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Partial $S$-goodness for partially sparse signal recovery

Abstract / Introduction Related Papers Cited by
  • In this paper, we will consider the problem of partially sparse signal recovery (PSSR), which is the signal recovery from a certain number of linear measurements when its part is known to be sparse. We establish and characterize partial $s$-goodness for a sensing matrix in PSSR. We show that the partial $s$-goodness condition is equivalent to the partial null space property (NSP), and is weaker than partial restricted isometry property. Moreover, this provides a verifiable approach for partial NSP via partial $s$-goodness constants. We also give exact and stable partially $s$-sparse recovery via the partial $l_1$-norm minimization under mild assumptions.
    Mathematics Subject Classification: Primary: 90C26, 65J22; Secondary: 65K10.

    Citation:

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  • [1]

    A. Bandeira, K. Scheinberg and L. N. Vicente, Computation of sparse low degree interpolating polynomials and their application to derivative-free optimization, Math. Program., 134 (2012), 223-257.doi: 10.1007/s10107-012-0578-z.

    [2]

    A. Bandeira, K. Scheinberg and L. N. Vicente, On partially sparse recovery, Tech. Rep., 2011.

    [3]

    A. M. Bruckstein, D. L. Donoho and M. Elad, From sparse solutions of systems of equations to sparse modeling of signals and images, SIAM Review, 51 (2009), 34-81.doi: 10.1137/060657704.

    [4]

    E. J. Candés, J. Romberg and T. Tao, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inform. Theory, 52 (2006), 489-509.doi: 10.1109/TIT.2005.862083.

    [5]

    E. J. Candés and T. Tao, Decoding by linear programming, IEEE Trans. Inform. Theory, 51 (2005), 4203-4215.doi: 10.1109/TIT.2005.858979.

    [6]

    E. J. Candés, M. B. Wakin and S. P. Boyd, Enhancing sparsity by reweighted l1 minimization, J Fourier Anal Appl., 14 (2008), 877-905.doi: 10.1007/s00041-008-9045-x.

    [7]

    D. L. Donoho, Compressed sensing, IEEE Trans. Inform. Theory, 52 (2006), 1289-1306.doi: 10.1109/TIT.2006.871582.

    [8]

    L. Jacques, A short note on compressed sensing with partially known signal support, Signal Processing, 90 (2010), 3308-3312.

    [9]

    A. Juditsky and A. S. Nemirovski, On verifiable sufficient conditions for sparse signal recovery via l1 minimization, Math. Program., 127 (2011), 57-88.doi: 10.1007/s10107-010-0417-z.

    [10]

    A. Juditsky, F. Karzan and A. S. Nemirovski, Verifiable conditions of l1-recovery of sparse signals with sign restrictions, Math. Program., 127 (2011), 89-122.doi: 10.1007/s10107-010-0418-y.

    [11]

    M. A. Khajehnejad, W. Xu, A. S. Avestimehr and B. Hassibi, Analyzing weighted minimization for sparse recovery with nonuniform sparse models, IEEE Trans. Signal Process., 59 (2011), 1985-2001.doi: 10.1109/TSP.2011.2107904.

    [12]

    A. Majumdar and R. K. Ward, An algorithm for sparse MRI reconstruction by Schatten p-norm minimization, Magnetic Resonance Imaging, 29 (2011), 408-417.

    [13]

    N. Vaswani and W. Lu, Modifed-CS: modifying compressive sensing for problems with partially known support, IEEE Trans. Signal Process., 58 (2010), 4595-4607.doi: 10.1109/TSP.2010.2051150.

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