메뉴 건너뛰기




Volumn 58, Issue 5, 2010, Pages 2613-2622

Best basis compressed sensing

Author keywords

Bandlets; Best basis; Compressed sensing; Cosine packets; Sparsity; Wavelet packets

Indexed keywords

IMAGE ENHANCEMENT; INVERSE PROBLEMS; ITERATIVE METHODS; RECOVERY; SIGNAL ANALYSIS;

EID: 77951150801     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2010.2042490     Document Type: Article
Times cited : (140)

References (42)
  • 1
    • 33947416035 scopus 로고    scopus 로고
    • Near-optimal signal recovery from random projections: Universal encoding strategies?
    • E. Candès and T. Tao, "Near-optimal signal recovery from random projections: Universal encoding strategies?," IEEE Trans. Inf. Theory, vol.52, no.12, pp. 5406-5425, 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candès, E.1    Tao, T.2
  • 2
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • E. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol.51, no.12, pp. 4203-4215, 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candès, E.1    Tao, T.2
  • 3
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol.52, no.4, pp. 1289-1306, 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.1
  • 4
    • 33646365077 scopus 로고    scopus 로고
    • For most large underdetermined systems of linear equations, the minimal norm solution is also the sparsest solution
    • D. Donoho, "For most large underdetermined systems of linear equations, the minimal norm solution is also the sparsest solution," Commun. Pure Appl. Math., vol.59, no.6, pp. 797-829, 2006.
    • (2006) Commun. Pure Appl. Math. , vol.59 , Issue.6 , pp. 797-829
    • Donoho, D.1
  • 6
    • 36849088522 scopus 로고    scopus 로고
    • Sparse MRI: The application of compressed sensing for rapid mr imaging
    • M. Lustig, D. Donoho, and J. M. Pauly, "Sparse MRI: The application of compressed sensing for rapid mr imaging," Magn. Reson. Med., vol.6, no.58, pp. 1182-1195, 2007.
    • (2007) Magn. Reson. Med. , vol.6 , Issue.58 , pp. 1182-1195
    • Lustig, M.1    Donoho, D.2    Pauly, J.M.3
  • 8
    • 33748423853 scopus 로고    scopus 로고
    • Bandelet image approximation and compression
    • E. Le Pennec and S. Mallat, "Bandelet image approximation and compression," SIAM Multiscale Model. Simul., vol.4, no.3, pp. 992-1039, 2005.
    • (2005) SIAM Multiscale Model. Simul. , vol.4 , Issue.3 , pp. 992-1039
    • Le Pennec, E.1    Mallat, S.2
  • 10
    • 0026686048 scopus 로고
    • Entropy-based algorithms for best basis selection
    • Mar.
    • R. Coifman and V. Wickerhauser, "Entropy-based algorithms for best basis selection," IEEE Trans. Inf. Theory, vol.IT-38, no.2, pp. 713-718, Mar. 1992.
    • (1992) IEEE Trans. Inf. Theory , vol.IT-38 , Issue.2 , pp. 713-718
    • Coifman, R.1    Wickerhauser, V.2
  • 11
    • 0030490346 scopus 로고    scopus 로고
    • Nonstationary subdivision schemes and multiresolution analysis
    • A. Cohen and N. Dyn, "Nonstationary subdivision schemes and multiresolution analysis," SIAM J. Math. Anal., vol.27, no.6, pp. 1745-1769, 1996.
    • (1996) SIAM J. Math. Anal. , vol.27 , Issue.6 , pp. 1745-1769
    • Cohen, A.1    Dyn, N.2
  • 12
    • 77951967232 scopus 로고    scopus 로고
    • Best basis denoising with non-stationary wavelet packets
    • N. Ouarti and G. Peyré, "Best basis denoising with non-stationary wavelet packets," Proc. ICIP 2009, 2009.
    • (2009) Proc. ICIP 2009
    • Ouarti, N.1    Peyré, G.2
  • 13
    • 0033248623 scopus 로고    scopus 로고
    • Wedgelets: Nearly minimax estimation of edges
    • D. Donoho, "Wedgelets: Nearly minimax estimation of edges," Ann. Statist., vol.27, no.3, pp. 859-897, 1999.
    • (1999) Ann. Statist. , vol.27 , Issue.3 , pp. 859-897
    • Donoho, D.1
  • 14
    • 17544369568 scopus 로고    scopus 로고
    • Sparse geometric image representations with bandelets
    • E. Le Pennec and S. Mallat, "Sparse geometric image representations with bandelets," IEEE Trans. Image Process., vol.14, no.4, pp. 423-438, 2005.
    • (2005) IEEE Trans. Image Process. , vol.14 , Issue.4 , pp. 423-438
    • Le Pennec, E.1    Mallat, S.2
  • 15
    • 52349096502 scopus 로고    scopus 로고
    • Orthogonal bandlets bases for geometric image approximation
    • S. Mallat and G. Peyré, "Orthogonal bandlets bases for geometric image approximation," Commun. Pure Appl. Math., vol.61, no.9, pp. 1173-1212, 2008.
    • (2008) Commun. Pure Appl. Math. , vol.61 , Issue.9 , pp. 1173-1212
    • Mallat, S.1    Peyré, G.2
  • 16
    • 33646038286 scopus 로고    scopus 로고
    • Surface compression with geometric bandelets
    • Aug.
    • G. Peyré and S. Mallat, "Surface compression with geometric bandelets," ACM Trans. Graph.(SIGGRAPH'05), vol.24, no.3, pp. 601-608, Aug. 2005.
    • (2005) ACM Trans. Graph.(SIGGRAPH'05) , vol.24 , Issue.3 , pp. 601-608
    • Peyré, G.1    Mallat, S.2
  • 17
    • 43749118418 scopus 로고    scopus 로고
    • Compressed sensing and redundant dictionaries
    • H. Rauhut, K. Schnass, and P. Vandergheynst, "Compressed sensing and redundant dictionaries," IEEE Trans. Inf. Theory, vol.54, no.5, pp. 2210-2219, 2008.
    • (2008) IEEE Trans. Inf. Theory , vol.54 , Issue.5 , pp. 2210-2219
    • Rauhut, H.1    Schnass, K.2    Vandergheynst, P.3
  • 18
    • 30844433547 scopus 로고    scopus 로고
    • Extensions of compressed sensing
    • DOI 10.1016/j.sigpro.2005.05.029, PII S0165168405002215, Sparse Approximations in Signal and Image Processing
    • D. Donoho and Y. Tsaig, "Extensions of compressed sensing," Signal Process., vol.86, no.3, pp. 549-571, 2006. (Pubitemid 43106571)
    • (2006) Signal Processing , vol.86 , Issue.3 , pp. 549-571
    • Tsaig, Y.1    Donoho, D.L.2
  • 20
    • 58849146227 scopus 로고    scopus 로고
    • Random projections of smooth manifolds
    • R. Baraniuk and M. Wakin, "Random projections of smooth manifolds," Found. Computat. Math., vol.9, no.1, pp. 51-77, 2009.
    • (2009) Found. Computat. Math. , vol.9 , Issue.1 , pp. 51-77
    • Baraniuk, R.1    Wakin, M.2
  • 21
    • 58149236874 scopus 로고    scopus 로고
    • Manifold models for signals and images
    • Feb.
    • G. Peyré, "Manifold models for signals and images," Comp. Vision Image Understand., vol.113, no.2, pp. 249-260, Feb. 2009.
    • (2009) Comp. Vision Image Understand. , vol.113 , Issue.2 , pp. 249-260
    • Peyré, G.1
  • 22
    • 70350743173 scopus 로고    scopus 로고
    • Robust recovery of signals from a union of subspaces
    • Y. C. Eldar and M. Mishali, "Robust recovery of signals from a union of subspaces," IEEE Trans. Inf. Theory, vol.55, no.11, pp. 5302-5316, 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.11 , pp. 5302-5316
    • Eldar, Y.C.1    Mishali, M.2
  • 24
    • 33645663025 scopus 로고    scopus 로고
    • Fast reconstruction of piecewise smooth signals from random projections
    • M. Duarte, M. Wakin, and R. Baraniuk, "Fast reconstruction of piecewise smooth signals from random projections," Proc. SPARS 2005, 2005.
    • (2005) Proc. SPARS 2005
    • Duarte, M.1    Wakin, M.2    Baraniuk, R.3
  • 25
    • 56749176252 scopus 로고    scopus 로고
    • Non-local regularization of inverse problems
    • D. A. Forsyth, P. H. S. Torr, and A. Zisserman, Eds. New York: Springer
    • G. Peyré, S. Bougleux, and L. D. Cohen, "Non-local regularization of inverse problems," in ECCV'08, ser. Lecture Notes in Comp. Sci., D. A. Forsyth, P. H. S. Torr, and A. Zisserman, Eds. New York: Springer, 2008, vol.5304, pp. 57-68.
    • (2008) ECCV'08, Ser. Lecture Notes in Comp. Sci. , vol.5304 , pp. 57-68
    • Peyré, G.1    Bougleux, S.2    Cohen, L.D.3
  • 27
    • 67649842407 scopus 로고    scopus 로고
    • Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization
    • Jul.
    • J. M. D. Carvajalino and G. Sapiro, "Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization," IEEE Trans. Image Process., vol.18, no.7, pp. 1395-1408, Jul. 2009.
    • (2009) IEEE Trans. Image Process. , vol.18 , Issue.7 , pp. 1395-1408
    • Carvajalino, J.M.D.1    Sapiro, G.2
  • 28
    • 36749022762 scopus 로고    scopus 로고
    • Optimized projections for compressed sensing
    • DOI 10.1109/TSP.2007.900760
    • M. Elad, "Optimized projections for compressed sensing," IEEE Trans. Signal Process., vol.5, no.12, pp. 5695-5702, 2007. (Pubitemid 350201203)
    • (2007) IEEE Transactions on Signal Processing , vol.55 , Issue.12 , pp. 5695-5702
    • Elad, M.1
  • 30
    • 42649140570 scopus 로고    scopus 로고
    • The restricted isometry property and its implications for compressed sensing
    • Paris, Série I
    • E. Candès, "The restricted isometry property and its implications for compressed sensing," Compte Rendus de l'Academie des Sciences, Paris, Série I, no.346, pp. 589-592, 2008.
    • (2008) Compte Rendus de l'Academie des Sciences , Issue.346 , pp. 589-592
    • Candès, E.1
  • 32
    • 52349092455 scopus 로고    scopus 로고
    • On sparse reconstruction from Fourier and Gaussian measurements
    • M. Rudelson and R. Vershynin, "On sparse reconstruction from Fourier and Gaussian measurements," Commun. Pure Appl. Math., vol.61, no.8, pp. 1025-1045, 2008.
    • (2008) Commun. Pure Appl. Math. , vol.61 , Issue.8 , pp. 1025-1045
    • Rudelson, M.1    Vershynin, R.2
  • 34
    • 77952927821 scopus 로고
    • Computation of the fast Walsh-Fourier transform
    • J. Shanks, "Computation of the fast Walsh-Fourier transform," IEEE Trans. Comput., vol.C, pp. 457-459, 1969.
    • (1969) IEEE Trans. Comput. , vol.C , pp. 457-459
    • Shanks, J.1
  • 35
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • DOI 10.1002/cpa.20124
    • E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math., vol.59, no.8, pp. 1207-1223, 2006. (Pubitemid 43988295)
    • (2006) Communications on Pure and Applied Mathematics , vol.59 , Issue.8 , pp. 1207-1223
    • Candes, E.J.1    Romberg, J.K.2    Tao, T.3
  • 36
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • DOI 10.1002/cpa.20042
    • I. Daubechies, M. Defrise, and C. D. Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math., vol.57, pp. 1413-1541, 2004. (Pubitemid 39427442)
    • (2004) Communications on Pure and Applied Mathematics , vol.57 , Issue.11 , pp. 1413-1457
    • Daubechies, I.1    Defrise, M.2    De Mol, C.3
  • 37
    • 3142656055 scopus 로고    scopus 로고
    • Redundant multiscale transforms and their application for morphological component analysis
    • J.-L. Starck, M. Elad, and D. Donoho, "Redundant multiscale transforms and their application for morphological component analysis," Adv. Imag. Electron Phys., vol.132, 2004.
    • (2004) Adv. Imag. Electron Phys. , vol.132
    • Starck, J.-L.1    Elad, M.2    Donoho, D.3
  • 38
    • 30844438177 scopus 로고    scopus 로고
    • Signal recovery by proximal forwardbackward splitting
    • P. L. Combettes and V. R.Wajs, "Signal recovery by proximal forwardbackward splitting," SIAM Multiscale Modeling Simul., vol.4, no.4, pp. 1168-1200, 2005.
    • (2005) SIAM Multiscale Modeling Simul , vol.4 , Issue.4 , pp. 1168-1200
    • Combettes, P.L.1    Wajs, V.R.2
  • 42
    • 0031508912 scopus 로고    scopus 로고
    • CART and best-ortho-basis: A connection
    • D. L. Donoho, "Cart and best-ortho-basis: A connection," Ann. Stat., vol.25, no.5, pp. 1870-1911, 1997. (Pubitemid 127138857)
    • (1997) Annals of Statistics , vol.25 , Issue.5 , pp. 1870-1911
    • Donoho, D.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.