Abstract

Within the range of validity of the Rytov approximation (RA), an innovative Bayesian compressive sensing (BCS) inverse scattering technique is developed. Potentialities and limitations of the BCS-RA method are validated through numerical experiments and representative results are discussed.

© 2012 Optical Society of America

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References

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  1. N. Garcia and M. Nieto, Opt. Lett. 18, 2090 (1993).
    [CrossRef]
  2. G. Bao and P. Li, Opt. Lett. 32, 1465 (2007).
    [CrossRef]
  3. T. S. Ralston, D. L. Marks, S. A. Boppart, and P. S. Carney, Opt. Lett. 31, 3585 (2006).
    [CrossRef]
  4. O. P. Bruno and J. Chaubell, Opt. Lett. 28, 2049 (2003).
    [CrossRef]
  5. J. C. Schotland, Opt. Lett. 35, 3309 (2010).
    [CrossRef]
  6. L. Crocco, M. D’Urso, and T. Isernia, J. Opt. Soc. Am. A 21, 622 (2004).
    [CrossRef]
  7. A. Litman and K. Belkebir, J. Opt. Soc. Am. A 23, 2737 (2006).
    [CrossRef]
  8. P. C. Chaumet, K. Belkebir, and R. Lencrerot, Opt. Express 14, 3415 (2006).
    [CrossRef]
  9. O. M. Bucci, L. Crocco, M. D’Urso, and T. Isernia, J. Opt. Soc. Am. A 23, 2566 (2006).
    [CrossRef]
  10. W. L. Chan, M. Moravec, R. Baraniuk, and D. Mittleman, Opt. Lett. 33, 974 (2008).
    [CrossRef]
  11. P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 1 (2009).
  12. P. Rocca, G. Oliveri, and A. Massa, IEEE Antennas Propag. Mag. 53, 38 (2011).
    [CrossRef]
  13. G. Oliveri, Y. Zhong, X. Chen, and A. Massa, J. Opt. Soc. Am. A 28, 2057 (2011).
    [CrossRef]
  14. G. Oliveri, P. Rocca, and A. Massa, IEEE Trans. Geosci. Remote Sens. 49, 3993 (2011).
    [CrossRef]
  15. A. J. Devaney, Opt. Lett. 6, 374 (1981).
    [CrossRef]
  16. M. Slaney, A. C. Kak, and L. E. Larsen, IEEE Trans. Microwave Theor. Tech. 32, 860 (1984).
  17. L. Poli, G. Oliveri, and A. Massa, “Complex-weight sparse linear array synthesis by Bayesian compressive sensing,” IEEE Trans. Antennas Propag. (to be published).
  18. G. Oliveri and A. Massa, IEEE Trans. Antennas Propag. 59, 467 (2011).
  19. G. Oliveri, M. Carlin, and A. Massa, IEEE Trans. Antennas Propag. (2012).
  20. S. Ji, Y. Xue, and L. Carin, IEEE Trans. Signal Process. 56, 2346 (2008).
    [CrossRef]
  21. S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing code” http://people.ee.duke.edu/~lihan/cs/ (2009).
  22. R. V. Kohn and A. McKenney, Inverse Probl. 6, 389 (1990).
    [CrossRef]

2012

G. Oliveri, M. Carlin, and A. Massa, IEEE Trans. Antennas Propag. (2012).

2011

P. Rocca, G. Oliveri, and A. Massa, IEEE Antennas Propag. Mag. 53, 38 (2011).
[CrossRef]

G. Oliveri, Y. Zhong, X. Chen, and A. Massa, J. Opt. Soc. Am. A 28, 2057 (2011).
[CrossRef]

G. Oliveri, P. Rocca, and A. Massa, IEEE Trans. Geosci. Remote Sens. 49, 3993 (2011).
[CrossRef]

G. Oliveri and A. Massa, IEEE Trans. Antennas Propag. 59, 467 (2011).

2010

2009

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 1 (2009).

2008

S. Ji, Y. Xue, and L. Carin, IEEE Trans. Signal Process. 56, 2346 (2008).
[CrossRef]

W. L. Chan, M. Moravec, R. Baraniuk, and D. Mittleman, Opt. Lett. 33, 974 (2008).
[CrossRef]

2007

2006

2004

2003

1993

1990

R. V. Kohn and A. McKenney, Inverse Probl. 6, 389 (1990).
[CrossRef]

1984

M. Slaney, A. C. Kak, and L. E. Larsen, IEEE Trans. Microwave Theor. Tech. 32, 860 (1984).

1981

Bao, G.

Baraniuk, R.

Belkebir, K.

Benedetti, M.

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 1 (2009).

Boppart, S. A.

Bruno, O. P.

Bucci, O. M.

Carin, L.

S. Ji, Y. Xue, and L. Carin, IEEE Trans. Signal Process. 56, 2346 (2008).
[CrossRef]

Carlin, M.

G. Oliveri, M. Carlin, and A. Massa, IEEE Trans. Antennas Propag. (2012).

Carney, P. S.

Chan, W. L.

Chaubell, J.

Chaumet, P. C.

Chen, X.

Crocco, L.

D’Urso, M.

Devaney, A. J.

Donelli, M.

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 1 (2009).

Franceschini, D.

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 1 (2009).

Garcia, N.

Isernia, T.

Ji, S.

S. Ji, Y. Xue, and L. Carin, IEEE Trans. Signal Process. 56, 2346 (2008).
[CrossRef]

Kak, A. C.

M. Slaney, A. C. Kak, and L. E. Larsen, IEEE Trans. Microwave Theor. Tech. 32, 860 (1984).

Kohn, R. V.

R. V. Kohn and A. McKenney, Inverse Probl. 6, 389 (1990).
[CrossRef]

Larsen, L. E.

M. Slaney, A. C. Kak, and L. E. Larsen, IEEE Trans. Microwave Theor. Tech. 32, 860 (1984).

Lencrerot, R.

Li, P.

Litman, A.

Marks, D. L.

Massa, A.

G. Oliveri, M. Carlin, and A. Massa, IEEE Trans. Antennas Propag. (2012).

G. Oliveri and A. Massa, IEEE Trans. Antennas Propag. 59, 467 (2011).

G. Oliveri, P. Rocca, and A. Massa, IEEE Trans. Geosci. Remote Sens. 49, 3993 (2011).
[CrossRef]

G. Oliveri, Y. Zhong, X. Chen, and A. Massa, J. Opt. Soc. Am. A 28, 2057 (2011).
[CrossRef]

P. Rocca, G. Oliveri, and A. Massa, IEEE Antennas Propag. Mag. 53, 38 (2011).
[CrossRef]

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 1 (2009).

L. Poli, G. Oliveri, and A. Massa, “Complex-weight sparse linear array synthesis by Bayesian compressive sensing,” IEEE Trans. Antennas Propag. (to be published).

McKenney, A.

R. V. Kohn and A. McKenney, Inverse Probl. 6, 389 (1990).
[CrossRef]

Mittleman, D.

Moravec, M.

Nieto, M.

Oliveri, G.

G. Oliveri, M. Carlin, and A. Massa, IEEE Trans. Antennas Propag. (2012).

G. Oliveri and A. Massa, IEEE Trans. Antennas Propag. 59, 467 (2011).

G. Oliveri, P. Rocca, and A. Massa, IEEE Trans. Geosci. Remote Sens. 49, 3993 (2011).
[CrossRef]

G. Oliveri, Y. Zhong, X. Chen, and A. Massa, J. Opt. Soc. Am. A 28, 2057 (2011).
[CrossRef]

P. Rocca, G. Oliveri, and A. Massa, IEEE Antennas Propag. Mag. 53, 38 (2011).
[CrossRef]

L. Poli, G. Oliveri, and A. Massa, “Complex-weight sparse linear array synthesis by Bayesian compressive sensing,” IEEE Trans. Antennas Propag. (to be published).

Poli, L.

L. Poli, G. Oliveri, and A. Massa, “Complex-weight sparse linear array synthesis by Bayesian compressive sensing,” IEEE Trans. Antennas Propag. (to be published).

Ralston, T. S.

Rocca, P.

P. Rocca, G. Oliveri, and A. Massa, IEEE Antennas Propag. Mag. 53, 38 (2011).
[CrossRef]

G. Oliveri, P. Rocca, and A. Massa, IEEE Trans. Geosci. Remote Sens. 49, 3993 (2011).
[CrossRef]

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 1 (2009).

Schotland, J. C.

Slaney, M.

M. Slaney, A. C. Kak, and L. E. Larsen, IEEE Trans. Microwave Theor. Tech. 32, 860 (1984).

Xue, Y.

S. Ji, Y. Xue, and L. Carin, IEEE Trans. Signal Process. 56, 2346 (2008).
[CrossRef]

Zhong, Y.

IEEE Antennas Propag. Mag.

P. Rocca, G. Oliveri, and A. Massa, IEEE Antennas Propag. Mag. 53, 38 (2011).
[CrossRef]

IEEE Trans. Antennas Propag.

L. Poli, G. Oliveri, and A. Massa, “Complex-weight sparse linear array synthesis by Bayesian compressive sensing,” IEEE Trans. Antennas Propag. (to be published).

G. Oliveri and A. Massa, IEEE Trans. Antennas Propag. 59, 467 (2011).

G. Oliveri, M. Carlin, and A. Massa, IEEE Trans. Antennas Propag. (2012).

IEEE Trans. Geosci. Remote Sens.

G. Oliveri, P. Rocca, and A. Massa, IEEE Trans. Geosci. Remote Sens. 49, 3993 (2011).
[CrossRef]

IEEE Trans. Microwave Theor. Tech.

M. Slaney, A. C. Kak, and L. E. Larsen, IEEE Trans. Microwave Theor. Tech. 32, 860 (1984).

IEEE Trans. Signal Process.

S. Ji, Y. Xue, and L. Carin, IEEE Trans. Signal Process. 56, 2346 (2008).
[CrossRef]

Inverse Probl.

R. V. Kohn and A. McKenney, Inverse Probl. 6, 389 (1990).
[CrossRef]

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, Inverse Probl. 25, 1 (2009).

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Other

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing code” http://people.ee.duke.edu/~lihan/cs/ (2009).

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Figures (4)

Fig. 1.
Fig. 1.

Single square scatterer (O=1, S=4, τ=0.5)—actual (a) and reconstructed (b), (c) profiles starting from (b) noiseless and (c) noisy (SNR=10dB) data.

Fig. 2.
Fig. 2.

Single square scatterer (O=4, S=1, SNR=10dB)—reconstructed profiles by (a), (b) BCS−RA, (c), (d) BCS−BA, and (e), (f) CG when (a), (c), (e) τ=1.0, (b), (d), (f) τ=2.0.

Fig. 3.
Fig. 3.

Single square scatterer (O=4, S=1)—behavior of ξ as a function of the scatterer contrast.

Fig. 4.
Fig. 4.

Multiple randomly displaced scatterers (O=S, τ={0.5,1.5,2.0}, SNR=10dB)—behavior of avg(ξ) (points), min(ξ) and max(ξ) (error bars) as a function of S.

Equations (7)

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

ϕv(r¯)=2Fv(r¯)DG(r¯r¯)Fv(r¯)τ(r¯)dr¯r¯C,r¯D,v=1,,V,
ϕ̲˜v=Gvτ¯+γ̲vv=1,,V,
gvmn=2DG(r̲vmr¯)Fv(r¯)χ(n)(r¯)dr¯Fv(r̲vm),
τ̲^v=arg{maxτ¯[p(τ¯|ϕ̲˜v)]}
p(τ¯)=limα1,α20p(τ¯|a̲v)p(a̲v)da̲v,
τ̲^v=[GvTGv/{γ^v2}+diag({a̲^v})]1GvTϕ̲˜v{γ^v2},v=1,,V,
({a̲^v},{γ^v2})=argmax(a̲v,γv2)[(2N)log2π+log|γv2I+Gvdiag(a̲v)1GvT|+ϕ̲˜vTγv2I+(Gvdiag(a̲v)1GvT)1ϕ̲˜v]

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