Quantization for Spectral Super-Resolution

Abstract We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, we define the over-sampling ratio %$\lambda %$ as the...
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Gespeichert in:

Autor*in:	Güntürk, C. Sinan [verfasserIn] Li, Weilin

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Quantization Super-resolution Spectral estimation Total variation ESPRIT

Anmerkung:	© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022

Übergeordnetes Werk:	Enthalten in: Constructive approximation - New York, NY : Springer, 1985, 56(2022), 3 vom: 13. Mai, Seite 619-648
Übergeordnetes Werk:	volume:56 ; year:2022 ; number:3 ; day:13 ; month:05 ; pages:619-648

Links:	Volltext

DOI / URN:	10.1007/s00365-022-09574-5

Katalog-ID:	SPR048843423

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520			\|a Abstract We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, we define the over-sampling ratio %$\lambda %$ as the largest integer such that %$\lfloor M/\lambda \rfloor - 1\ge 4/\Delta %$, where M denotes the number of Fourier measurements and %$\Delta %$ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number %$K\ge 2%$ of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order %$O(M^{1/4}\lambda ^{5/4} K^{- \lambda /2})%$ and %$O(M^{3/2} \lambda ^{1/2} K^{- \lambda })%$, respectively, where the implicit constants are independent of M, K and %$\lambda %$. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order %$O(M^{-1}K^{-1})%$ only, regardless of the reconstruction algorithm.
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allfields	10.1007/s00365-022-09574-5 doi (DE-627)SPR048843423 (SPR)s00365-022-09574-5-e DE-627 ger DE-627 rakwb eng Güntürk, C. Sinan verfasserin aut Quantization for Spectral Super-Resolution 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, we define the over-sampling ratio %$\lambda %$ as the largest integer such that %$\lfloor M/\lambda \rfloor - 1\ge 4/\Delta %$, where M denotes the number of Fourier measurements and %$\Delta %$ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number %$K\ge 2%$ of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order %$O(M^{1/4}\lambda ^{5/4} K^{- \lambda /2})%$ and %$O(M^{3/2} \lambda ^{1/2} K^{- \lambda })%$, respectively, where the implicit constants are independent of M, K and %$\lambda %$. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order %$O(M^{-1}K^{-1})%$ only, regardless of the reconstruction algorithm. Quantization (dpeaa)DE-He213 Super-resolution (dpeaa)DE-He213 Spectral estimation (dpeaa)DE-He213 Total variation (dpeaa)DE-He213 ESPRIT (dpeaa)DE-He213 Li, Weilin aut Enthalten in Constructive approximation New York, NY : Springer, 1985 56(2022), 3 vom: 13. Mai, Seite 619-648 (DE-627)265505518 (DE-600)1463844-7 1432-0940 nnns volume:56 year:2022 number:3 day:13 month:05 pages:619-648 https://dx.doi.org/10.1007/s00365-022-09574-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 56 2022 3 13 05 619-648
spelling	10.1007/s00365-022-09574-5 doi (DE-627)SPR048843423 (SPR)s00365-022-09574-5-e DE-627 ger DE-627 rakwb eng Güntürk, C. Sinan verfasserin aut Quantization for Spectral Super-Resolution 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, we define the over-sampling ratio %$\lambda %$ as the largest integer such that %$\lfloor M/\lambda \rfloor - 1\ge 4/\Delta %$, where M denotes the number of Fourier measurements and %$\Delta %$ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number %$K\ge 2%$ of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order %$O(M^{1/4}\lambda ^{5/4} K^{- \lambda /2})%$ and %$O(M^{3/2} \lambda ^{1/2} K^{- \lambda })%$, respectively, where the implicit constants are independent of M, K and %$\lambda %$. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order %$O(M^{-1}K^{-1})%$ only, regardless of the reconstruction algorithm. Quantization (dpeaa)DE-He213 Super-resolution (dpeaa)DE-He213 Spectral estimation (dpeaa)DE-He213 Total variation (dpeaa)DE-He213 ESPRIT (dpeaa)DE-He213 Li, Weilin aut Enthalten in Constructive approximation New York, NY : Springer, 1985 56(2022), 3 vom: 13. Mai, Seite 619-648 (DE-627)265505518 (DE-600)1463844-7 1432-0940 nnns volume:56 year:2022 number:3 day:13 month:05 pages:619-648 https://dx.doi.org/10.1007/s00365-022-09574-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 56 2022 3 13 05 619-648
allfields_unstemmed	10.1007/s00365-022-09574-5 doi (DE-627)SPR048843423 (SPR)s00365-022-09574-5-e DE-627 ger DE-627 rakwb eng Güntürk, C. Sinan verfasserin aut Quantization for Spectral Super-Resolution 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, we define the over-sampling ratio %$\lambda %$ as the largest integer such that %$\lfloor M/\lambda \rfloor - 1\ge 4/\Delta %$, where M denotes the number of Fourier measurements and %$\Delta %$ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number %$K\ge 2%$ of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order %$O(M^{1/4}\lambda ^{5/4} K^{- \lambda /2})%$ and %$O(M^{3/2} \lambda ^{1/2} K^{- \lambda })%$, respectively, where the implicit constants are independent of M, K and %$\lambda %$. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order %$O(M^{-1}K^{-1})%$ only, regardless of the reconstruction algorithm. Quantization (dpeaa)DE-He213 Super-resolution (dpeaa)DE-He213 Spectral estimation (dpeaa)DE-He213 Total variation (dpeaa)DE-He213 ESPRIT (dpeaa)DE-He213 Li, Weilin aut Enthalten in Constructive approximation New York, NY : Springer, 1985 56(2022), 3 vom: 13. Mai, Seite 619-648 (DE-627)265505518 (DE-600)1463844-7 1432-0940 nnns volume:56 year:2022 number:3 day:13 month:05 pages:619-648 https://dx.doi.org/10.1007/s00365-022-09574-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 56 2022 3 13 05 619-648
allfieldsGer	10.1007/s00365-022-09574-5 doi (DE-627)SPR048843423 (SPR)s00365-022-09574-5-e DE-627 ger DE-627 rakwb eng Güntürk, C. Sinan verfasserin aut Quantization for Spectral Super-Resolution 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, we define the over-sampling ratio %$\lambda %$ as the largest integer such that %$\lfloor M/\lambda \rfloor - 1\ge 4/\Delta %$, where M denotes the number of Fourier measurements and %$\Delta %$ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number %$K\ge 2%$ of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order %$O(M^{1/4}\lambda ^{5/4} K^{- \lambda /2})%$ and %$O(M^{3/2} \lambda ^{1/2} K^{- \lambda })%$, respectively, where the implicit constants are independent of M, K and %$\lambda %$. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order %$O(M^{-1}K^{-1})%$ only, regardless of the reconstruction algorithm. Quantization (dpeaa)DE-He213 Super-resolution (dpeaa)DE-He213 Spectral estimation (dpeaa)DE-He213 Total variation (dpeaa)DE-He213 ESPRIT (dpeaa)DE-He213 Li, Weilin aut Enthalten in Constructive approximation New York, NY : Springer, 1985 56(2022), 3 vom: 13. Mai, Seite 619-648 (DE-627)265505518 (DE-600)1463844-7 1432-0940 nnns volume:56 year:2022 number:3 day:13 month:05 pages:619-648 https://dx.doi.org/10.1007/s00365-022-09574-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 56 2022 3 13 05 619-648
allfieldsSound	10.1007/s00365-022-09574-5 doi (DE-627)SPR048843423 (SPR)s00365-022-09574-5-e DE-627 ger DE-627 rakwb eng Güntürk, C. Sinan verfasserin aut Quantization for Spectral Super-Resolution 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 Abstract We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, we define the over-sampling ratio %$\lambda %$ as the largest integer such that %$\lfloor M/\lambda \rfloor - 1\ge 4/\Delta %$, where M denotes the number of Fourier measurements and %$\Delta %$ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number %$K\ge 2%$ of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order %$O(M^{1/4}\lambda ^{5/4} K^{- \lambda /2})%$ and %$O(M^{3/2} \lambda ^{1/2} K^{- \lambda })%$, respectively, where the implicit constants are independent of M, K and %$\lambda %$. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order %$O(M^{-1}K^{-1})%$ only, regardless of the reconstruction algorithm. Quantization (dpeaa)DE-He213 Super-resolution (dpeaa)DE-He213 Spectral estimation (dpeaa)DE-He213 Total variation (dpeaa)DE-He213 ESPRIT (dpeaa)DE-He213 Li, Weilin aut Enthalten in Constructive approximation New York, NY : Springer, 1985 56(2022), 3 vom: 13. Mai, Seite 619-648 (DE-627)265505518 (DE-600)1463844-7 1432-0940 nnns volume:56 year:2022 number:3 day:13 month:05 pages:619-648 https://dx.doi.org/10.1007/s00365-022-09574-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 56 2022 3 13 05 619-648
language	English
source	Enthalten in Constructive approximation 56(2022), 3 vom: 13. Mai, Seite 619-648 volume:56 year:2022 number:3 day:13 month:05 pages:619-648
sourceStr	Enthalten in Constructive approximation 56(2022), 3 vom: 13. Mai, Seite 619-648 volume:56 year:2022 number:3 day:13 month:05 pages:619-648
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Quantization Super-resolution Spectral estimation Total variation ESPRIT
isfreeaccess_bool	false
container_title	Constructive approximation
authorswithroles_txt_mv	Güntürk, C. Sinan @@aut@@ Li, Weilin @@aut@@
publishDateDaySort_date	2022-05-13T00:00:00Z
hierarchy_top_id	265505518
id	SPR048843423
language_de	englisch
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More precisely, we define the over-sampling ratio %$\lambda %$ as the largest integer such that %$\lfloor M/\lambda \rfloor - 1\ge 4/\Delta %$, where M denotes the number of Fourier measurements and %$\Delta %$ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number %$K\ge 2%$ of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order %$O(M^{1/4}\lambda ^{5/4} K^{- \lambda /2})%$ and %$O(M^{3/2} \lambda ^{1/2} K^{- \lambda })%$, respectively, where the implicit constants are independent of M, K and %$\lambda %$. 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author	Güntürk, C. Sinan
spellingShingle	Güntürk, C. Sinan misc Quantization misc Super-resolution misc Spectral estimation misc Total variation misc ESPRIT Quantization for Spectral Super-Resolution
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topic_title	Quantization for Spectral Super-Resolution Quantization (dpeaa)DE-He213 Super-resolution (dpeaa)DE-He213 Spectral estimation (dpeaa)DE-He213 Total variation (dpeaa)DE-He213 ESPRIT (dpeaa)DE-He213
topic	misc Quantization misc Super-resolution misc Spectral estimation misc Total variation misc ESPRIT
topic_unstemmed	misc Quantization misc Super-resolution misc Spectral estimation misc Total variation misc ESPRIT
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title	Quantization for Spectral Super-Resolution
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title_full	Quantization for Spectral Super-Resolution
author_sort	Güntürk, C. Sinan
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author-letter	Güntürk, C. Sinan
doi_str_mv	10.1007/s00365-022-09574-5
title_sort	quantization for spectral super-resolution
title_auth	Quantization for Spectral Super-Resolution
abstract	Abstract We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, we define the over-sampling ratio %$\lambda %$ as the largest integer such that %$\lfloor M/\lambda \rfloor - 1\ge 4/\Delta %$, where M denotes the number of Fourier measurements and %$\Delta %$ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number %$K\ge 2%$ of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order %$O(M^{1/4}\lambda ^{5/4} K^{- \lambda /2})%$ and %$O(M^{3/2} \lambda ^{1/2} K^{- \lambda })%$, respectively, where the implicit constants are independent of M, K and %$\lambda %$. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order %$O(M^{-1}K^{-1})%$ only, regardless of the reconstruction algorithm. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022
abstractGer	Abstract We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, we define the over-sampling ratio %$\lambda %$ as the largest integer such that %$\lfloor M/\lambda \rfloor - 1\ge 4/\Delta %$, where M denotes the number of Fourier measurements and %$\Delta %$ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number %$K\ge 2%$ of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order %$O(M^{1/4}\lambda ^{5/4} K^{- \lambda /2})%$ and %$O(M^{3/2} \lambda ^{1/2} K^{- \lambda })%$, respectively, where the implicit constants are independent of M, K and %$\lambda %$. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order %$O(M^{-1}K^{-1})%$ only, regardless of the reconstruction algorithm. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022
abstract_unstemmed	Abstract We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, we define the over-sampling ratio %$\lambda %$ as the largest integer such that %$\lfloor M/\lambda \rfloor - 1\ge 4/\Delta %$, where M denotes the number of Fourier measurements and %$\Delta %$ is the minimum separation distance associated with the atomic measure to be resolved. We prove that for any number %$K\ge 2%$ of quantization levels available for the real and imaginary parts of the measurements, our quantization method combined with either TV-min/BLASSO or ESPRIT guarantees reconstruction accuracy of order %$O(M^{1/4}\lambda ^{5/4} K^{- \lambda /2})%$ and %$O(M^{3/2} \lambda ^{1/2} K^{- \lambda })%$, respectively, where the implicit constants are independent of M, K and %$\lambda %$. In contrast, naive rounding or memoryless scalar quantization for the same alphabet offers a guarantee of order %$O(M^{-1}K^{-1})%$ only, regardless of the reconstruction algorithm. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022
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container_issue	3
title_short	Quantization for Spectral Super-Resolution
url	https://dx.doi.org/10.1007/s00365-022-09574-5
remote_bool	true
author2	Li, Weilin
author2Str	Li, Weilin
ppnlink	265505518
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doi_str	10.1007/s00365-022-09574-5
up_date	2024-07-03T21:49:37.317Z
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