Superresolution without separation
This article provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination of $M$ shifted copies of a known waveform with unknown sh...
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| Published in | Information and inference Vol. 7; no. 1; pp. 1 - 30 |
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| Format | Journal Article |
| Language | English |
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Oxford University Press
15.03.2018
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| Abstract | This article provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination of $M$ shifted copies of a known waveform with unknown shifts and amplitudes, and one only observes a finite collection of evaluations of this signal. We characterize properties of the base waveform such that the exact translations and amplitudes can be recovered from $2M+1$ observations. This recovery can be achieved by solving a weighted version of basis pursuit over a continuous dictionary. Our analysis shows that $\ell_1$-based methods enjoy the same separation-free recovery guarantees as polynomial root finding techniques, such as de Prony’s method or Vetterli’s method for signals of finite rate of innovation. Our proof techniques combine classical polynomial interpolation techniques with contemporary tools from compressed sensing. |
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| AbstractList | This article provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination of $M$ shifted copies of a known waveform with unknown shifts and amplitudes, and one only observes a finite collection of evaluations of this signal. We characterize properties of the base waveform such that the exact translations and amplitudes can be recovered from $2M+1$ observations. This recovery can be achieved by solving a weighted version of basis pursuit over a continuous dictionary. Our analysis shows that $\ell_1$-based methods enjoy the same separation-free recovery guarantees as polynomial root finding techniques, such as de Prony’s method or Vetterli’s method for signals of finite rate of innovation. Our proof techniques combine classical polynomial interpolation techniques with contemporary tools from compressed sensing. Abstract This article provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination of $M$ shifted copies of a known waveform with unknown shifts and amplitudes, and one only observes a finite collection of evaluations of this signal. We characterize properties of the base waveform such that the exact translations and amplitudes can be recovered from $2M+1$ observations. This recovery can be achieved by solving a weighted version of basis pursuit over a continuous dictionary. Our analysis shows that $\ell_1$-based methods enjoy the same separation-free recovery guarantees as polynomial root finding techniques, such as de Prony’s method or Vetterli’s method for signals of finite rate of innovation. Our proof techniques combine classical polynomial interpolation techniques with contemporary tools from compressed sensing. |
| Author | Robeva, Elina Recht, Benjamin Schiebinger, Geoffrey |
| Author_xml | – sequence: 1 givenname: Geoffrey surname: Schiebinger fullname: Schiebinger, Geoffrey organization: Department of Statistics, University of California, Evans Hall, Berkeley, CA, USA – sequence: 2 givenname: Elina surname: Robeva fullname: Robeva, Elina organization: Department of Mathematics, University of California, Evans Hall, Berkeley, CA, USA – sequence: 3 givenname: Benjamin surname: Recht fullname: Recht, Benjamin organization: Departments of Statistics and Electrical Engineering and Computer Science, University of California, Soda Hall, Berkeley, CA, USA |
| BackLink | https://www.osti.gov/biblio/1430374$$D View this record in Osti.gov |
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| Cites_doi | 10.1109/TSP.2002.1003065 10.1007/s00041-013-9292-3 10.1109/TIT.2011.2167214 10.1109/TSP.2011.2107904 10.1109/TIT.2006.871582 10.1007/s10208-014-9228-6 10.1109/TSP.2008.928510 10.1109/TSP.2010.2051150 10.1038/nmeth.3442 10.1109/TSP.2013.2273443 10.1016/0024-3795(87)90313-2 10.1016/j.jmaa.2012.05.011 10.1090/S0025-5718-2011-02539-1 10.1137/0523074 10.1137/090757034 10.1038/nmeth929 10.1080/02331930902730070 10.1038/nmeth.f.235 10.1109/TIT.2005.862083 10.1109/TIT.2013.2277451 10.1038/nmeth.1978 10.1051/cocv/2011205 10.1051/0004-6361:20042320 10.1109/TSP.2009.2014277 10.1109/TSP.2010.2086452 10.1093/imaiai/iaw001 10.1109/RADAR.2007.374203 10.1137/15M1016552 10.1090/chel/345 10.1109/TSP.2017.2656841 10.1109/TIT.2014.2368122 10.1109/MSP.2007.4286571 10.1016/j.acha.2006.05.002 10.1007/s10208-012-9135-7 10.1529/biophysj.106.091116 10.1126/science.1127344 10.1007/BF03014795 10.1137/15M1035793 10.1002/cpa.21455 10.1109/CAMSAP.2007.4497980 10.1016/j.sigpro.2011.11.010 10.1007/BF01449883 10.1109/JPROC.2010.2042415 10.1016/j.jmaa.2016.04.077 10.1137/0149053 10.1109/TSP.2005.850882 10.1090/S0025-5718-1995-1265014-7 10.1109/TSP.2006.890907 10.1109/MSP.2007.914731 10.1016/j.acha.2012.08.003 |
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| References | de Prony (2020030521144820900_B23) 1795; 1 Bonifacino (2020030521144820900_B11) 2006; 313 Dragotti (2020030521144820900_B27) 2007; 55 Bendory (2020030521144820900_B7) 2014; 442 Batenkov (2020030521144820900_B5) 2012; 81 Carathéodory (2020030521144820900_B18) 1907; 64 Donoho (2020030521144820900_B24) 1992; 23 Fernandez-Granda (2020030521144820900_B34) 2013 Vaswani (2020030521144820900_B60) 2010; 58 Tchebycheff (2020030521144820900_B59) 1887; 55 Vetterli (2020030521144820900_B61) 2002; 50 Baraniuk (2020030521144820900_B3) 2007; 24 Candès (2020030521144820900_B17) 2008; 25 Eckhoff (2020030521144820900_B30) 1995; 64 Tang (2020030521144820900_B57) 2015; 61 Ekanadham (2020030521144820900_B31) 2011 Candès (2020030521144820900_B14) 2013; 19 Duval (2020030521144820900_B29) 2015; 15 Karlin (2020030521144820900_B42) 1967 Rauhut (2020030521144820900_B49) 2007; 22 Donoho (2020030521144820900_B25) 2006; 52 Boyd (2020030521144820900_B12) 2015; 27 Friedlander (2020030521144820900_B35) 2012; 58 Ando (2020030521144820900_B1) 1987; 90 Bajwa (2020030521144820900_B2) 2010; 98 Candès (2020030521144820900_B15) 2013; 67 Zhu (2020030521144820900_B63) 2012; 9 Duarte (2020030521144820900_B28) 2013; 35 Gantmacher (2020030521144820900_B37) 2002 Sage (2020030521144820900_B10) 2015; 12 Morgenshtern (2020030521144820900_B45) 2015; 9 Carathéodory (2020030521144820900_B19) 1911; 32 Chandrasekaran (2020030521144820900_B21) 2012; 12 Shah (2020030521144820900_B52) 2012 Tan (2020030521144820900_B56) 2008; 56 Cetin (2020030521144820900_B20) 2005; 53 Hess (2020030521144820900_B40) 2006; 91 Herman (2020030521144820900_B39) 2009; 57 Fuchs (2020030521144820900_B36) 2005 Bhaskar (2020030521144820900_B9) 2013; 61 Heckel (2020030521144820900_B38) 2016; 5 Puschmann (2020030521144820900_B48) 2005; 436 Stoica (2020030521144820900_B55) 2011; 59 Shapiro (2020030521144820900_B53) 2009; 58 Donoho (2020030521144820900_B26) 1989; 49 Tang (2020030521144820900_B58) 2013; 59 De Castro (2020030521144820900_B22) 2012; 395 Pinkus (2020030521144820900_B47) 2010 Bendory (2020030521144820900_B6) 2017; 65 Bredies (2020030521144820900_B13) 2013; 19 Evanko (2020030521144820900_B32) 2009; 6 Candès (2020030521144820900_B16) 2006; 52 Rust (2020030521144820900_B51) 2006; 3 Krein (2020030521144820900_B44) 1959; 12 Baraniuk (2020030521144820900_B4) 2007 Fannjiang (2020030521144820900_B33) 2010; 3 Von Borries (2020030521144820900_B62) 2007 Nobelprize.org (2020030521144820900_B46) 2014 Khajehnejad (2020030521144820900_B43) 2011; 59 Beurling (2020030521144820900_B8) 1938 Karlin (2020030521144820900_B41) 1968 Stoica (2020030521144820900_B54) 2012; 92 Rauhut (2020030521144820900_B50) 2015 |
| References_xml | – volume: 50 start-page: 1417 year: 2002 ident: 2020030521144820900_B61 article-title: Sampling signals with finite rate of innovation. publication-title: IEEE Trans. Sig. Process. doi: 10.1109/TSP.2002.1003065 – volume: 19 start-page: 1229 year: 2013 ident: 2020030521144820900_B14 article-title: Super-resolution from noisy data. publication-title: J. Fourier Anal. Appl. doi: 10.1007/s00041-013-9292-3 – volume: 58 start-page: 1122 year: 2012 ident: 2020030521144820900_B35 article-title: Recovering compressively sampled signals using partial support information. publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2011.2167214 – volume: 59 start-page: 1985 year: 2011 ident: 2020030521144820900_B43 article-title: Analyzing weighted minimization for sparse recovery with nonuniform sparse models. publication-title: IEEE Trans. Sig. Process. doi: 10.1109/TSP.2011.2107904 – year: 2014 ident: 2020030521144820900_B46 publication-title: The Nobel Prize in Chemistry – volume: 52 start-page: 1289 year: 2006 ident: 2020030521144820900_B25 article-title: Compressed sensing. publication-title: IEEE Trans. Inf. Thy. doi: 10.1109/TIT.2006.871582 – year: 2010 ident: 2020030521144820900_B47 publication-title: Totally Positive Matrices – volume: 15 start-page: 1315 year: 2015 ident: 2020030521144820900_B29 article-title: Exact support recovery for sparse spikes deconvolution. publication-title: Found. Comput. Math. doi: 10.1007/s10208-014-9228-6 – volume-title: In year: 2012 ident: 2020030521144820900_B52 article-title: Linear system identification via atomic norm regularization. – volume: 56 start-page: 5135 year: 2008 ident: 2020030521144820900_B56 article-title: Estimating signals with finite rate of innovation from noisy samples: A stochastic algorithm. publication-title: IEEE Trans. Sig. Process. doi: 10.1109/TSP.2008.928510 – volume: 58 start-page: 4595 year: 2010 ident: 2020030521144820900_B60 article-title: Modified-cs: Modifying compressive sensing for problems with partially known support. publication-title: IEEE Trans. Sig. Process., doi: 10.1109/TSP.2010.2051150 – volume: 12 start-page: 717 year: 2015 ident: 2020030521144820900_B10 article-title: Quantitative evaluation of software packages for single-molecule localization microscopy. publication-title: Nat. Methods doi: 10.1038/nmeth.3442 – volume: 61 start-page: 5987 year: 2013 ident: 2020030521144820900_B9 article-title: Atomic norm denoising with applications to line spectral estimation. publication-title: IEEE Trans. Sig. Process. doi: 10.1109/TSP.2013.2273443 – volume: 90 start-page: 165 year: 1987 ident: 2020030521144820900_B1 article-title: Totally positive matrices. publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(87)90313-2 – volume-title: Neural Spike Identifcation with Continuous Basis Pursuit. year: 2011 ident: 2020030521144820900_B31 – volume: 395 start-page: 336 year: 2012 ident: 2020030521144820900_B22 article-title: Exact reconstruction using beurling minimal extrapolation. publication-title: J Math Anal Appl. doi: 10.1016/j.jmaa.2012.05.011 – volume: 81 start-page: 277 year: 2012 ident: 2020030521144820900_B5 article-title: Algebraic fourier reconstruction of piecewise smooth functions. publication-title: Math. Comput. doi: 10.1090/S0025-5718-2011-02539-1 – volume: 23 start-page: 1309 year: 1992 ident: 2020030521144820900_B24 article-title: Superresolution via sparsity constraints. publication-title: SIAM J. Math. Anal. doi: 10.1137/0523074 – volume: 3 start-page: 595 year: 2010 ident: 2020030521144820900_B33 article-title: Compressed remote sensing of sparse objects. publication-title: SIAM J. Imag. Sci. doi: 10.1137/090757034 – volume: 3 start-page: 793 year: 2006 ident: 2020030521144820900_B51 article-title: Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm). publication-title: Nat. Methods doi: 10.1038/nmeth929 – volume: 58 start-page: 133 year: 2009 ident: 2020030521144820900_B53 article-title: Semi-infinite programming, duality, discretization and optimality conditions. publication-title: Optim. doi: 10.1080/02331930902730070 – volume: 6 start-page: 19 year: 2009 ident: 2020030521144820900_B32 article-title: Primer: fluorescence imaging under the diffraction limit. publication-title: Nat. Methods doi: 10.1038/nmeth.f.235 – volume: 55 start-page: 156 year: 1887 ident: 2020030521144820900_B59 article-title: On two theorems with respect to probabilities. publication-title: Zap. Akad. Nauk S.-Petersburg – volume: 52 start-page: 489 year: 2006 ident: 2020030521144820900_B16 article-title: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. publication-title: IEEE Trans. Inf. Thy. doi: 10.1109/TIT.2005.862083 – volume: 12 start-page: 1 year: 1959 ident: 2020030521144820900_B44 article-title: The ideas of P.L. Tchebycheff and A.A. Markov in the theory of limiting values of integrals and their futher development. publication-title: Am. Math. Soc. Transl. Ser. 2. – volume: 59 start-page: 7465 year: 2013 ident: 2020030521144820900_B58 article-title: Compressed sensing off the grid. publication-title: IEEE Trans. Inf. Theor. doi: 10.1109/TIT.2013.2277451 – volume: 9 start-page: 721 year: 2012 ident: 2020030521144820900_B63 article-title: Faster storm using compressed sensing. publication-title: Nat. Methods doi: 10.1038/nmeth.1978 – volume: 19 start-page: 190 year: 2013 ident: 2020030521144820900_B13 article-title: Inverse problems in spaces of measures. publication-title: ESAIM Control Optimisation Calculus Var. doi: 10.1051/cocv/2011205 – volume: 436 start-page: 373 year: 2005 ident: 2020030521144820900_B48 article-title: On super-resolution in astronomical imaging. publication-title: Astron. Astrophys. doi: 10.1051/0004-6361:20042320 – year: 2005 ident: 2020030521144820900_B36 article-title: Sparsity and uniqueness for some specific under-determined linear systems. Acoustics, Speech, and Signal Processing, 2005. Proceedings. – volume: 57 start-page: 2275 year: 2009 ident: 2020030521144820900_B39 article-title: High-resolution radar via compressed sensing. publication-title: IEEE Trans. Sig. Process. doi: 10.1109/TSP.2009.2014277 – volume: 59 start-page: 35 year: 2011 ident: 2020030521144820900_B55 article-title: New method of sparse parameter estimation in separable models and its use for spectral analysis of irregularly sampled data. publication-title: IEEE Trans. Sig. Process. doi: 10.1109/TSP.2010.2086452 – volume-title: Tchebycheff Systems: with Applications in Analysis and Statistics year: 1967 ident: 2020030521144820900_B42 – volume: 5 start-page: 22 year: 2016 ident: 2020030521144820900_B38 article-title: Super-resolution radar. publication-title: Inf inference doi: 10.1093/imaiai/iaw001 – start-page: 128 volume-title: Radar Conference, 2007 IEEE year: 2007 ident: 2020030521144820900_B4 article-title: Compressive radar imaging. doi: 10.1109/RADAR.2007.374203 – volume: 9 start-page: 412 year: 2015 ident: 2020030521144820900_B45 article-title: Super-resolution of positive sources: the discrete setup. publication-title: SIAM J. Imaging Sci. doi: 10.1137/15M1016552 – volume-title: Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems year: 2002 ident: 2020030521144820900_B37 doi: 10.1090/chel/345 – volume: 65 start-page: 2114 year: 2017 ident: 2020030521144820900_B6 article-title: Robust recovery of positive stream of pulses. publication-title: IEEE Trans. Signal Process doi: 10.1109/TSP.2017.2656841 – year: 2015 ident: 2020030521144820900_B50 article-title: Interpolation via weighted $l_1$ minimization. publication-title: Appl. Comput. Harmon. Anal. – volume: 61 start-page: 499 year: 2015 ident: 2020030521144820900_B57 article-title: Near minimax line spectral estimation. publication-title: IEEE Trans. Inf. Theor. doi: 10.1109/TIT.2014.2368122 – volume: 24 start-page: 118 year: 2007 ident: 2020030521144820900_B3 article-title: Compressive sensing [lecture notes]. publication-title: IEEE Sig. Process Mag doi: 10.1109/MSP.2007.4286571 – volume: 22 start-page: 16 year: 2007 ident: 2020030521144820900_B49 article-title: Random sampling of sparse trigonometric polynomials. publication-title: Appl. Comput. Hamon. Anal. doi: 10.1016/j.acha.2006.05.002 – volume: 12 start-page: 805 year: 2012 ident: 2020030521144820900_B21 article-title: The convex geometry of linear inverse problems. publication-title: Found. Comput. Math. doi: 10.1007/s10208-012-9135-7 – volume: 91 start-page: 4258 year: 2006 ident: 2020030521144820900_B40 article-title: Ultra-high resolution imaging by fluorescence photoactivation localization microscopy. publication-title: Biophys. J. doi: 10.1529/biophysj.106.091116 – volume: 313 start-page: 1642 year: 2006 ident: 2020030521144820900_B11 article-title: Imaging intracellular fluorescent proteins at nanometer resolution. publication-title: Science doi: 10.1126/science.1127344 – volume: 32 start-page: 193 year: 1911 ident: 2020030521144820900_B19 article-title: Ueber den Variabilitaetsbereich der Fourier’schen Konstanten von positiven harmonischen Funktionen. publication-title: Rend. Circ. Mat. doi: 10.1007/BF03014795 – start-page: 145 year: 2013 ident: 2020030521144820900_B34 article-title: Support detection in super-resolution. Proceedings of the 10th International Conference on Sampling Theory and Applications (SampTA 2013) – volume: 27 start-page: 616 year: 2015 ident: 2020030521144820900_B12 article-title: The alternating descent conditional gradient method for sparse inverse problems. publication-title: SIAM J Optimiz. doi: 10.1137/15M1035793 – start-page: 345 year: 1938 ident: 2020030521144820900_B8 article-title: Sur les intégrales de fourier absolument convergentes et leur application à une transformation fonctionnelle. publication-title: Ninth Scandinavian Mathematical Congress – volume: 67 start-page: 906 year: 2013 ident: 2020030521144820900_B15 article-title: Towards a mathematical theory of super resolution. publication-title: Comm. Pure Appl. Math doi: 10.1002/cpa.21455 – start-page: 121 year: 2007 ident: 2020030521144820900_B62 article-title: Compressed sensing using prior information. In publication-title: Computational Advances in Multi-Sensor Adaptive Processing, 2007. CAMPSAP 2007. 2nd IEEE International Workshop on doi: 10.1109/CAMSAP.2007.4497980 – volume: 92 start-page: 1580 year: 2012 ident: 2020030521144820900_B54 article-title: Spice and likes: Two hyperparameter-free methods for sparse-parameter estimation. publication-title: Sig. Process doi: 10.1016/j.sigpro.2011.11.010 – volume: 64 start-page: 95 year: 1907 ident: 2020030521144820900_B18 article-title: Ueber den Variabilitaetsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehman. publication-title: Math. Ann. doi: 10.1007/BF01449883 – volume-title: Total Positivity year: 1968 ident: 2020030521144820900_B41 – volume: 98 start-page: 1058 year: 2010 ident: 2020030521144820900_B2 article-title: Compressed channel sensing: a new approach to estimating sparse multipath channels. publication-title: Proc. IEEE doi: 10.1109/JPROC.2010.2042415 – volume: 442 start-page: 511 year: 2014 ident: 2020030521144820900_B7 article-title: Robust recovery of stream of pulses using convex optimization. publication-title: J Math Anal Appl. doi: 10.1016/j.jmaa.2016.04.077 – volume: 1 start-page: 24 year: 1795 ident: 2020030521144820900_B23 article-title: Essai éxperimental et analytique: sur les lois de la dilatabilité de fluides élastique et sur celles de la force expansive de la vapeur de l’alkool, à différentes températures. publication-title: Journal de l’école Polytechnique – volume: 49 start-page: 906 year: 1989 ident: 2020030521144820900_B26 article-title: Uncertainty principles and signal recovery. publication-title: SIAM J. Appl. Math doi: 10.1137/0149053 – volume: 53 start-page: 3010 year: 2005 ident: 2020030521144820900_B20 article-title: A sparse signal reconstruction perspective for source localization with sensor arrays. publication-title: IEEE Trans. Sig. Process doi: 10.1109/TSP.2005.850882 – volume: 64 start-page: 671 year: 1995 ident: 2020030521144820900_B30 article-title: Accurate reconstructions of functions of finite regularity from truncated fourier series expansions. publication-title: Math. Comput doi: 10.1090/S0025-5718-1995-1265014-7 – volume: 55 start-page: 1741 year: 2007 ident: 2020030521144820900_B27 article-title: Sampling moments and reconstructing signals of finite rate of innovation: Shannon meets strang-fix. publication-title: IEEE Trans. Sig. Process. doi: 10.1109/TSP.2006.890907 – volume: 25 start-page: 21 year: 2008 ident: 2020030521144820900_B17 article-title: An introduction to compressive sampling. publication-title: IEEE Sig. Process. Mag. doi: 10.1109/MSP.2007.914731 – volume: 35 start-page: 111 year: 2013 ident: 2020030521144820900_B28 article-title: Spectral compressive sensing. publication-title: Appl. Comput. Harmon. Anal. doi: 10.1016/j.acha.2012.08.003 |
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| Snippet | This article provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in... Abstract This article provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be... |
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| Title | Superresolution without separation |
| URI | https://www.osti.gov/biblio/1430374 |
| Volume | 7 |
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