Compressed remote sensing of sparse objects

SIAM Journal on Imaging Sciences

Volumn 3, Issue 3, 2010, Pages 595-618

  Fannjiang, Albert C ^a   Strohmer, Thomas ^a   Yan, Pengchong ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Compressed sensing; Incoherence; Random sensor array; Rayleigh resolution; Threshold aperture

Indexed keywords

COMPRESSED SENSING; INCOHERENCE; RANDOM SENSOR ARRAY; RAYLEIGH; THRESHOLD APERTURE;

INVERSE PROBLEMS; REMOTE SENSING; SENSOR ARRAYS;

SIGNAL RECONSTRUCTION;

EID: 78651591980     PISSN: None     EISSN: 19364954     Source Type: Journal    
DOI: 10.1137/090757034     Document Type: Article

References (42)

1. A.B. Baggeroer, W.A. Kuperman, and P.N. Mikhalevsky, An overview of matched field methodsin ocean acoustics, IEEE J. Oceanic Engrg., 18 (1993), pp. 401-424.
2. R. Baraniuk and P. Steeghs, Compressive radar imaging, in IEEE Radar Conference, IEEE, Washington,DC, 2007, pp. 128-133.
3. B. Borden, Radar Imaging of Airborne Targets, Institute of Physics Publishing, Bristol, UK, 1999.
4. M. Born and E. Wolf, Principles of Optics, 7th ed., Cambridge University Press, Cambridge, UK,1999.
5. A.M. Bruckstein, D.L. Donoho, and M. Elad, From sparse solutions of systems of equations tosparse modeling of signals and images, SIAM Rev., 51 (2009), pp. 34-81.
6. E.J. Candès, The restricted isometry property and its implications for compressed sensing, C. R. Math.Acad. Sci. Paris, 346 (2008), pp. 589-592.
7. E. Candès, J. Romberg, and T. Tao, Robust uncertainty principles: Exact signal reconstruction fromhighly incomplete frequency information, IEEE Trans. Inform. Theory, 52 (2006), pp. 489-509.
8. E.J. Candès, J. Romberg, and T. Tao, Stable signal recovery from incomplete and inaccurate measurements,Comm. Pure Appl. Math., 59 (2006), pp. 1207-1223.
9. E.J. Candès and T. Tao, Decoding by linear programming, IEEE Trans. Inform. Theory, 51 (2005), pp.4203-4215.
10. W.L. Chan, K. Charan, D. Takhar, K.F. Kelly, R.G. Baraniuk, and D.M. Mittleman, A singlepixelterahertz imaging system based on compressed sensing, Appl. Phys. Lett., 93 (2008), 121105.
11. J.C. Curlander and R.N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing,Wiley-Interscience, New York, 1991.
12. W. Dai and O. Milenkovic, Subspace pursuit for compressive sensing and reconstruction, IEEE Trans.Inform. Theory, 55 (2009), pp. 2230-2249.
13. P. Delsarte, J.M. Goethals, and J.J. Seidel, Bounds for systems of lines and Jacobi polynomials,Philips Res. Repts., 30 (1975), p. 91105.
14. D.L. Donoho, Compressed sensing, IEEE Trans. Inform. Theory, 52 (2006), pp. 1289-1306.
15. D.L. Donoho and M. Elad, Optimally sparse representation in general (nonorthogonal) dictionariesvia _1 minimization, Proc. Natl. Acad. Sci. USA, 100 (2003), pp. 2197-2202.
16. D.L. Donoho, M. Elad, and V.N. Temlyakov, Stable recovery of sparse overcomplete representationsin the presence of noise, IEEE Trans. Inform. Theory, 52 (2006), pp. 6-18.
17. D.L. Donoho and X. Huo, Uncertainty principle and ideal atomic decomposition, IEEE Trans. Inform.Theory, 47 (2001), pp. 2845-2862.
18. M.F. Duarte, M.A. Davenport, D. Takhar, J.N. Laska, T. Sun, K.F. Kelly, and R. Baraniuk,Single-pixel imaging via compressive sampling, IEEE Signal Process. Mag., 2008, pp. 83-91.
19. A.C. Fannjiang, Compressive imaging of subwavelength structures, SIAM J. Imaging Sci., 2 (2009),pp. 1277-1291.
20. A.C. Fannjiang, Compressive inverse scattering I. High-frequency SIMO/MISO and MIMO measurements,Inverse Problems, 26 (2010), 035008.
21. A.C. Fannjiang, Compressive inverse scattering II. Multi-shot SISO measurements with Born scatterers,Inverse Problems, 26 (2010), 035009.
22. A.C. Fannjiang and P. Yan, Multi-frequency imaging of multiple targets in Rician fading channels:Stability and resolution, Inverse Problems, 23 (2007), pp. 1801-1819.
23. A.C. Fannjiang, K. Solna, and P. Yan, Synthetic aperture imaging of multiple point targets in Ricianfading media, SIAM J. Imaging Sci., 2 (2009), pp. 344-366.
24. R. Gribonval and M. Nielsen, Sparse representation in unions of bases, IEEE Trans. Inform. Theory,49 (2003), pp. 3320-3325.
25. A.C. Gurbuz, J.H. McClellan, and W.R. Scott, Compressive sensing for subsurface imaging usingground penetrating radar, Signal Process., 89 (2009), pp. 1959-1972.
26. M. Herman and T. Strohmer, High-resolution radar via compressed sensing, IEEE Trans. SignalProcess., 57 (2009), pp. 2275-2284.
27. M. Herman and T. Strohmer, General deviants: An analysis of perturbations in compressed sensing,IEEE J. Sel. Topics Signal Process., Special Issue on Compressive Sensing, 4 (2010), pp. 342-349.
28. W. Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc.,58 (1963), pp. 13-30.
29. M. Lax, Multiple scattering of waves, Rev. Mod. Phys., 23 (1951), pp. 287-310.
30. D. Needell, J.A. Tropp, and R. Vershynin, Greedy signal recovery review, in Proceedings of the42nd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, 2008.
31. D. Needell and R. Vershynin, Uniform uncertainty principle and signal recovery via regularized orthogonalmatching pursuit, Found. Comput. Math., 9 (2009), pp. 317-334.
32. G.E. Pfander, H. Rauhut, and J. Tanner, Identification of matrices having a sparse representation,IEEE Trans. Signal Process., 56 (2008), pp. 5376-5388.
33. H. Rauhut, Stability results for random sampling of sparse trigonometric polynomials, IEEE Trans.Inform. Theory, 54 (2008), pp. 5661-5670.
34. M. Rudelson and R. Vershynin, On sparse reconstruction from Fourier and Gaussian measurements,Comm. Pure Appl. Math., 111 (2008), pp. 1025-1045.
35. A. Tolstoy, Matched Field Processing in Underwater Acoustics, World Scientific, Singapore, 1993.
36. J.A. Tropp, Greed is good: Algorithmic results for sparse approximation, IEEE Trans. Inform. Theory,50 (2004), pp. 2231-2242.
37. J.A. Tropp, Just relax: Convex programming methods for identifying sparse signals in noise, IEEE Trans.Inform. Theory, 52 (2006), pp. 1030-1051.
38. J.A. Tropp, Corrigendum in "Just relax: Convex programming methods for identifying sparse signals innoise," IEEE Trans. Inform. Theory, 55 (2009), pp. 917-918.
39. J.A. Tropp, On the conditioning of random subdictionaries, Appl. Comput. Harmon. Anal., 25 (2008),1-24.
40. H.C. van de Hulst, Light Scattering by Small Particles, Dover, New York, 1981.
41. L. Welch, Lower bounds on the maximum cross-correlation of signals, IEEE Trans. Inform. Theory, 20(1974), pp. 397-399.
42. J. Yang and Y. Zhang, Alternating direction algorithms for _1-problems in compressive sensing,preprint, 2009.