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Volumn 206, Issue 2, 2008, Pages 980-988

Compressed sensing by inverse scale space and curvelet thresholding

Author keywords

Aerospace remote sensing; Compressed sensing; Geometric wavelets; Image recovery; Incomplete measurements; Inverse problem

Indexed keywords

INVERSE PROBLEMS; NUMERICAL METHODS; REMOTE SENSING; SIGNAL RECONSTRUCTION; SPACE OPTICS;

EID: 56949108156     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.10.011     Document Type: Article
Times cited : (31)

References (46)
  • 1
    • 85032751965 scopus 로고    scopus 로고
    • A lecture on compressive sensing
    • Baraniuk R. A lecture on compressive sensing. IEEE Signal Process. Mag. 24 4 (2007) 118-121
    • (2007) IEEE Signal Process. Mag. , vol.24 , Issue.4 , pp. 118-121
    • Baraniuk, R.1
  • 2
    • 56949086885 scopus 로고    scopus 로고
    • R. Berinde, P. Indyk, Sparse recovery using sparse random matrices, Tech. Report of MIT, 2008.
    • R. Berinde, P. Indyk, Sparse recovery using sparse random matrices, Tech. Report of MIT, 2008.
  • 3
    • 56949084400 scopus 로고    scopus 로고
    • J. Bobin, J. Starck, R. Ottensamer, Compressed sensing in astronomy, IEEE J. Sel. Top. Signal Process., submitted for publication.
    • J. Bobin, J. Starck, R. Ottensamer, Compressed sensing in astronomy, IEEE J. Sel. Top. Signal Process., submitted for publication.
  • 4
    • 56949105383 scopus 로고    scopus 로고
    • T. Blumensath, M. Davies, Iterative thresholding for sparse approximations, J. Fourier Anal. Appl., in press.
    • T. Blumensath, M. Davies, Iterative thresholding for sparse approximations, J. Fourier Anal. Appl., in press.
  • 7
  • 8
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate information
    • Candès E., Romberg J., and Tao T. Stable signal recovery from incomplete and inaccurate information. Commun. Pure Appl. Math. 59 (2005) 1207-1233
    • (2005) Commun. Pure Appl. Math. , vol.59 , pp. 1207-1233
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 9
    • 33947416035 scopus 로고    scopus 로고
    • Near optimal signal recovery from random projections: universal encoding strategies
    • Candès E., and Tao T. Near optimal signal recovery from random projections: universal encoding strategies. IEEE Trans. Inform. Theory 52 12 (2006) 5406-5425
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candès, E.1    Tao, T.2
  • 10
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
    • Candès E., Romberg J., and Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52 2 (2006) 489-590
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.2 , pp. 489-590
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 11
    • 84878104490 scopus 로고    scopus 로고
    • E. Candès, Compressive sampling, in: Int. Congr. Math., vol. 3, Madrid, Spain, 2006, pp. 1433-1452.
    • E. Candès, Compressive sampling, in: Int. Congr. Math., vol. 3, Madrid, Spain, 2006, pp. 1433-1452.
  • 12
    • 2442458882 scopus 로고    scopus 로고
    • New tight frames of curvelets and optimal representations of objects with piecewise singularities
    • Candès E., and Donoho D. New tight frames of curvelets and optimal representations of objects with piecewise singularities. Commun. Pure Appl. Math. 57 (2004) 219-266
    • (2004) Commun. Pure Appl. Math. , vol.57 , pp. 219-266
    • Candès, E.1    Donoho, D.2
  • 14
    • 0026821645 scopus 로고
    • Image selective smoothing and edge detection by nonlinear diffusion
    • Catté F., Lions P., Morel J., and Coll T. Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 32 (1992) 1895-1909
    • (1992) SIAM J. Numer. Anal. , vol.32 , pp. 1895-1909
    • Catté, F.1    Lions, P.2    Morel, J.3    Coll, T.4
  • 15
    • 30844438177 scopus 로고    scopus 로고
    • Signal recovery by proximal forward-backward splitting
    • Combettes P., and Wajs V. Signal recovery by proximal forward-backward splitting. Multiscale Modell. Simul. 4 (2005) 1168-1200
    • (2005) Multiscale Modell. Simul. , vol.4 , pp. 1168-1200
    • Combettes, P.1    Wajs, V.2
  • 16
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • Daubechies I., De Friese M., and De Mol C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57 (2004) 1413-1457
    • (2004) Commun. Pure Appl. Math. , vol.57 , pp. 1413-1457
    • Daubechies, I.1    De Friese, M.2    De Mol, C.3
  • 17
    • 36248929865 scopus 로고    scopus 로고
    • Deterministic constructions of compressed sensing matrices
    • DeVore R.A. Deterministic constructions of compressed sensing matrices. J. Complex. 23 (2007) 918-925
    • (2007) J. Complex. , vol.23 , pp. 918-925
    • DeVore, R.A.1
  • 18
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Donoho D. Compressed sensing. IEEE Trans. Inform. Theory 52 4 (2006) 1289-1306
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.1
  • 19
    • 56949091545 scopus 로고    scopus 로고
    • D. Donoho, Y. Tsaig, I. Drori, J. Starck, Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit, IEEE Trans. Inform. Theory, in press.
    • D. Donoho, Y. Tsaig, I. Drori, J. Starck, Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit, IEEE Trans. Inform. Theory, in press.
  • 20
    • 36749022762 scopus 로고    scopus 로고
    • Optimized projections for compressed sensing
    • Elad M. Optimized projections for compressed sensing. IEEE Trans. Signal Process. 55 12 (2007) 5695-5702
    • (2007) IEEE Trans. Signal Process. , vol.55 , Issue.12 , pp. 5695-5702
    • Elad, M.1
  • 21
    • 0035619136 scopus 로고    scopus 로고
    • An analysis of the Perona-Malik scheme
    • Esedoglu S. An analysis of the Perona-Malik scheme. Commun. Pure Appl. Math. 54 (2001) 1442-1487
    • (2001) Commun. Pure Appl. Math. , vol.54 , pp. 1442-1487
    • Esedoglu, S.1
  • 22
    • 39449126969 scopus 로고    scopus 로고
    • Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems
    • Figueiredo M., Nowak R., and Wright S. Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1 4 (2007) 586-597
    • (2007) IEEE J. Sel. Top. Signal Process. , vol.1 , Issue.4 , pp. 586-597
    • Figueiredo, M.1    Nowak, R.2    Wright, S.3
  • 23
    • 56949105516 scopus 로고    scopus 로고
    • L. Gan, T. Do, T. Tran, Fast compressive imaging using scrambled block Hadamard ensemble, 2008, preprint.
    • L. Gan, T. Do, T. Tran, Fast compressive imaging using scrambled block Hadamard ensemble, 2008, preprint.
  • 24
    • 56949087834 scopus 로고    scopus 로고
    • L. He, T. Chang, S. Osher, T. Fang, P. Speier, MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods, UCLA CAM Report 06-35, 2006.
    • L. He, T. Chang, S. Osher, T. Fang, P. Speier, MR image reconstruction by using the iterative refinement method and nonlinear inverse scale space methods, UCLA CAM Report 06-35, 2006.
  • 25
    • 0031256990 scopus 로고    scopus 로고
    • The Perona-Malik paradox
    • Kichenassamy S. The Perona-Malik paradox. SIAM J. Appl. Math. 57 5 (1997) 1328-1342
    • (1997) SIAM J. Appl. Math. , vol.57 , Issue.5 , pp. 1328-1342
    • Kichenassamy, S.1
  • 26
    • 33846267334 scopus 로고    scopus 로고
    • Inverse scale spaces for nonlinear filtering
    • Lie J., and Nordbotten J. Inverse scale spaces for nonlinear filtering. J. Math. Imaging Vis. 27 1 (2007) 41-50
    • (2007) J. Math. Imaging Vis. , vol.27 , Issue.1 , pp. 41-50
    • Lie, J.1    Nordbotten, J.2
  • 27
    • 36849088522 scopus 로고    scopus 로고
    • Sparse MRI: the application of compressed sensing for rapid MR imaging
    • Lustig M., Donoho D., and Pauly J. Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58 6 (2007) 1182-1195
    • (2007) Magn. Reson. Med. , vol.58 , Issue.6 , pp. 1182-1195
    • Lustig, M.1    Donoho, D.2    Pauly, J.3
  • 29
    • 33846962921 scopus 로고    scopus 로고
    • Combined complex ridgelet shrinkage and total variation minimization
    • Ma J., and Fenn M. Combined complex ridgelet shrinkage and total variation minimization. SIAM J. Sci. Comput. 28 3 (2006) 984-1000
    • (2006) SIAM J. Sci. Comput. , vol.28 , Issue.3 , pp. 984-1000
    • Ma, J.1    Fenn, M.2
  • 30
    • 34548226939 scopus 로고    scopus 로고
    • Combined curvelet shrinkage and nonlinear anisotropic diffusion
    • Ma J., and Plonka G. Combined curvelet shrinkage and nonlinear anisotropic diffusion. IEEE Trans. Image Process. 16 9 (2007) 2198-2206
    • (2007) IEEE Trans. Image Process. , vol.16 , Issue.9 , pp. 2198-2206
    • Ma, J.1    Plonka, G.2
  • 31
    • 56949105773 scopus 로고    scopus 로고
    • J. Ma, Compressed sensing for surface metrology, IEEE Trans. Instrum. Measure., submitted for publication.
    • J. Ma, Compressed sensing for surface metrology, IEEE Trans. Instrum. Measure., submitted for publication.
  • 32
    • 56949093501 scopus 로고    scopus 로고
    • J. Ma, F.-X. Le Dimet, Deblurring from highly incomplete measurements for remote sensing, IEEE Trans. Geosci. Remote Sensing, in press.
    • J. Ma, F.-X. Le Dimet, Deblurring from highly incomplete measurements for remote sensing, IEEE Trans. Geosci. Remote Sensing, in press.
  • 33
    • 33845665702 scopus 로고    scopus 로고
    • Curvelet-based snake for multiscale detection and tracking of geophysical fluids
    • Ma J., Antoniadis A., and Le Dimet F.-X. Curvelet-based snake for multiscale detection and tracking of geophysical fluids. IEEE Trans. Geosci. Remote Sensing 44 12 (2006) 3626-3638
    • (2006) IEEE Trans. Geosci. Remote Sensing , vol.44 , Issue.12 , pp. 3626-3638
    • Ma, J.1    Antoniadis, A.2    Le Dimet, F.-X.3
  • 34
    • 19844370110 scopus 로고    scopus 로고
    • An iterative regularization method for total variation based image restoration
    • Osher S., Burger M., Goldfarb D., Xu J., and Ying W. An iterative regularization method for total variation based image restoration. Multiscale Modell. Simul. 4 (2005) 460-489
    • (2005) Multiscale Modell. Simul. , vol.4 , pp. 460-489
    • Osher, S.1    Burger, M.2    Goldfarb, D.3    Xu, J.4    Ying, W.5
  • 35
    • 0025465145 scopus 로고
    • Scale-space and edge detection using anisotropic diffusion
    • Perona P., and Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12 (1990) 629-639
    • (1990) IEEE Trans. Pattern Anal. Mach. Intell. , vol.12 , pp. 629-639
    • Perona, P.1    Malik, J.2
  • 36
    • 37249085237 scopus 로고    scopus 로고
    • G. Peyré, Best basis compressed sensing, in: Proc. SSVM07, June 2007, pp. 80-91.
    • G. Peyré, Best basis compressed sensing, in: Proc. SSVM07, June 2007, pp. 80-91.
  • 37
    • 48349084183 scopus 로고    scopus 로고
    • Nonlinear regularized reaction-diffusion filters for denoising of images with textures
    • Plonka G., and Ma J. Nonlinear regularized reaction-diffusion filters for denoising of images with textures. IEEE Trans. Image Process. 17 8 (2008) 1283-1294
    • (2008) IEEE Trans. Image Process. , vol.17 , Issue.8 , pp. 1283-1294
    • Plonka, G.1    Ma, J.2
  • 38
    • 56949084399 scopus 로고    scopus 로고
    • J. Romberg, Compressive sensing by random convolution, SIAM J. Image Sci., submitted for publication.
    • J. Romberg, Compressive sensing by random convolution, SIAM J. Image Sci., submitted for publication.
  • 39
    • 0013293203 scopus 로고    scopus 로고
    • Inverse scale space theory for inverse problems
    • Scale-Space, 2001. Kerckhove M. (Ed), Springer, New York
    • Scherzer O., and Groetsch C. Inverse scale space theory for inverse problems. In: Kerckhove M. (Ed). Scale-Space, 2001. LNCS vol. 2106 (2001), Springer, New York 317-325
    • (2001) LNCS , vol.2106 , pp. 317-325
    • Scherzer, O.1    Groetsch, C.2
  • 40
    • 51849111547 scopus 로고    scopus 로고
    • F. Sebert, Y. Zou, L. Ying, Toeplitz block matrices in compressed sensing and their applications in imaging, in: Int. Conf. Tech. Appl. Biomed., 30-31 May, 2008, pp. 47-50.
    • F. Sebert, Y. Zou, L. Ying, Toeplitz block matrices in compressed sensing and their applications in imaging, in: Int. Conf. Tech. Appl. Biomed., 30-31 May, 2008, pp. 47-50.
  • 41
    • 13244274395 scopus 로고    scopus 로고
    • On the equivalence of soft wavelet shrinkage total variation diffusion, total variation regularization, and sides
    • Steidl G., Weickert J., Brox T., Mrázek P., and Welk M. On the equivalence of soft wavelet shrinkage total variation diffusion, total variation regularization, and sides. SIAM J. Numer. Anal. 42 2 (2004) 686-713
    • (2004) SIAM J. Numer. Anal. , vol.42 , Issue.2 , pp. 686-713
    • Steidl, G.1    Weickert, J.2    Brox, T.3    Mrázek, P.4    Welk, M.5
  • 43
    • 64649083745 scopus 로고    scopus 로고
    • Signal recovery from random measurements via orthogonal matching pursuit
    • Tropp J., and Gilbert A. Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inform. Theory 53 12 (2008) 4655-4666
    • (2008) IEEE Trans. Inform. Theory , vol.53 , Issue.12 , pp. 4655-4666
    • Tropp, J.1    Gilbert, A.2
  • 44
    • 24644509839 scopus 로고    scopus 로고
    • A four-pixel scheme for singular differential equations
    • Scale-Space and PDE Methods in Computer Vision. Kimmel R., et al. (Ed), Springer, Berlin
    • Welk M., Steidl G., and Weickert J. A four-pixel scheme for singular differential equations. In: Kimmel R., et al. (Ed). Scale-Space and PDE Methods in Computer Vision. LNCS (2005), Springer, Berlin 610-621
    • (2005) LNCS , pp. 610-621
    • Welk, M.1    Steidl, G.2    Weickert, J.3
  • 45
    • 33847715169 scopus 로고    scopus 로고
    • Iterative regularization and nonlinear inverse scale space applied to wavelet based denoising
    • Xu J., and Osher S. Iterative regularization and nonlinear inverse scale space applied to wavelet based denoising. IEEE Trans. Image Process. 16 2 (2007) 534-544
    • (2007) IEEE Trans. Image Process. , vol.16 , Issue.2 , pp. 534-544
    • Xu, J.1    Osher, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.