Abstract

We present an automatic target recognition algorithm using the recently developed theory of sparse representations and compressive sensing. We show how sparsity can be helpful for efficient utilization of data for target recognition. We verify the efficacy of the proposed algorithm in terms of the recognition rate and confusion matrices on the well known Comanche (Boeing–Sikorsky, USA) forward-looking IR data set consisting of ten different military targets at different orientations.

© 2011 Optical Society of America

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  1. F. Sadjadi, “Infrared target detection with probability density functions of wavelet transform subbands,” Appl. Opt. 43, 315–323 (2004).
    [CrossRef] [PubMed]
  2. L. Wang, S. Z. Der, and N. M. Nasrabadi, “Automatic target recognition using a feature-decomposition and data-decomposition modular neural network,” IEEE Trans. Image Process. 7, 1113–1121 (1998).
    [CrossRef]
  3. L. A. Chan and N. M. Nasrabadi, “Application of wavelet-based vector quantization in target recognition,” Int. J. Art. Intel. Tools 6, 165–178 (1997).
    [CrossRef]
  4. P. Bharadwaj and L. Carin, “Infrared image classification using hidden Markov trees,” IEEE Trans. Pattern Anal. Mach. Intel. 24, 1394–1397 (2002).
    [CrossRef]
  5. B. Li, R. Chellappa, Q. Zheng, S. Der, N. M. Nasrabadi, L. Chan, and L. Wang, “Experimental evaluation of forward-looking IR data set automatic target recognition approaches—a comparative study,” Comput. Vision Image Underst. 84, 5–24 (2001).
    [CrossRef]
  6. J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intel. 31, 210–227 (2009).
    [CrossRef]
  7. V. M. Patel, N. M. Nasrabadi, and R. Chellappa, “Sparsity-Inspired automatic target recognition,” Proc. SPIE 7696, 76960Q (2010).
    [CrossRef]
  8. D. L. Donoho and X. Huo, “Uncertainty principle and ideal atomic decomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
    [CrossRef]
  9. D. L. Donoho and M. Elad, “On the stability of the basis pursuit in the presence of noise,” EURASIP J. Adv. Signal Processing 86, 511–532 (2006).
    [CrossRef]
  10. E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2006).
    [CrossRef]
  11. H. Rauhut, K. Schnass, and P. Vandergheynst, “Compressed sensing and redundant dictionaries,” IEEE Trans. Inf. Theory 54, 2210–2219 (2008).
    [CrossRef]
  12. R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24, 118–121 (2007).
    [CrossRef]
  13. S. Chen, D. Donoho, and M. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20, 33–61 (1998).
    [CrossRef]
  14. ∥x∥0 returns the number of nonzero elements of x.
  15. J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655–4666 (2007).
    [CrossRef]
  16. R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. Ser. B. Methodol. 58, 267–288(1996).
  17. E. van der Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. 31, 890–912 (2008).
    [CrossRef]
  18. H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” J. R. Stat. Soc. B 67, 301–320(2005).
    [CrossRef]
  19. Y. C. Eldar and M. Mishali, “Robust recovery of signals from a structured union of subspaces,” IEEE Trans. Inf. Theory 55, 5302–5316 (2009).
    [CrossRef]
  20. Y. C. Eldar, P. Kuppinger, and H. B. Bolcskei, “Block-sparse signals: uncertainty relations and efficient recovery,” IEEE Trans. Signal Process. 58, 3042–3054 (2010).
    [CrossRef]
  21. M. Yuan and Y. Lin, “Model selection and estimation in regression with grouped variables,” J. R. Stat. Soc. B 68, 49–67(2006).
    [CrossRef]
  22. L. Meier, S. van der Geer, and P. Buhlman, “The group lasso for logistic regression,” J. R. Stat. Soc. B 70, 53–71 (2008).
    [CrossRef]
  23. M. Stojnic, F. Parvaresh, and B. Hassibi, “On the reconstruction of block-sparse signals with an optimal number of measurements,” IEEE Trans. Signal Process. 57, 3075–3085(2009).
    [CrossRef]
  24. Given C classes, the confusion matrix is of size C×C, whose diagonal entries are the number of targets that are correctly classified, while the off-diagonal entries are the number of misclassifications.
  25. Y. Tsaig and D. L. Donoho, “Extensions of compressed sensing,” Signal Process. 86, 549–571 (2006).
    [CrossRef]
  26. E. Candès and J. K. Romberg, “Signal recovery from random projections,” Proc. SPIE 5674, 76–86 (2005).
    [CrossRef]
  27. Exact recovery of sparse coefficients also depends on the matrix GA. That is, GA must satisfy certain properties such as the mutual coherence property and the restricted isometry property. See for more details.
  28. P. J. Phillips, “Matching pursuit filters applied to face identification,” IEEE Trans. Image Process. 7, 1150–1164 (1998).
    [CrossRef]
  29. D. Needell and J. A. Tropp, “CoSaMP: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
    [CrossRef]
  30. F. Rodriguez and G. Sapiro, “Sparse representations for image classification: learning discriminative and reconstructive nonparametric dictionaries,” Tech. Report (University of Minnesota, Dec. 2007).
  31. P. Sprechmann and G. Sapiro, “Dictionary learning and sparse coding for unsupervised clustering,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2010), pp. 2042–2045.
    [CrossRef]
  32. F. M. Caimi, D. M. Kocak, F. Dalgleish, and J. Watson, “Underwater imaging and optics: recent advances,” Oceans 2008 2008, 1–9 (2008).
    [CrossRef]

2010 (2)

V. M. Patel, N. M. Nasrabadi, and R. Chellappa, “Sparsity-Inspired automatic target recognition,” Proc. SPIE 7696, 76960Q (2010).
[CrossRef]

Y. C. Eldar, P. Kuppinger, and H. B. Bolcskei, “Block-sparse signals: uncertainty relations and efficient recovery,” IEEE Trans. Signal Process. 58, 3042–3054 (2010).
[CrossRef]

2009 (4)

D. Needell and J. A. Tropp, “CoSaMP: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
[CrossRef]

M. Stojnic, F. Parvaresh, and B. Hassibi, “On the reconstruction of block-sparse signals with an optimal number of measurements,” IEEE Trans. Signal Process. 57, 3075–3085(2009).
[CrossRef]

J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intel. 31, 210–227 (2009).
[CrossRef]

Y. C. Eldar and M. Mishali, “Robust recovery of signals from a structured union of subspaces,” IEEE Trans. Inf. Theory 55, 5302–5316 (2009).
[CrossRef]

2008 (4)

E. van der Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. 31, 890–912 (2008).
[CrossRef]

H. Rauhut, K. Schnass, and P. Vandergheynst, “Compressed sensing and redundant dictionaries,” IEEE Trans. Inf. Theory 54, 2210–2219 (2008).
[CrossRef]

F. M. Caimi, D. M. Kocak, F. Dalgleish, and J. Watson, “Underwater imaging and optics: recent advances,” Oceans 2008 2008, 1–9 (2008).
[CrossRef]

L. Meier, S. van der Geer, and P. Buhlman, “The group lasso for logistic regression,” J. R. Stat. Soc. B 70, 53–71 (2008).
[CrossRef]

2007 (2)

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24, 118–121 (2007).
[CrossRef]

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655–4666 (2007).
[CrossRef]

2006 (4)

D. L. Donoho and M. Elad, “On the stability of the basis pursuit in the presence of noise,” EURASIP J. Adv. Signal Processing 86, 511–532 (2006).
[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2006).
[CrossRef]

M. Yuan and Y. Lin, “Model selection and estimation in regression with grouped variables,” J. R. Stat. Soc. B 68, 49–67(2006).
[CrossRef]

Y. Tsaig and D. L. Donoho, “Extensions of compressed sensing,” Signal Process. 86, 549–571 (2006).
[CrossRef]

2005 (2)

E. Candès and J. K. Romberg, “Signal recovery from random projections,” Proc. SPIE 5674, 76–86 (2005).
[CrossRef]

H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” J. R. Stat. Soc. B 67, 301–320(2005).
[CrossRef]

2004 (1)

2002 (1)

P. Bharadwaj and L. Carin, “Infrared image classification using hidden Markov trees,” IEEE Trans. Pattern Anal. Mach. Intel. 24, 1394–1397 (2002).
[CrossRef]

2001 (2)

B. Li, R. Chellappa, Q. Zheng, S. Der, N. M. Nasrabadi, L. Chan, and L. Wang, “Experimental evaluation of forward-looking IR data set automatic target recognition approaches—a comparative study,” Comput. Vision Image Underst. 84, 5–24 (2001).
[CrossRef]

D. L. Donoho and X. Huo, “Uncertainty principle and ideal atomic decomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
[CrossRef]

1998 (3)

L. Wang, S. Z. Der, and N. M. Nasrabadi, “Automatic target recognition using a feature-decomposition and data-decomposition modular neural network,” IEEE Trans. Image Process. 7, 1113–1121 (1998).
[CrossRef]

S. Chen, D. Donoho, and M. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20, 33–61 (1998).
[CrossRef]

P. J. Phillips, “Matching pursuit filters applied to face identification,” IEEE Trans. Image Process. 7, 1150–1164 (1998).
[CrossRef]

1997 (1)

L. A. Chan and N. M. Nasrabadi, “Application of wavelet-based vector quantization in target recognition,” Int. J. Art. Intel. Tools 6, 165–178 (1997).
[CrossRef]

1996 (1)

R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. Ser. B. Methodol. 58, 267–288(1996).

Baraniuk, R.

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24, 118–121 (2007).
[CrossRef]

Bharadwaj, P.

P. Bharadwaj and L. Carin, “Infrared image classification using hidden Markov trees,” IEEE Trans. Pattern Anal. Mach. Intel. 24, 1394–1397 (2002).
[CrossRef]

Bolcskei, H. B.

Y. C. Eldar, P. Kuppinger, and H. B. Bolcskei, “Block-sparse signals: uncertainty relations and efficient recovery,” IEEE Trans. Signal Process. 58, 3042–3054 (2010).
[CrossRef]

Buhlman, P.

L. Meier, S. van der Geer, and P. Buhlman, “The group lasso for logistic regression,” J. R. Stat. Soc. B 70, 53–71 (2008).
[CrossRef]

Caimi, F. M.

F. M. Caimi, D. M. Kocak, F. Dalgleish, and J. Watson, “Underwater imaging and optics: recent advances,” Oceans 2008 2008, 1–9 (2008).
[CrossRef]

Candès, E.

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2006).
[CrossRef]

E. Candès and J. K. Romberg, “Signal recovery from random projections,” Proc. SPIE 5674, 76–86 (2005).
[CrossRef]

Carin, L.

P. Bharadwaj and L. Carin, “Infrared image classification using hidden Markov trees,” IEEE Trans. Pattern Anal. Mach. Intel. 24, 1394–1397 (2002).
[CrossRef]

Chan, L.

B. Li, R. Chellappa, Q. Zheng, S. Der, N. M. Nasrabadi, L. Chan, and L. Wang, “Experimental evaluation of forward-looking IR data set automatic target recognition approaches—a comparative study,” Comput. Vision Image Underst. 84, 5–24 (2001).
[CrossRef]

Chan, L. A.

L. A. Chan and N. M. Nasrabadi, “Application of wavelet-based vector quantization in target recognition,” Int. J. Art. Intel. Tools 6, 165–178 (1997).
[CrossRef]

Chellappa, R.

V. M. Patel, N. M. Nasrabadi, and R. Chellappa, “Sparsity-Inspired automatic target recognition,” Proc. SPIE 7696, 76960Q (2010).
[CrossRef]

B. Li, R. Chellappa, Q. Zheng, S. Der, N. M. Nasrabadi, L. Chan, and L. Wang, “Experimental evaluation of forward-looking IR data set automatic target recognition approaches—a comparative study,” Comput. Vision Image Underst. 84, 5–24 (2001).
[CrossRef]

Chen, S.

S. Chen, D. Donoho, and M. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20, 33–61 (1998).
[CrossRef]

Dalgleish, F.

F. M. Caimi, D. M. Kocak, F. Dalgleish, and J. Watson, “Underwater imaging and optics: recent advances,” Oceans 2008 2008, 1–9 (2008).
[CrossRef]

Der, S.

B. Li, R. Chellappa, Q. Zheng, S. Der, N. M. Nasrabadi, L. Chan, and L. Wang, “Experimental evaluation of forward-looking IR data set automatic target recognition approaches—a comparative study,” Comput. Vision Image Underst. 84, 5–24 (2001).
[CrossRef]

Der, S. Z.

L. Wang, S. Z. Der, and N. M. Nasrabadi, “Automatic target recognition using a feature-decomposition and data-decomposition modular neural network,” IEEE Trans. Image Process. 7, 1113–1121 (1998).
[CrossRef]

Donoho, D.

S. Chen, D. Donoho, and M. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20, 33–61 (1998).
[CrossRef]

Donoho, D. L.

D. L. Donoho and M. Elad, “On the stability of the basis pursuit in the presence of noise,” EURASIP J. Adv. Signal Processing 86, 511–532 (2006).
[CrossRef]

Y. Tsaig and D. L. Donoho, “Extensions of compressed sensing,” Signal Process. 86, 549–571 (2006).
[CrossRef]

D. L. Donoho and X. Huo, “Uncertainty principle and ideal atomic decomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
[CrossRef]

Elad, M.

D. L. Donoho and M. Elad, “On the stability of the basis pursuit in the presence of noise,” EURASIP J. Adv. Signal Processing 86, 511–532 (2006).
[CrossRef]

Eldar, Y. C.

Y. C. Eldar, P. Kuppinger, and H. B. Bolcskei, “Block-sparse signals: uncertainty relations and efficient recovery,” IEEE Trans. Signal Process. 58, 3042–3054 (2010).
[CrossRef]

Y. C. Eldar and M. Mishali, “Robust recovery of signals from a structured union of subspaces,” IEEE Trans. Inf. Theory 55, 5302–5316 (2009).
[CrossRef]

Friedlander, M. P.

E. van der Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. 31, 890–912 (2008).
[CrossRef]

Ganesh, A.

J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intel. 31, 210–227 (2009).
[CrossRef]

Gilbert, A. C.

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655–4666 (2007).
[CrossRef]

Hassibi, B.

M. Stojnic, F. Parvaresh, and B. Hassibi, “On the reconstruction of block-sparse signals with an optimal number of measurements,” IEEE Trans. Signal Process. 57, 3075–3085(2009).
[CrossRef]

Hastie, T.

H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” J. R. Stat. Soc. B 67, 301–320(2005).
[CrossRef]

Huo, X.

D. L. Donoho and X. Huo, “Uncertainty principle and ideal atomic decomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
[CrossRef]

Kocak, D. M.

F. M. Caimi, D. M. Kocak, F. Dalgleish, and J. Watson, “Underwater imaging and optics: recent advances,” Oceans 2008 2008, 1–9 (2008).
[CrossRef]

Kuppinger, P.

Y. C. Eldar, P. Kuppinger, and H. B. Bolcskei, “Block-sparse signals: uncertainty relations and efficient recovery,” IEEE Trans. Signal Process. 58, 3042–3054 (2010).
[CrossRef]

Li, B.

B. Li, R. Chellappa, Q. Zheng, S. Der, N. M. Nasrabadi, L. Chan, and L. Wang, “Experimental evaluation of forward-looking IR data set automatic target recognition approaches—a comparative study,” Comput. Vision Image Underst. 84, 5–24 (2001).
[CrossRef]

Lin, Y.

M. Yuan and Y. Lin, “Model selection and estimation in regression with grouped variables,” J. R. Stat. Soc. B 68, 49–67(2006).
[CrossRef]

Ma, Y.

J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intel. 31, 210–227 (2009).
[CrossRef]

Meier, L.

L. Meier, S. van der Geer, and P. Buhlman, “The group lasso for logistic regression,” J. R. Stat. Soc. B 70, 53–71 (2008).
[CrossRef]

Mishali, M.

Y. C. Eldar and M. Mishali, “Robust recovery of signals from a structured union of subspaces,” IEEE Trans. Inf. Theory 55, 5302–5316 (2009).
[CrossRef]

Nasrabadi, N. M.

V. M. Patel, N. M. Nasrabadi, and R. Chellappa, “Sparsity-Inspired automatic target recognition,” Proc. SPIE 7696, 76960Q (2010).
[CrossRef]

B. Li, R. Chellappa, Q. Zheng, S. Der, N. M. Nasrabadi, L. Chan, and L. Wang, “Experimental evaluation of forward-looking IR data set automatic target recognition approaches—a comparative study,” Comput. Vision Image Underst. 84, 5–24 (2001).
[CrossRef]

L. Wang, S. Z. Der, and N. M. Nasrabadi, “Automatic target recognition using a feature-decomposition and data-decomposition modular neural network,” IEEE Trans. Image Process. 7, 1113–1121 (1998).
[CrossRef]

L. A. Chan and N. M. Nasrabadi, “Application of wavelet-based vector quantization in target recognition,” Int. J. Art. Intel. Tools 6, 165–178 (1997).
[CrossRef]

Needell, D.

D. Needell and J. A. Tropp, “CoSaMP: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
[CrossRef]

Parvaresh, F.

M. Stojnic, F. Parvaresh, and B. Hassibi, “On the reconstruction of block-sparse signals with an optimal number of measurements,” IEEE Trans. Signal Process. 57, 3075–3085(2009).
[CrossRef]

Patel, V. M.

V. M. Patel, N. M. Nasrabadi, and R. Chellappa, “Sparsity-Inspired automatic target recognition,” Proc. SPIE 7696, 76960Q (2010).
[CrossRef]

Phillips, P. J.

P. J. Phillips, “Matching pursuit filters applied to face identification,” IEEE Trans. Image Process. 7, 1150–1164 (1998).
[CrossRef]

Rauhut, H.

H. Rauhut, K. Schnass, and P. Vandergheynst, “Compressed sensing and redundant dictionaries,” IEEE Trans. Inf. Theory 54, 2210–2219 (2008).
[CrossRef]

Rodriguez, F.

F. Rodriguez and G. Sapiro, “Sparse representations for image classification: learning discriminative and reconstructive nonparametric dictionaries,” Tech. Report (University of Minnesota, Dec. 2007).

Romberg, J.

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2006).
[CrossRef]

Romberg, J. K.

E. Candès and J. K. Romberg, “Signal recovery from random projections,” Proc. SPIE 5674, 76–86 (2005).
[CrossRef]

Sadjadi, F.

Sapiro, G.

F. Rodriguez and G. Sapiro, “Sparse representations for image classification: learning discriminative and reconstructive nonparametric dictionaries,” Tech. Report (University of Minnesota, Dec. 2007).

P. Sprechmann and G. Sapiro, “Dictionary learning and sparse coding for unsupervised clustering,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2010), pp. 2042–2045.
[CrossRef]

Sastry, S. S.

J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intel. 31, 210–227 (2009).
[CrossRef]

Saunders, M.

S. Chen, D. Donoho, and M. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20, 33–61 (1998).
[CrossRef]

Schnass, K.

H. Rauhut, K. Schnass, and P. Vandergheynst, “Compressed sensing and redundant dictionaries,” IEEE Trans. Inf. Theory 54, 2210–2219 (2008).
[CrossRef]

Sprechmann, P.

P. Sprechmann and G. Sapiro, “Dictionary learning and sparse coding for unsupervised clustering,” in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2010), pp. 2042–2045.
[CrossRef]

Stojnic, M.

M. Stojnic, F. Parvaresh, and B. Hassibi, “On the reconstruction of block-sparse signals with an optimal number of measurements,” IEEE Trans. Signal Process. 57, 3075–3085(2009).
[CrossRef]

Tao, T.

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2006).
[CrossRef]

Tibshirani, R.

R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. Ser. B. Methodol. 58, 267–288(1996).

Tropp, J. A.

D. Needell and J. A. Tropp, “CoSaMP: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
[CrossRef]

J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Trans. Inf. Theory 53, 4655–4666 (2007).
[CrossRef]

Tsaig, Y.

Y. Tsaig and D. L. Donoho, “Extensions of compressed sensing,” Signal Process. 86, 549–571 (2006).
[CrossRef]

van der Berg, E.

E. van der Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions,” SIAM J. Sci. Comput. 31, 890–912 (2008).
[CrossRef]

van der Geer, S.

L. Meier, S. van der Geer, and P. Buhlman, “The group lasso for logistic regression,” J. R. Stat. Soc. B 70, 53–71 (2008).
[CrossRef]

Vandergheynst, P.

H. Rauhut, K. Schnass, and P. Vandergheynst, “Compressed sensing and redundant dictionaries,” IEEE Trans. Inf. Theory 54, 2210–2219 (2008).
[CrossRef]

Wang, L.

B. Li, R. Chellappa, Q. Zheng, S. Der, N. M. Nasrabadi, L. Chan, and L. Wang, “Experimental evaluation of forward-looking IR data set automatic target recognition approaches—a comparative study,” Comput. Vision Image Underst. 84, 5–24 (2001).
[CrossRef]

L. Wang, S. Z. Der, and N. M. Nasrabadi, “Automatic target recognition using a feature-decomposition and data-decomposition modular neural network,” IEEE Trans. Image Process. 7, 1113–1121 (1998).
[CrossRef]

Watson, J.

F. M. Caimi, D. M. Kocak, F. Dalgleish, and J. Watson, “Underwater imaging and optics: recent advances,” Oceans 2008 2008, 1–9 (2008).
[CrossRef]

Wright, J.

J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intel. 31, 210–227 (2009).
[CrossRef]

Yang, A. Y.

J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry, and Y. Ma, “Robust face recognition via sparse representation,” IEEE Trans. Pattern Anal. Mach. Intel. 31, 210–227 (2009).
[CrossRef]

Yuan, M.

M. Yuan and Y. Lin, “Model selection and estimation in regression with grouped variables,” J. R. Stat. Soc. B 68, 49–67(2006).
[CrossRef]

Zheng, Q.

B. Li, R. Chellappa, Q. Zheng, S. Der, N. M. Nasrabadi, L. Chan, and L. Wang, “Experimental evaluation of forward-looking IR data set automatic target recognition approaches—a comparative study,” Comput. Vision Image Underst. 84, 5–24 (2001).
[CrossRef]

Zou, H.

H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” J. R. Stat. Soc. B 67, 301–320(2005).
[CrossRef]

Appl. Comput. Harmon. Anal. (1)

D. Needell and J. A. Tropp, “CoSaMP: iterative signal recovery from incomplete and inaccurate samples,” Appl. Comput. Harmon. Anal. 26, 301–321 (2009).
[CrossRef]

Appl. Opt. (1)

Comm. Pure Appl. Math. (1)

E. Candès, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math. 59, 1207–1223 (2006).
[CrossRef]

Comput. Vision Image Underst. (1)

B. Li, R. Chellappa, Q. Zheng, S. Der, N. M. Nasrabadi, L. Chan, and L. Wang, “Experimental evaluation of forward-looking IR data set automatic target recognition approaches—a comparative study,” Comput. Vision Image Underst. 84, 5–24 (2001).
[CrossRef]

EURASIP J. Adv. Signal Processing (1)

D. L. Donoho and M. Elad, “On the stability of the basis pursuit in the presence of noise,” EURASIP J. Adv. Signal Processing 86, 511–532 (2006).
[CrossRef]

IEEE Signal Process. Mag. (1)

R. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag. 24, 118–121 (2007).
[CrossRef]

IEEE Trans. Image Process. (2)

L. Wang, S. Z. Der, and N. M. Nasrabadi, “Automatic target recognition using a feature-decomposition and data-decomposition modular neural network,” IEEE Trans. Image Process. 7, 1113–1121 (1998).
[CrossRef]

P. J. Phillips, “Matching pursuit filters applied to face identification,” IEEE Trans. Image Process. 7, 1150–1164 (1998).
[CrossRef]

IEEE Trans. Inf. Theory (4)

H. Rauhut, K. Schnass, and P. Vandergheynst, “Compressed sensing and redundant dictionaries,” IEEE Trans. Inf. Theory 54, 2210–2219 (2008).
[CrossRef]

D. L. Donoho and X. Huo, “Uncertainty principle and ideal atomic decomposition,” IEEE Trans. Inf. Theory 47, 2845–2862 (2001).
[CrossRef]

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Other (5)

Exact recovery of sparse coefficients also depends on the matrix GA. That is, GA must satisfy certain properties such as the mutual coherence property and the restricted isometry property. See for more details.

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∥x∥0 returns the number of nonzero elements of x.

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Figures (10)

Fig. 1
Fig. 1

Overview of our approach using SR. Test target chip is represented as a linear combination of image chips from a dictionary containing all training images.

Fig. 2
Fig. 2

SR-based ATR algorithm.

Fig. 3
Fig. 3

Side view of all 10 targets present in the SIG data set.

Fig. 4
Fig. 4

Some sample target chips from the ROI data set.

Fig. 5
Fig. 5

Examples of different features used in this paper: (a) original target chip, (b) Haar wavelet features, (c) downsampled image, (d) PCA features, (e) random projection.

Fig. 6
Fig. 6

Confusion matrices corresponding to the SIG data set using different features: (a) downsampled, (b) random projection, (c) PCA, (d) Haar wavelet.

Fig. 7
Fig. 7

Confusion matrices corresponding to the ROI data set using different features: (a) downsampled, (b) random projection, (c) PCA, (d) Haar wavelet.

Fig. 8
Fig. 8

Recognition results on the TEST-SIG and TEST-ROI sets using different features.

Fig. 9
Fig. 9

Target orientation detection. Dictionary matrix A contains training images with known orientation. This can be used to identify the aspect angle of a test target.

Fig. 10
Fig. 10

Recognition rate versus feature dimension.

Tables (1)

Tables Icon

Table 1 Recognition Rates (in %) for Different Methods

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

A = [ A 1 , , A L ] R N × ( n . L ) = [ x 11 , , x 1 n | x 21 , , x 2 n | | x L 1 , , x L n ] .
y = i = 1 L j = 1 n α i j x i j
y = A α ,
α = [ α 11 , , α 1 n | α 21 , , α 2 n | | α L 1 , , α L n ] T
α ^ = arg min α α 1 subject to     y = A α ,
α ^ = arg min α α 1 subject to     y A α 2 ε ,
y = A α + η
( 1 δ K ) v 2 2 A v 2 2 ( 1 + δ K ) v 2 2
y ˜ Gy = GA α + η ˜ R M ˜ ,
α ^ = arg min α α 1 subject to     y ˜ GA α 2 ε ˜ ,
r k ( y ) = y A χ k ( α ^ ) 2 .
d = arg min k r k ( y ) .
SCI ( α ) = L . max χ i ( α ) 1 α 1 1 L 1 .
min y A α 2 2 subject to     α 1 τ ,
min 1 2 y A α 2 2 + λ α 1 ,
α ^ = min a 1 2 + a 2 2 + + a L 2 subject to     y A α ε ,
α α ^ 2 C 1 K 1 2 α α K 2 , J + C 2 ε ,
( 1 δ K | J ) v 2 2 A v 2 2 ( 1 + δ K | J ) v 2 2
α ^ = min a 1 2 + a 2 2 + + a 720 2 subject to     y A α ε ,

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