), A First Course on Wavelets, Boca Raton (FL): CRC Press.
  • Chen, D. R., (2000), On the splitting trick and wavelet frame packets, SIAM J. Math. Anal., 31, pp. –739.
  • Long, R. and Chen, W., (1997), Wavelet basis packets and wavelet frame packets, J. Fourier Anal. Appl., 3, pp. 239–256.
  • Pathak, R. S., (2005), Wavelets in a generalized Sobolev space, Comput. Math. Appl., 49, 823–839.
  • Pathak, R. S. and Kumar, M., (2015), Wavelet packet in Sobolev space, Applicable Anal., 94, pp. –1084.
  • Shen, Z., (1995), Nontensor product wavelet packets in L(Rs), SIAM J. Math. Anal., 26, pp. 1061–
  • Walter, G. G., (1992), Discrete wavelets, SIAM J. Math. Anal., 23, pp. 1004–1014.
  • Walter, G. G., (1994), Wavelets and other orthogonal systems with applications, Boca Raton (FL): CRC Press.

Yıl 2020, Cilt: 10 Sayı: 1, 138 - 149, 01.01.2020

R. Kumar M. Chauhan

Öz

Kaynakça

  • Bastin, F. and Boigelot, C., (1998), Biorthogonal wavelets in Hm(R), J. Fourier Anal. Appl., 4, pp. –768.
  • Bastin, F. and Laubin, B., (1997), Compactly supported wavelets in Sobolev spaces of integer order
  • Appl. Comput. Harmon. Anal., 4, pp. 51–57. Bastin, F. and Laubin, B., (1997), Regular compactly supported wavelets in Sobolev spaces, Duke Math. J., 87, pp. 481–508.
  • Buzykanov, S., (2012), Enhancement of poor resolution text images in the weighted Sobolev space, in
  • Proceedings of the 19th International Conference on Systems, Signals and Image Processing (IWSSIP ), Vienna, Austria, April, pp. 536–539. Cohen, A. and Daubechies, I., (1993), On the instability of arbitrary biorthogonal wavelet packets
  • SIAM J. Math. Anal., 24, pp. 1340–1354.
  • Coifman, R. and Meyer, Y., Orthogonal wave packet bases, preprint. Coifman, R., Meyer, Y., Quake, S. and Wickerhauser, M. V., (1989), Signal Processing and compres- sion with wave packets, In: proceedings of the conference on wavelets, Marseilles: Spring.
  • Chui, C. R. and Li, C., (1993), Non-orthogonal wavelet packets, SIAM J. Math. Anal., 24, pp. 712–738.
  • Dayong, L. and Dengfeng, L., (2011), A characterization of orthonormal wavelet families in Sobolev spaces, Acta Math. Sci. Ser. B Engl. Ed., 31, pp. 1475–1488.
  • Ehler, M., (2010), The multiresolution structure of pairs of dual wavelet frames for a pair of Sobolev spaces, Jaen J. Approx, 2(2), pp. 193–214.
  • Han, B. and Shen, Z., (2009), Daul wavelet frames and rise bases in Sobolev spaces, Constr. Approx., , pp. 369–406.
  • Hern´andez, E. and Weiss, G., (1996), A First Course on Wavelets, Boca Raton (FL): CRC Press.
  • Chen, D. R., (2000), On the splitting trick and wavelet frame packets, SIAM J. Math. Anal., 31, pp. –739.
  • Long, R. and Chen, W., (1997), Wavelet basis packets and wavelet frame packets, J. Fourier Anal. Appl., 3, pp. 239–256.
  • Pathak, R. S., (2005), Wavelets in a generalized Sobolev space, Comput. Math. Appl., 49, 823–839.
  • Pathak, R. S. and Kumar, M., (2015), Wavelet packet in Sobolev space, Applicable Anal., 94, pp. –1084.
  • Shen, Z., (1995), Nontensor product wavelet packets in L(Rs), SIAM J. Math. Anal., 26, pp. 1061–
  • Walter, G. G., (1992), Discrete wavelets, SIAM J. Math. Anal., 23, pp. 1004–1014.
  • Walter, G. G., (1994), Wavelets and other orthogonal systems with applications, Boca Raton (FL): CRC Press.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

R. Kumar Bu kişi benim

M. Chauhan Bu kişi benim

Yayımlanma Tarihi 1 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 1

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