Super-resolution by means of Beurling minimal extrapolation

Au-Yeung, 2015, Generalized Fourier frames in terms of balayage, J. Fourier Anal. Appl., 21, 472, 10.1007/s00041-014-9369-7 Aubel, 2017, A theory of super-resolution from short-time Fourier transform measurements, J. Fourier Anal. Appl., 1 Azaïs, 2015, Spike detection from inaccurate samplings, Appl. Comput. Harmon. Anal., 38, 177, 10.1016/j.acha.2014.03.004 Benedetto, 1996 Benedetto, 2009 John J. Benedetto, Weilin Li, Super-resolution of singular continuous measures on Td, 2018, in preparation. Beurling, 1989, Balayage of Fourier–Stieltjes transforms, 341 Beurling, 1989, Interpolation for an interval in R1, 351 Bhaskar, 2013, Atomic norm denoising with applications to line spectral estimation, IEEE Trans. Signal Process., 61, 5987, 10.1109/TSP.2013.2273443 Boyd, 2017, The alternating descent conditional gradient method for sparse inverse problems, SIAM J. Optim., 27, 616, 10.1137/15M1035793 Candès, 2013, Super-resolution from noisy data, J. Fourier Anal. Appl., 19, 1229, 10.1007/s00041-013-9292-3 Candès, 2014, Towards a mathematical theory of super-resolution, Comm. Pure Appl. Math., 67, 906, 10.1002/cpa.21455 Candès, 2006, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inform. Theory, 52, 489, 10.1109/TIT.2005.862083 Chandrasekaran, 2012, The convex geometry of linear inverse problems, Found. Comput. Math., 12, 805, 10.1007/s10208-012-9135-7 Chen, 2001, Atomic decomposition by basis pursuit, SIAM Rev., 43, 129, 10.1137/S003614450037906X Childers, 1978 De Castro, 2012, Exact reconstruction using Beurling minimal extrapolation, J. Math. Anal. Appl., 395, 336, 10.1016/j.jmaa.2012.05.011 De Castro, 2017, Exact solutions to super resolution on semi-algebraic domains in higher dimensions, IEEE Trans. Inform. Theory, 63, 621, 10.1109/TIT.2016.2619368 Donoho, 2006, Compressed sensing, IEEE Trans. Inform. Theory, 52, 1289, 10.1109/TIT.2006.871582 Dumitrescu, 2007 Duval, 2015, Exact support recovery for sparse spikes deconvolution, Found. Comput. Math., 15, 1315, 10.1007/s10208-014-9228-6 Esseen, 1945, Fourier analysis of distribution functions. A mathematical study of the Laplace–Gaussian law, Acta Math., 77, 1, 10.1007/BF02392223 Esseen, 1954, A note on Fourier–Stieltjes transforms and absolutely continuous functions, Math. Scand., 2, 153, 10.7146/math.scand.a-10403 Fatemi, 2016, Shapes from pixels, IEEE Trans. Image Process., 25, 1193, 10.1109/TIP.2016.2514507 Fernandez-Granda, 2016, Super-resolution of point sources via convex programming, Inform. Inference, 1 Greenspan, 2009, Super-resolution in medical imaging, Comput. J., 52, 43, 10.1093/comjnl/bxm075 Hewitt, 1955, The maximum value of a Fourier–Stieltjes transform, Math. Scand., 3, 97, 10.7146/math.scand.a-10429 Hille, 1929, Remarks on a known example of a monotone continuous function, Amer. Math. Monthly, 36, 255, 10.1080/00029890.1929.11986950 Kahane, 1963 Katznelson, 2004 Khaidukov, 2004, Diffraction imaging by focusing-defocusing: an outlook on seismic superresolution, Geophysics, 69, 1478, 10.1190/1.1836821 Landau, 1987, Maximum entropy and the moment problem, Bull. Amer. Math. Soc., 16, 47, 10.1090/S0273-0979-1987-15464-4 Lindberg, 2012, Mathematical concepts of optical superresolution, J. Opt., 14, 10.1088/2040-8978/14/8/083001 Ongie, 2017, Convex recovery of continuous domain piecewise constant images from non-uniform Fourier samples, IEEE Trans. Signal Process., 66, 236, 10.1109/TSP.2017.2750111 Ongie, 2016, Off-the-grid recovery of piecewise constant images from few Fourier samples, SIAM J. Imaging Sci., 9, 1004, 10.1137/15M1042280 Pan, 2014, Sampling curves with finite rate of innovation, IEEE Trans. Signal Process., 62, 458, 10.1109/TSP.2013.2292033 Park, 2003, Super-resolution image reconstruction: a technical overview, IEEE Signal Process. Mag., 20, 21, 10.1109/MSP.2003.1203207 Puschmann, 2005, On super-resolution in astronomical imaging, Astron. Astrophys., 436, 373, 10.1051/0004-6361:20042320 Rieke, 1999 Rudin, 1962 Salem, 1942, On singular monotonic functions of the Cantor type, J. Math. Phys., 21, 69, 10.1002/sapm194221169 Tang, 2015, Near minimax line spectral estimation, IEEE Trans. Inform. Theory, 61, 499, 10.1109/TIT.2014.2368122 Tang, 2013, Compressed sensing off the grid, IEEE Trans. Inform. Theory, 59, 7465, 10.1109/TIT.2013.2277451 Turán, 1946, On rational polynomials, Acta Univ. Szeged., Sect. Sci., 106 Xu, 2014, Precise semidefinite programming formulation of atomic norm minimization for recovering d-dimensional (D≥2) off-the-grid frequencies, 1 Zygmund, 1959, 2002