Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2014, Cilt: 27 Sayı: 4, 1021 - 1030, 24.11.2014

Shiqing Wang , Limin Su

Öz

Kaynakça

  • Donoho, D. L. and Huo, X., “Uncertainty principles and ideal atomic decomposition”, IEEE Trans. Inf. Theory, 47: 2845-2862, (2001).
  • Donoho, D. L., “Compressed sensing”, IEEE Trans. Inf. Theory, 52: 1289-1306, (2006).
  • Candes, E. J. and Tao, T., “Decoding by linear programming”, IEEE Trans. Inf. Theory, 51, 4203-4215, (2005).
  • Candes, E. J., Romberg, J. and Tao, T., “Stable signal recovery from incomplete and inaccurate measurements”, Comm. Pure Appl. Math., 59, 1207-1223, (2006a).
  • Candes, E. J. and Tao, T., “Near-optimal signal recovery from random projections: Universal encoding strategies”, IEEE Trans. Inf. Theory, 52, 5406-5425, (2006b).
  • Candes, E. J. and Tao, T., “The Dantzig selector: Statistical estimation when p is much larger than n (with discussion)”, Ann. Stat., 35, 2313-2351, (2007).
  • Cai, T., Wang, L. and Xu, G., “Shifting inequality and recovery of sparse signals”, IEEE Trans. Signal Process., 58: 1300-1308, (2010a).
  • Cai, T., Wang, L. and Xu, G., “Stable recovery of sparse signals and an oracle inequality”, IEEE Trans. Inf. Theory, 56: 3516-3522, (2010b).
  • Bickel, P. J., Ritov, Y. and Tsybakov A. B., “Simultaneous analysis of Lasso and Dantzig selector”, Ann. Stat., 37: 1705-1732, (2009).
  • Wang, S. Q. and Su, L. M., “The oracle inequalities on simultaneous Lasso and Dantzig selector in high dimensional nonparametric regression”, Math. Probl. Eng., (2013). doi:10.1155/2013/571361
  • Wang, S. Q. and Su, L. M. (2013b). “Recovery of high-dimensional spares signals via L1-minimization”, J. Appl. Math., (2013).
  • Wang, S. Q. and Su, L. M., “Simultaneous Lasso and Dantzig selector in high dimensional nonparametric regression”, Int. J. Appl. Math. Stat.,42: 103-118, (2013). [13] Cai, T., Xu, G. and Zhang, J., “On recovery of sparse signals via L minimization”, IEEE Trans. Inf. Theory, 1L 55: 3388-3397, (2009).
  • Baraniuk, R., Davenport, M., DeVore, R. and Wakin, M., “A simple proof of the restricted isometry property for random matrices”, Constr. Approx., 28: 253-263. (2008).
  • Davies, M. E. and Gribonval, R., “Restricted isometry constants where L sparse recovery can fail p
  • for 0< ≤ ”, IEEE Trans. Inf. Theory, 55: 203-2214, 1 p (2009).
  • Candes, E. J., “The restricted isometry property and its implications for compressed sensing”, Comptes Rendus Mathematique, 346: 589-592, (2008).
  • Foucart, S. and Lai, M., “Sparsest solutions of underdetermined linear systems via L minimization for q
  • 0< ≤ ”, Appl. Comput. Harmon. Anal., 26: 395-407, q1 (2009).
  • Foucart, S., “A note on guaranteed sparse recovery via L minimization”, Appl. Comput. Harmon. Anal., 29: 97-103, (2010).
  • Mo, Q. and Li, S., “New bounds on the restricted isometry constantδ 2k
  • ”, Appl. Comput. Harmon. Anal., 31: 460-468, (2011).
  • Cai, T., Wang, L. and Xu, G., “New bounds for restricted isometry constants”, IEEE Trans. Inf. Theory, 56: 4388-4394, (2010c).
  • Ji, J. and Peng, J., “Improved Bounds for Restricted Isometry Constants”, Discrete Dyn. Nat. Soc., (2012). doi:10.1155/2012/841261

Some Bounds and the Conditional Maximum Bound for Restricted Isometry Constants

Yıl 2014, Cilt: 27 Sayı: 4, 1021 - 1030, 24.11.2014

Shiqing Wang , Limin Su

Öz

Compressed sensing seeks to recover an unknown sparse signal with  entries by making far fewer than  measurements. The restricted isometry Constants (RIC) has become a dominant tool used for such cases since if RIC satisfies some bound then sparse signals are guaranteed to be recovered exactly when no noise is present and sparse signals can be estimated stably in the noisy case. During the last few years, a great deal of attention has been focused on bounds of RIC, see, e. g., Candes (2008), Foucart et al (2009), Foucart (2010), Cai et al (2010), Mo et al (2011), Ji et al (2012). Finding bounds of RIC has theoretical and applied significance. In this paper, we obtain a bound of RIC. It improves the results by Cai et al (2010) and Ji et al (2012). Further, we discuss the problems related larger bound of RIC, and give the conditional maximum bound.

Anahtar Kelimeler

Compressed sensing Lminimization restricted isometry property sparse signal recovery

Kaynakça

  • Donoho, D. L. and Huo, X., “Uncertainty principles and ideal atomic decomposition”, IEEE Trans. Inf. Theory, 47: 2845-2862, (2001).
  • Donoho, D. L., “Compressed sensing”, IEEE Trans. Inf. Theory, 52: 1289-1306, (2006).
  • Candes, E. J. and Tao, T., “Decoding by linear programming”, IEEE Trans. Inf. Theory, 51, 4203-4215, (2005).
  • Candes, E. J., Romberg, J. and Tao, T., “Stable signal recovery from incomplete and inaccurate measurements”, Comm. Pure Appl. Math., 59, 1207-1223, (2006a).
  • Candes, E. J. and Tao, T., “Near-optimal signal recovery from random projections: Universal encoding strategies”, IEEE Trans. Inf. Theory, 52, 5406-5425, (2006b).
  • Candes, E. J. and Tao, T., “The Dantzig selector: Statistical estimation when p is much larger than n (with discussion)”, Ann. Stat., 35, 2313-2351, (2007).
  • Cai, T., Wang, L. and Xu, G., “Shifting inequality and recovery of sparse signals”, IEEE Trans. Signal Process., 58: 1300-1308, (2010a).
  • Cai, T., Wang, L. and Xu, G., “Stable recovery of sparse signals and an oracle inequality”, IEEE Trans. Inf. Theory, 56: 3516-3522, (2010b).
  • Bickel, P. J., Ritov, Y. and Tsybakov A. B., “Simultaneous analysis of Lasso and Dantzig selector”, Ann. Stat., 37: 1705-1732, (2009).
  • Wang, S. Q. and Su, L. M., “The oracle inequalities on simultaneous Lasso and Dantzig selector in high dimensional nonparametric regression”, Math. Probl. Eng., (2013). doi:10.1155/2013/571361
  • Wang, S. Q. and Su, L. M. (2013b). “Recovery of high-dimensional spares signals via L1-minimization”, J. Appl. Math., (2013).
  • Wang, S. Q. and Su, L. M., “Simultaneous Lasso and Dantzig selector in high dimensional nonparametric regression”, Int. J. Appl. Math. Stat.,42: 103-118, (2013). [13] Cai, T., Xu, G. and Zhang, J., “On recovery of sparse signals via L minimization”, IEEE Trans. Inf. Theory, 1L 55: 3388-3397, (2009).
  • Baraniuk, R., Davenport, M., DeVore, R. and Wakin, M., “A simple proof of the restricted isometry property for random matrices”, Constr. Approx., 28: 253-263. (2008).
  • Davies, M. E. and Gribonval, R., “Restricted isometry constants where L sparse recovery can fail p
  • for 0< ≤ ”, IEEE Trans. Inf. Theory, 55: 203-2214, 1 p (2009).
  • Candes, E. J., “The restricted isometry property and its implications for compressed sensing”, Comptes Rendus Mathematique, 346: 589-592, (2008).
  • Foucart, S. and Lai, M., “Sparsest solutions of underdetermined linear systems via L minimization for q
  • 0< ≤ ”, Appl. Comput. Harmon. Anal., 26: 395-407, q1 (2009).
  • Foucart, S., “A note on guaranteed sparse recovery via L minimization”, Appl. Comput. Harmon. Anal., 29: 97-103, (2010).
  • Mo, Q. and Li, S., “New bounds on the restricted isometry constantδ 2k
  • ”, Appl. Comput. Harmon. Anal., 31: 460-468, (2011).
  • Cai, T., Wang, L. and Xu, G., “New bounds for restricted isometry constants”, IEEE Trans. Inf. Theory, 56: 4388-4394, (2010c).
  • Ji, J. and Peng, J., “Improved Bounds for Restricted Isometry Constants”, Discrete Dyn. Nat. Soc., (2012). doi:10.1155/2012/841261
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Mathematics
Yazarlar

Shiqing Wang

Limin Su

Yayımlanma Tarihi 24 Kasım 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 27 Sayı: 4

Kaynak Göster

APA Wang, S., & Su, L. (2014). Some Bounds and the Conditional Maximum Bound for Restricted Isometry Constants. Gazi University Journal of Science, 27(4), 1021-1030.
AMA Wang S, Su L. Some Bounds and the Conditional Maximum Bound for Restricted Isometry Constants. Gazi University Journal of Science. Kasım 2014;27(4):1021-1030.
Chicago Wang, Shiqing, ve Limin Su. “Some Bounds and the Conditional Maximum Bound for Restricted Isometry Constants”. Gazi University Journal of Science 27, sy. 4 (Kasım 2014): 1021-30.
EndNote Wang S, Su L (01 Kasım 2014) Some Bounds and the Conditional Maximum Bound for Restricted Isometry Constants. Gazi University Journal of Science 27 4 1021–1030.
IEEE S. Wang ve L. Su, “Some Bounds and the Conditional Maximum Bound for Restricted Isometry Constants”, Gazi University Journal of Science, c. 27, sy. 4, ss. 1021–1030, 2014.
ISNAD Wang, Shiqing - Su, Limin. “Some Bounds and the Conditional Maximum Bound for Restricted Isometry Constants”. Gazi University Journal of Science 27/4 (Kasım 2014), 1021-1030.
JAMA Wang S, Su L. Some Bounds and the Conditional Maximum Bound for Restricted Isometry Constants. Gazi University Journal of Science. 2014;27:1021–1030.
MLA Wang, Shiqing ve Limin Su. “Some Bounds and the Conditional Maximum Bound for Restricted Isometry Constants”. Gazi University Journal of Science, c. 27, sy. 4, 2014, ss. 1021-30.
Vancouver Wang S, Su L. Some Bounds and the Conditional Maximum Bound for Restricted Isometry Constants. Gazi University Journal of Science. 2014;27(4):1021-30.