The Experts below are selected from a list of 108789 Experts worldwide ranked by ideXlab platform
Hai Zhang - One of the best experts on this subject based on the ideXlab platform.
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a Mathematical Theory of super resolution by using a system of sub wavelength helmholtz resonators
Communications in Mathematical Physics, 2015Co-Authors: Habib Ammari, Hai ZhangAbstract:A rigorous Mathematical Theory is developed to explain the super-resolution phenomenon observed in the experiment (Lemoult et al., Phys Rev Lett 107:064301, 2011). A key ingredient is the calculation of the resonances and the Green function in the half space with the presence of a system of Helmholtz resonators in the quasi-stationary regime. By using boundary integral equations and generalized Rouche’s theorem, the existence and the leading asymptotic of the resonances are rigorously derived. The integral equation formulation also yields the leading order terms in the asymptotics of the Green function. The methodology developed in the paper provides an elegant and systematic way for calculating resonant frequencies for Helmholtz resonators in assorted space settings, as well as in various frequency regimes. By using the asymptotics of the Green function, the analysis of the imaging functional of the time-reversal wave fields becomes possible, which clearly demonstrates the super-resolution property. The result provides the first Mathematical Theory of super-resolution in the context of a deterministic medium and sheds light on the mechanism of super-resolution and super-focusing for waves in deterministic complex media.
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a Mathematical Theory of super resolution by using a system of sub wavelength helmholtz resonators
arXiv: Analysis of PDEs, 2014Co-Authors: Habib Ammari, Hai ZhangAbstract:A rigorous Mathematical Theory is developed to explain the super-resolution phenomenon observed in the experiment by F.Lemoult, M.Fink and G.Lerosey (Acoustic resonators for far-field control of sound on a subwavelength scale, Phys. Rev. Lett., 107 (2011)). A key ingredient is the calculation of the resonances and the Green function in the half space with the presence of a system of Helmholtz resonators in the quasi-stationary regime. By using boundary integral equations and generalized Rouche's theorem, the existence and the leading asymptotic of the resonances are rigorously derived. The integral equation formulation also yields the leading order terms in the asymptotics of the Green function. The methodology developed in the paper provides an elegant and systematic way for calculating resonant frequencies for Helmholtz resonators in assorted space settings as well as in various frequency regimes. By using the asymptotics of the Green function, the analysis of the imaging functional of the time-reversal wave fields becomes possible, which clearly demonstrates the super-resolution property. The result provides the first Mathematical Theory of super-resolution in the context of a deterministic medium and sheds light to the mechanism of super-resolution and super-focusing for waves in deterministic complex media.
Carlos Fernandezgranda - One of the best experts on this subject based on the ideXlab platform.
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towards a Mathematical Theory of super resolution
Communications on Pure and Applied Mathematics, 2014Co-Authors: Emmanuel J Candes, Carlos FernandezgrandaAbstract:This paper develops a Mathematical Theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object—the high end of its spectrum—from coarse scale information only—from samples at the low end of the spectrum. Suppose we have many point sources at unknown locations in [0,1] and with unknown complex-valued amplitudes. We only observe Fourier samples of this object up to a frequency cutoff fc. We show that one can super-resolve these point sources with infinite precision—i.e., recover the exact locations and amplitudes—by solving a simple convex optimization problem, which can essentially be reformulated as a semidefinite program. This holds provided that the distance between sources is at least 2/fc. This result extends to higher dimensions and other models. In one dimension, for instance, it is possible to recover a piecewise smooth function by resolving the discontinuity points with infinite precision as well. We also show that the Theory and methods are robust to noise. In particular, in the discrete setting we develop some theoretical results explaining how the accuracy of the super-resolved signal is expected to degrade when both the noise level and the super-resolution factor vary. © 2014 Wiley Periodicals, Inc.
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towards a Mathematical Theory of super resolution
arXiv: Information Theory, 2012Co-Authors: Emmanuel J Candes, Carlos FernandezgrandaAbstract:This paper develops a Mathematical Theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples at the low end of the spectrum. Suppose we have many point sources at unknown locations in $[0,1]$ and with unknown complex-valued amplitudes. We only observe Fourier samples of this object up until a frequency cut-off $f_c$. We show that one can super-resolve these point sources with infinite precision---i.e. recover the exact locations and amplitudes---by solving a simple convex optimization problem, which can essentially be reformulated as a semidefinite program. This holds provided that the distance between sources is at least $2/f_c$. This result extends to higher dimensions and other models. In one dimension for instance, it is possible to recover a piecewise smooth function by resolving the discontinuity points with infinite precision as well. We also show that the Theory and methods are robust to noise. In particular, in the discrete setting we develop some theoretical results explaining how the accuracy of the super-resolved signal is expected to degrade when both the noise level and the {\em super-resolution factor} vary.
Habib Ammari - One of the best experts on this subject based on the ideXlab platform.
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a Mathematical Theory of super resolution by using a system of sub wavelength helmholtz resonators
Communications in Mathematical Physics, 2015Co-Authors: Habib Ammari, Hai ZhangAbstract:A rigorous Mathematical Theory is developed to explain the super-resolution phenomenon observed in the experiment (Lemoult et al., Phys Rev Lett 107:064301, 2011). A key ingredient is the calculation of the resonances and the Green function in the half space with the presence of a system of Helmholtz resonators in the quasi-stationary regime. By using boundary integral equations and generalized Rouche’s theorem, the existence and the leading asymptotic of the resonances are rigorously derived. The integral equation formulation also yields the leading order terms in the asymptotics of the Green function. The methodology developed in the paper provides an elegant and systematic way for calculating resonant frequencies for Helmholtz resonators in assorted space settings, as well as in various frequency regimes. By using the asymptotics of the Green function, the analysis of the imaging functional of the time-reversal wave fields becomes possible, which clearly demonstrates the super-resolution property. The result provides the first Mathematical Theory of super-resolution in the context of a deterministic medium and sheds light on the mechanism of super-resolution and super-focusing for waves in deterministic complex media.
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a Mathematical Theory of super resolution by using a system of sub wavelength helmholtz resonators
arXiv: Analysis of PDEs, 2014Co-Authors: Habib Ammari, Hai ZhangAbstract:A rigorous Mathematical Theory is developed to explain the super-resolution phenomenon observed in the experiment by F.Lemoult, M.Fink and G.Lerosey (Acoustic resonators for far-field control of sound on a subwavelength scale, Phys. Rev. Lett., 107 (2011)). A key ingredient is the calculation of the resonances and the Green function in the half space with the presence of a system of Helmholtz resonators in the quasi-stationary regime. By using boundary integral equations and generalized Rouche's theorem, the existence and the leading asymptotic of the resonances are rigorously derived. The integral equation formulation also yields the leading order terms in the asymptotics of the Green function. The methodology developed in the paper provides an elegant and systematic way for calculating resonant frequencies for Helmholtz resonators in assorted space settings as well as in various frequency regimes. By using the asymptotics of the Green function, the analysis of the imaging functional of the time-reversal wave fields becomes possible, which clearly demonstrates the super-resolution property. The result provides the first Mathematical Theory of super-resolution in the context of a deterministic medium and sheds light to the mechanism of super-resolution and super-focusing for waves in deterministic complex media.
Gudderstan - One of the best experts on this subject based on the ideXlab platform.
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Mathematical Theory of Duality Quantum Computers
Quantum Information Processing, 2007Co-Authors: GudderstanAbstract:We present a Mathematical Theory for a new type of quantum computer called a duality quantum computer that has recently been proposed. We discuss the nonunitarity of certain circuits of a duality q...
Stan Gudder - One of the best experts on this subject based on the ideXlab platform.
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Mathematical Theory of Duality Quantum Computers
Quantum Information Processing, 2006Co-Authors: Stan GudderAbstract:We present a Mathematical Theory for a new type of quantum computer called a duality quantum computer that has recently been proposed. We discuss the nonunitarity of certain circuits of a duality quantum computer and point out a paradoxical situation that occurs when mixed states are considered. It is shown that a duality quantum computer can measure itself without needing a separate measurement apparatus to determine its final state.
