http://iet.metastore.ingenta.com
1887

Perturbation analysis of signal space fast iterative hard thresholding with redundant dictionaries

Perturbation analysis of signal space fast iterative hard thresholding with redundant dictionaries

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Signal Processing — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

Practically, sparsity is expressed not in terms of an orthonormal basis but in terms an overcomplete dictionary. There are many practical examples in which a signal of interest is sparse in an overcomplete dictionary. The authors propose a new algorithm signal space fast iterative hard thresholding (SSFIHT) for the recovery of dictionary-sparse signals. Under total perturbations, using D -restricted isometry property ( D -RIP), the authors provide the proof of convergence for SSFIHT. Comparing with the error of oracle recovery, it is easy to see that SSFIHT can provide oracle-order recovery performance against total perturbations. Numerical simulations are performed to verify the conclusions.

References

    1. 1)
      • 1. Candès, E.J., Romberg, J., Tao, T.: ‘Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information’, IEEE Trans. Inf. Theory, 2006, 52, (2), pp. 489509.
    2. 2)
      • 2. Tropp, J.: ‘Greed is good: algorithmic results for sparse approximation’, IEEE Trans. Inf. Theory, 2004, 50, (10), pp. 22312242.
    3. 3)
      • 3. Dai, W., Milenkovic, O.: ‘Subspace pursuit for compressive sensing signal reconstruction’, IEEE Trans. Inf. Theory, 2009, 55, (5), pp. 22302249.
    4. 4)
      • 4. Needell, D., Tropp, J.: ‘CoSaMP: iterative signal recovery from in-complete and inaccurate samples’, Appl. Comput. Harmon. Anal., 2009, 26, (3), pp. 301321.
    5. 5)
      • 5. Wang, J., Kwon, S., Shim, B.: ‘Generalized orthogonal matching pursuit’, IEEE Trans. Signal Process., 2012, 60, (12), pp. 62026216.
    6. 6)
      • 6. Foucart, S.: ‘Hard thresholding pursuit: an algorithm for compressive sensing’, SIAM J. Numer. Anal., 2011, 49, (6), pp. 25432563.
    7. 7)
      • 7. Blumensath, T., Davies, M: ‘Normalized iterative hard thresholding: Guaranteed stability and performance’, IEEE Journal of selected topics in signal processing, 2010, 4, (2), pp. 298309.
    8. 8)
      • 8. Blanchard, J., Tanner, J., Wei, K.: ‘CGIHT: conjugate gradient iterative hard thresholding for compressed sensing and matrix completion’, Information and Inference, 2015, 4, (4), pp. 289327.
    9. 9)
      • 9. Wei, K.: ‘Fast iterative hard thresholding for compressed sensing’, IEEE Signal Process. Lett., 2015, 22, (5), pp. 593597.
    10. 10)
      • 10. Candès, E., Tao, T.: ‘Decoding by linear programming’, IEEE Trans. Inf. Theory, 2005, 51, (12), pp. 42034215.
    11. 11)
      • 11. Giryes, R., Needell, D.: ‘Near oracle performace and block analysis of signal space greedy methods’, J. Approx. Theory, 2015, 194, pp. 157174.
    12. 12)
      • 12. Chen, X., Wang, H., Wang, R.: ‘A null space analysis of the 1-synthesis method in dictionary-based compressed sensing’, Appl. Comput. Harmon. Anal., 2014, 37, (3), pp. 492515.
    13. 13)
      • 13. Candès, E., Eldar, Y., Needell, D., et al: ‘Compressed sensing with coherent and redundant dictionaries’, Appl. Comput. Harmon. Anal., 2011, 31, (1), pp. 5973.
    14. 14)
      • 14. Prater, A., Shen, L.: ‘Separation of undersampled composite signals using the Dantzig selector with overcomplete dictionaries’, IET Signal Process., 2015, 9, (3), pp. 226234.
    15. 15)
      • 15. Rauhut, H., Schnass, K., Vandergheynst, P.: ‘Compressed sensing with coherent dictionaries’, IEEE Trans. Inf. Theory, 2008, 54, (5), pp. 22102219.
    16. 16)
      • 16. Lin, J., Li, S.: ‘Sparse recovery with coherent tight frame via analysis Dantzig selector and analysis lasso’, Appl. Comput. Harmon. Anal., 2014, 37, (1), pp. 126139.
    17. 17)
      • 17. Shen, Y., Han, B., Braverman, E.: ‘Stable recovery of analysis based approaches’, Appl. Comput. Harmon. Anal., 2015, 39, (1), pp. 161172.
    18. 18)
      • 18. Aldroubi, A., Chen, X., Powell, A.: ‘Perturbations of measurement matrices and dictionaries in compressed sensing’, Appl. Comput. Harmon. Anal., 2012, 33, (1), pp. 282291.
    19. 19)
      • 19. Davenport, M., Needell, D., Wakin, M.: ‘Signal space CoSaMP for sparse recovery with redundant dictionaries’, IEEE Trans. Inf. Theory, 2013, 59, (10), pp. 68206829.
    20. 20)
      • 20. Giryes, R., Needell, D.: ‘Greedy signal space methods for incoherence and beyond’, Appl. Comput. Harmon. Anal., 2015, 39, (1), pp. 120.
    21. 21)
      • 21. Ding, J., Chen, L., Gu, Y.: ‘Perturbation analysis of orthogonal matching pursuit’, IEEE Trans. Signal Process., 2013, 61, (2), pp. 398410.
    22. 22)
      • 22. Chen, L., Gu, Y.: ‘Oracle-order recovery performance of greedy pursuits with replacement against general perturbations’, IEEE Trans. Signal Process., 2013, 61, (18), pp. 46254636.
    23. 23)
      • 23. Ding, F., Wang, Y., Ding, J.: ‘Recursive least squares parameter identification algorithms for systems with colored noise using the filtering technique and the auxilary model’, Digit. Signal Process., 2015, 37, pp. 100108.
    24. 24)
      • 24. Wang, D., Liu, H., Ding, F.: ‘Highly efficient identification methods for dual-rate hammerstein systems’, IEEE Trans.Control Syst.Technol., 2015, 23, (5), pp. 19521960.
    25. 25)
      • 25. Wang, X., Ding, F.: ‘Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle’, Signal Process., 2015, 117, pp. 208218.
    26. 26)
      • 26. Ding, F., Duan, H.: ‘Two-stage parameter estimation algorithms for Box-Jenkins systems’, IET Signal Process., 2013, 7, (8), pp. 646654.
    27. 27)
      • 27. Gu, Y., Ding, F., Li, J.: ‘State filtering and parameter estimation for linear systems with d-step state-delay’, IET Signal Process., 2014, 8, (6), pp. 639646.
    28. 28)
      • 28. Hegde, C., Indyk, P., Schmidt, L.: ‘Approximation-tolerant model-based compressive sensing’. Proc. 25th ACM-SIAM Annual Symp. Discrete Algorithms (SODA), 2014, pp. 15441561.
    29. 29)
      • 29. Kyrillidis, A., Cevher, V.: ‘Sublinear time, approximate model-based sparse recovery for all’. arxiv:1203.4746 [cs.IT], 2012.
    30. 30)
      • 30. Blumensath, T.: ‘Sampling and reconstructing signals from a union of linear subspaces’, IEEE Trans. Inf. Theory, 2011, 57, (7), pp. 46604671.
    31. 31)
      • 31. Giryes, R., Elad, M.: ‘Iterative hard thresholding with near optimal projection for signal recovery’. Proc. of the 10th Int. Conf. on Sampling Theory and Applications, 2013, pp. 212215.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-spr.2015.0366
Loading

Related content

content/journals/10.1049/iet-spr.2015.0366
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address