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Sparse Signal Recovery by Difference of Convex Functions Algorithms

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Intelligent Information and Database Systems (ACIIDS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7803))

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Abstract

This paper deals with the problem of signal recovery which is formulated as a l 0-minimization problem. Using two appropriate continuous approximations of l 0 − norm, we reformulate the problem as a DC (Difference of Convex functions) program. DCA (DC Algorithm) is then developed to solve the resulting problems. Computational experiments on several datasets show the efficiency of our methods.

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References

  1. Amaldi, E., Kann, V.: On the approximability of minimizing non zero variables or unsatisfied relations in linear systems. Theoretical Computer Science 209, 237–260 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bradley, P.S., Mangasarian, O.L.: Feature Selection via concave minimization and support vector machines. In: Proceeding of International Conference on Machina Learning, ICML 1998 (1998)

    Google Scholar 

  3. Candès, E., Tao, T.: Near optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inform. Theory 52(12), 5406–5425 (2006)

    Article  MathSciNet  Google Scholar 

  4. Candès, E., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59(8), 1207–1223 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Candès, E., Romberg, J., Tao, T.: Robust uncertainty principles: Exact signal reconstruction from highly incomplete Fourier information. IEEE Trans. Inform. Theory 52, 489–509 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Candès, E., Tao, T.: The Dantzig selector: Statistical estimation when p is much larger than n. Ann. Stat. 35(6), 2313–2351 (2007)

    Article  MATH  Google Scholar 

  7. Candès, E.J., Wakin, M.B., Boyd, S.P.: Enhancing Sparsity by Reweighted l 1 Minimization. J. Fourier Anal. Appl. 14, 877–905 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Duarte, M.F., Eldar, Y.C.: Structured Compressed Sensing: From Theory to Applications. IEEE Transactions on Signal Processing 59(9), 4053–4085 (2011)

    Article  MathSciNet  Google Scholar 

  9. Donoho, D.L.: Compressed sensing. IEEE Trans. Inform. Theory 52(4), 1289–1306 (2006)

    Article  MathSciNet  Google Scholar 

  10. Figueiredo, M.A.T., Nowak, R.D., Wright, S.J.: Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. IEEE Journal of Selected Topics in Signal Processing 1(4), 586–597 (2007)

    Article  Google Scholar 

  11. Fan, J., Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties. J. of the American Stat. Association 96(456), 1348–1360 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hastie, T., Tibshirani, R., Friedman, J.: The elements of statistical learning. Springer, Heidelberg (2001)

    MATH  Google Scholar 

  13. Le Thi, H.A.: Contribution à l’optimisation non convexe et l’optimisation globale: Théorie, Algoritmes et Applications, Habilitation à Diriger des Recherches, Université de Rouen (1997)

    Google Scholar 

  14. Le Thi, H.A.: DC programming and DCA, http://lita.sciences.univ-metz.fr/~lethi/english/DCA.html

  15. Le Thi, H.A., Pham Dinh, T.: The DC (difference of convex functions) Programming and DCA revisited with DC models of real world nonconvex optimization problems. Annals of Operations Research 133, 23–46 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Le Thi, H.A., Le Hoai, M., Van Nguyen, V., Pham Dinh, T.: A DC Programming approach for Feature Selection in Support Vector Machines learning. Journal of Advances in Data Analysis and Classification 2(3), 259–278 (2008)

    Article  Google Scholar 

  17. Le Thi, H.A., Van Nguyen, V., Ouchani, S.: Gene Selection for Cancer Classification Using DCA. In: Tang, C., Ling, C.X., Zhou, X., Cercone, N.J., Li, X. (eds.) ADMA 2008. LNCS (LNAI), vol. 5139, pp. 62–72. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  18. Thiao, M.: Approches de la programmation DC et DCA en Data mining, Thèse de doctorat à l’INSA-Rouen, France (2011)

    Google Scholar 

  19. Tibshirani, R.: Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society 46, 431–439 (1996)

    Google Scholar 

  20. SPARCO: A toolbox for testing sparse reconstruction algorithms, http://www.cs.ubc.ca/labs/scl/sparco/

  21. Weston, J., Elisseeff, A., Scholkopf, B., Tipping, M.: Use of the Zero-Norm with Linear Models and Kernel Methods. Journal of Machine Learning Research 3, 1439–1461 (2003)

    MATH  Google Scholar 

  22. Zou, H., Hastie, T.: Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B 7, 301–320 (2005)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Laboratory of Theoretical and Applied Computer Science - LITA EA 3097, University of Lorraine, Ile de Saulcy, 57045, Metz, France

    Hoai An Le Thi, Bich Thuy Nguyen Thi & Hoai Minh Le

Authors
  1. Hoai An Le Thi
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  2. Bich Thuy Nguyen Thi
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  3. Hoai Minh Le
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science and Information Systems, Department of Software Engineering, Universiti Teknologi Malaysia, 81310, Johar Baharu, Johor, Malaysia

    Ali Selamat  & Habibollah Haron  & 

  2. Institute of Informatics, Division of Knowledge Managements Systems, Wrocław University of Technology, Str. Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Ngoc Thanh Nguyen

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Le Thi, H.A., Nguyen Thi, B.T., Le, H.M. (2013). Sparse Signal Recovery by Difference of Convex Functions Algorithms. In: Selamat, A., Nguyen, N.T., Haron, H. (eds) Intelligent Information and Database Systems. ACIIDS 2013. Lecture Notes in Computer Science(), vol 7803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36543-0_40

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  • DOI: https://doi.org/10.1007/978-3-642-36543-0_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36542-3

  • Online ISBN: 978-3-642-36543-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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