Stable super-resolution limit and smallest singular value of restricted Fourier matrices
Tài liệu tham khảo
Fannjiang, 2010, Compressed remote sensing of sparse objects, SIAM J. Imaging Sci., 3, 595, 10.1137/090757034
Fannjiang
Fannjiang, 2010, Compressive inverse scattering: I. high-frequency simo/miso and mimo measurements, Inverse Probl., 26, 10.1088/0266-5611/26/3/035008
Krim, 1996, Two decades of array signal processing research: the parametric approach, IEEE Signal Process. Mag., 13, 67, 10.1109/79.526899
Schmidt, 1986, Multiple emitter location and signal parameter estimation, IEEE Trans. Antennas Propag., 34, 276, 10.1109/TAP.1986.1143830
Stoica, 1997
Den Dekker, 1997, A survey, J. Opt. Soc. Am., 14, 547, 10.1364/JOSAA.14.000547
Riche de Prony, 1795, Essai expérimentale et analytique, J. Éc. Polytech., 1, 24
Batenkov, 2013, On the accuracy of solving confluent Prony systems, SIAM J. Appl. Math., 73, 134, 10.1137/110836584
Golub, 2003, Separable nonlinear least squares: the variable projection method and its applications, Inverse Probl., 19, R1, 10.1088/0266-5611/19/2/201
Beylkin, 2005, On approximation of functions by exponential sums, Appl. Comput. Harmon. Anal., 19, 17, 10.1016/j.acha.2005.01.003
Potts, 2010, Parameter estimation for exponential sums by approximate Prony method, Signal Process., 90, 1631, 10.1016/j.sigpro.2009.11.012
Roy, 1989, ESPRIT – estimation of signal parameters via rotational invariance techniques, IEEE Trans. Acoust. Speech Signal Process., 37, 984, 10.1109/29.32276
Hua, 1990, Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise, IEEE Trans. Acoust. Speech Signal Process., 38, 814, 10.1109/29.56027
Candès, 2013, Super-resolution from noisy data, J. Fourier Anal. Appl., 19, 1229, 10.1007/s00041-013-9292-3
Fernandez-Granda, 2013, Support detection in super-resolution, 145
Azaïs, 2015, Spike detection from inaccurate samplings, Appl. Comput. Harmon. Anal., 38, 177, 10.1016/j.acha.2014.03.004
Duval, 2015, Exact support recovery for sparse spikes deconvolution, Found. Comput. Math., 15, 1315, 10.1007/s10208-014-9228-6
Li
Duarte, 2013, Spectral compressive sensing, Appl. Comput. Harmon. Anal., 35, 111, 10.1016/j.acha.2012.08.003
Fannjiang, 2012, Coherence-pattern guided compressive sensing with unresolved grids, SIAM J. Imaging Sci., 5, 179, 10.1137/110838509
Bredies, 2013, Inverse problems in spaces of measures, ESAIM Control Optim. Calc. Var., 19, 190, 10.1051/cocv/2011205
Boyd, 2017, The alternating descent conditional gradient method for sparse inverse problems, SIAM J. Optim., 27, 616, 10.1137/15M1035793
Denoyelle, 2019, The sliding Frank–Wolfe algorithm and its application to super-resolution microscopy, Inverse Probl., 36, 10.1088/1361-6420/ab2a29
Fannjiang, 2011, The MUSIC algorithm for sparse objects: a compressed sensing analysis, Inverse Probl., 27, 10.1088/0266-5611/27/3/035013
Liao, 2016, MUSIC for single-snapshot spectral estimation: stability and super-resolution, Appl. Comput. Harmon. Anal., 40, 33, 10.1016/j.acha.2014.12.003
Liao, 2015, Music for multidimensional spectral estimation: stability and super-resolution, IEEE Trans. Signal Process., 63, 6395, 10.1109/TSP.2015.2463255
Moitra, 2015, Super-resolution, extremal functions and the condition number of Vandermonde matrices
Fannjiang, 2011, Mismatch and resolution in compressive imaging
Chi, 2011, Sensitivity to basis mismatch in compressed sensing, IEEE Trans. Signal Process., 59, 2182, 10.1109/TSP.2011.2112650
Candès, 2006, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inf. Theory, 52, 489, 10.1109/TIT.2005.862083
Donoho, 2006, Compressed sensing, IEEE Trans. Inf. Theory, 52, 1289, 10.1109/TIT.2006.871582
Morgenshtern, 2016, Super-resolution of positive sources: the discrete setup, SIAM J. Imaging Sci., 9, 412, 10.1137/15M1016552
Denoyelle, 2017, Support recovery for sparse super-resolution of positive measures, J. Fourier Anal. Appl., 23, 1153, 10.1007/s00041-016-9502-x
Morgenshtern
Benedetto, 2020, Super-resolution by means of Beurling minimal extrapolation, Appl. Comput. Harmon. Anal., 48, 218, 10.1016/j.acha.2018.05.002
Donoho, 1992, Superresolution via sparsity constraints, SIAM J. Math. Anal., 23, 1309, 10.1137/0523074
Demanet
Batenkov
Odendaal, 1994, Two-dimensional superresolution radar imaging using the music algorithm, IEEE Trans. Antennas Propag., 42, 1386, 10.1109/8.320744
Stoica, 1995, On the resolution performance of spectral analysis, Signal Process., 44, 153, 10.1016/0165-1684(95)00021-5
Lee, 1992, The Cramér–Rao bound on frequency estimates of signals closely spaced in frequency, IEEE Trans. Signal Process., 40, 1507, 10.1109/78.139253
Lee, 1992, Eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency, IEEE Trans. Signal Process., 40, 2518, 10.1109/78.157293
Turán, 1946, On rational polynomials, Acta Univ. Szeged., Sect. Sci. Math., 106
Noga, 1992, Uniform dilations, Geom. Funct. Anal., 2, 1, 10.1007/BF01895704
Konyagin, 2000, On uniformly distributed dilates of finite integer sequences, J. Number Theory, 82, 165, 10.1006/jnth.1999.2420
Gautschi, 1987, Lower bounds for the condition number of Vandermonde matrices, Numer. Math., 52, 241, 10.1007/BF01398878
Beckermann, 2000, The condition number of real Vandermonde, Krylov and positive definite Hankel matrices, Numer. Math., 85, 553, 10.1007/PL00005392
Eisinberg, 2001, Rectangular Vandermonde matrices on Chebyshev nodes, Linear Algebra Appl., 338, 27, 10.1016/S0024-3795(01)00355-X
Eisinberg, 2001, Vandermonde matrices on integer nodes: the rectangular case, Numer. Math., 87, 663, 10.1007/PL00005428
Ryan, 2009, Asymptotic behavior of random Vandermonde matrices with entries on the unit circle, IEEE Trans. Inf. Theory, 55, 3115, 10.1109/TIT.2009.2021317
Tucci, 2011, Eigenvalue results for large scale random Vandermonde matrices with unit complex entries, IEEE Trans. Inf. Theory, 57, 3938, 10.1109/TIT.2011.2137110
Tucci, 2014, Asymptotic behavior of the maximum and minimum singular value of random Vandermonde matrices, J. Theor. Probab., 27, 826, 10.1007/s10959-012-0466-8
Bazán, 2000, Conditioning of rectangular Vandermonde matrices with nodes in the unit disk, SIAM J. Matrix Anal. Appl., 21, 679, 10.1137/S0895479898336021
Aubel, 2017, Vandermonde matrices with nodes in the unit disk and the large sieve, Appl. Comput. Harmon. Anal.
Ferreira, 1999, Super-resolution, the recovery of missing samples and Vandermonde matrices on the unit circle
Berman, 2007, On perfect conditioning of Vandermonde matrices on the unit circle, Electron. J. Linear Algebra, 16, 13
Walter, 1962, On inverses of Vandermonde and confluent Vandermonde matrices, Numer. Math., 4, 117, 10.1007/BF01386302
Batenkov, 2020, Conditioning of partial nonuniform Fourier matrices with clustered nodes, SIAM J. Matrix Anal. Appl., 41, 199, 10.1137/18M1212197
Kunis, 2020, On the condition number of Vandermonde matrices with pairs of nearly-colliding nodes, Numer. Algorithms, 1
Diederichs
Kunis, 2020, On the smallest singular value of multivariate Vandermonde matrices with clustered nodes, Linear Algebra Appl., 604, 1, 10.1016/j.laa.2020.06.003
Batenkov, 2021, The spectral properties of Vandermonde matrices with clustered nodes, Linear Algebra Appl., 609, 37, 10.1016/j.laa.2020.08.034
Barnett
Candes, 2008, The restricted isometry property and its implications for compressed sensing, C. R. Math., 346, 589, 10.1016/j.crma.2008.03.014
Rudelson, 2008, On sparse reconstruction from Fourier and Gaussian measurements, Commun. Pure Appl. Math., 61, 1025, 10.1002/cpa.20227
Liu
Wedin, 1972, Perturbation bounds in connection with singular value decomposition, BIT Numer. Math., 12, 99, 10.1007/BF01932678
Meckes, 2007, On the spectral norm of a random Toeplitz matrix, Electron. Commun. Probab., 12, 315, 10.1214/ECP.v12-1313
Adamczak, 2010, A few remarks on the operator norm of random Toeplitz matrices, J. Theor. Probab., 23, 85, 10.1007/s10959-008-0201-7
Tropp, 2012, User-friendly tail bounds for sums of random matrices, Found. Comput. Math., 12, 389, 10.1007/s10208-011-9099-z
Stoica, 1989, Maximum likelihood, and Cramer–Rao bound, IEEE Trans. Acoust. Speech Signal Process., 37, 720, 10.1109/29.17564
Ottersten, 1991, Performance analysis of the total least squares esprit algorithm, IEEE Trans. Signal Process., 39, 1122, 10.1109/78.80967
Fannjiang
Li, 2020, Super-resolution limit of the esprit algorithm, IEEE Trans. Inf. Theory, 66, 4593, 10.1109/TIT.2020.2974174