RSS feeds
РусскийEnglish
Issue 12, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2001

 / 

May

←  →

Reviews of topical problems


Wavelets and their uses

, ,
Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation

This review paper is intended to give a useful guide for those who want to apply the discrete wavelet transform in practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous proofs of mathematical statements are omitted, and the reader is just referred to the corresponding literature. The multiresolution analysis and fast wavelet transform have become a standard procedure for dealing with discrete wavelets. The proper choice of a wavelet and use of nonstandard matrix multiplication are often crucial for the achievement of a goal. Analysis of various functions with the help of wavelets allows one to reveal fractal structures, singularities etc. The wavelet transform of operator expressions helps solve some equations. In practical applications one often deals with the discretized functions, and the problem of stability of the wavelet transform and corresponding numerical algorithms becomes important. After discussing all these topics we turn to practical applications of the wavelet machinery. They are so numerous that we have to limit ourselves to a few examples only. The authors would be grateful for any comments which would move us closer to the goal proclaimed in the first phrase of the abstract.

Fulltext pdf (742 KB)
Fulltext is also available at DOI: 10.1070/PU2001v044n05ABEH000918
PACS: 02.60.−x, 02.70.−c, 05.40.−a, 87.57.−s (all)
DOI: 10.1070/PU2001v044n05ABEH000918
URL: https://ufn.ru/en/articles/2001/5/a/
000170938900001
Citation: Dremin I M, Ivanov O V, Nechitailo V A "Wavelets and their uses" Phys. Usp. 44 447–478 (2001)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Дремин И М, Иванов О В, Нечитайло В А «Вейвлеты и их использование» УФН 171 465–501 (2001); DOI: 10.3367/UFNr.0171.200105a.0465

References (92) Cited by (161) ↓ Similar articles (20)

  1. Goshvarpour A, Goshvarpour A Cogn Comput 17 (1) (2025)
  2. Bondarenko V I, Rekhviashvili S S, Chukhovskii F N Crystallogr. Rep. 69 629 (2024)
  3. Gorbunov S A, Volkov A E et al Uspekhi Fizicheskikh Nauk 194 826 (2024)
  4. [Gorbunov S A, Volkov A E et al Phys. Usp. 67 779 (2024)]
  5. Bondarenko V I, Rekhviashvili S S, Chukhovskii F N Kristallografiâ 69 755 (2024)
  6. Uchendu N, Muggleton Je M, White P R Mechanical Systems And Signal Processing 221 111727 (2024)
  7. Aleksanyan G, Gorbatenko N et al BIO Web Conf. 84 03001 (2024)
  8. Bernalte S P, Segovia R I et al Structural Health Monitoring (2024)
  9. Kolpakov A A, Beilekchi D V 2024 International Russian Automation Conference (RusAutoCon), (2024) p. 685
  10. Makhov V E, Shirobokov V V, Emelyanov A V Td (309) 42 (2024)
  11. Kolpakov A A, Beilekchi D V, Proskuryakov A Yu 2023 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), (2023) p. 1102
  12. Subba N, Haldar P K Eur. Phys. J. Plus 138 (12) (2023)
  13. Khatua P, Ray K Ch Circuits Syst Signal Process 42 7297 (2023)
  14. Zadiraka V, Luts L, Shvidchenko I Theory of integrals computing from fast oscillating functions (2023)
  15. Dick O E Neurosci Behav Physi (2023)
  16. Cooray S, Takeuchi T T et al 75 S85 (2023)
  17. Motiwala Z, Sandholu A S et al IScience 26 107031 (2023)
  18. Dosko S I, Sheptunov S A et al 2023 International Conference on Quality Management, Transport and Information Security, Information Technologies (IT&QM&IS), (2023) p. 115
  19. Sinevich A A, Chernyshov A A et al Geomagn. Aeron. 63 747 (2023)
  20. Kulikova L I, Makhortykh S A Pattern Recognit. Image Anal. 33 1273 (2023)
  21. Sinitsyn I N Pattern Recognit. Image Anal. 33 862 (2023)
  22. Khan M A, Haque A et al E-Prime - Advances In Electrical Engineering, Electronics And Energy 3 100093 (2023)
  23. Zamorano M, Gómez G M Je, Castejón C Journal Of Vibration And Control 28 3152 (2022)
  24. Abanin O I EJSI (1 (121)) (2022)
  25. Khatua P, Ray K Ch J Sign Process Syst 94 1381 (2022)
  26. Teoh L, Ihalage A A et al PLoS ONE 17 e0268962 (2022)
  27. Arts L P A, van den Broek E L Nat Comput Sci 2 47 (2022)
  28. Anyutin A P, Khodykina T M et al IJERPH 19 14714 (2022)
  29. Frick P G, Sokoloff D D, Stepanov R A Phys.-Usp. 65 62 (2022)
  30. Khatua P, Ray K Ch Circuits Syst Signal Process 41 6462 (2022)
  31. Belov A A, Kolpakov A A, Proskuryakov A Yu 2022 International Russian Automation Conference (RusAutoCon), (2022) p. 252
  32. Pan P, Mandal R K et al International Transactions On Electrical Energy Systems 2022 1 (2022)
  33. Saberivahidaval M, Ranjbar A et al Braz J Phys 52 (3) (2022)
  34. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 1 (2021) p. 1
  35. Bibikova E A, Kundikova N D et al Computer Optics 45 (5) (2021)
  36. Singh R, Bhushan B Advances In Intelligent Systems And Computing Vol. Computational Methods and Data EngineeringFault Classification Using Support Vectors for Unmanned Helicopters1227 Chapter 28 (2021) p. 369
  37. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 2 (2021) p. 15
  38. Anisimov S V, Shikhova N M, Kleimenova N G Geomagn. Aeron. 61 180 (2021)
  39. Hramov A E, Maksimenko V A, Pisarchik A N Physics Reports 918 1 (2021)
  40. Zadiraka V K, Luts L V, Shvidchenko I V (4) 47 (2020)
  41. Guliyeva F 19 50 (2020)
  42. Méneroux Y, Le Guilcher A et al Int J Data Sci Anal 10 101 (2020)
  43. Strelkovskaya I, Solovskaya I et al 2020 IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom), (2020) p. 1
  44. Chugunin D V, Chernyshov A A et al Geomagn. Aeron. 60 538 (2020)
  45. Bidyuk P, Manuilenko R, Pantyeyev R 2020 IEEE 2nd International Conference on System Analysis & Intelligent Computing (SAIC), (2020) p. 1
  46. Sinitsyn I N, Sinitsyn V I et al Autom Remote Control 81 2046 (2020)
  47. Guliyeva F A J. Phys.: Conf. Ser. 1564 012018 (2020)
  48. Abanin O I, Soloviev S V EJSI (6 (90)) (2019)
  49. Belov A A, A Yu P 2019 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), (2019) p. 1
  50. Kalyakulina A I, Yusipov I I et al Radiophys Quantum El 61 689 (2019)
  51. Khristenko L A, Stepanov Ju I et al Practical and Theoretical Aspects of Geological Interpretation of Gravitational, Magnetic and Electric Fields Springer Proceedings In Earth And Environmental Sciences Chapter 36 (2019) p. 313
  52. Strelkovskaya I, Solovskaya I et al 2019 International Conference on Information and Telecommunication Technologies and Radio Electronics (UkrMiCo), (2019) p. 1
  53. Belov A A 2019 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), (2019) p. 1
  54. Tielieha V V, Lysiuk I R, Khyzhniak T A Mìkrosist. Elektron. Akust. 24 51 (2019)
  55. Grishina D S, Pavlov A N et al Tech. Phys. Lett. 45 820 (2019)
  56. Smirnov V M, Filatov V N 2019 Wave Electronics and its Application in Information and Telecommunication Systems (WECONF), (2019) p. 1
  57. Belov A A, Kropotov Y A 2018 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), (2018) p. 1
  58. Proskuryakov A Yu, Kropotov Yu A 2018 3rd Russian-Pacific Conference on Computer Technology and Applications (RPC), (2018) p. 1
  59. Kropotov Yu, Kropotov Yu i dr 2018 67 (2018)
  60. Yamnenko Yu S, Levchenko V V, Niemchinova K S Mìkrosist. Elektron. Akust. 23 42 (2018)
  61. Bagmanov V Kh, Potapov A A et al J. Commun. Technol. Electron. 63 1163 (2018)
  62. Belov A A, Proskuryakov A Y 2018 XIV International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE), (2018) p. 391
  63. Kropotov Y A, Proskuryakov A Y, Belov A A 2018 Moscow Workshop on Electronic and Networking Technologies (MWENT), (2018) p. 1
  64. Pavlova O N, Pavlov A N Tech. Phys. Lett. 44 640 (2018)
  65. Hololobova O O, Havrilyuk V I STP (1(67)) 7 (2017)
  66. Kropotov Yu, Kropotov Yu i dr 2017 65 (2017)
  67. Efremov V I, Parfinenko L D, Solov’ev A A Geomagn. Aeron. 57 1045 (2017)
  68. Proskuryakov A Y 2017 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), (2017) p. 1
  69. Zelinsky N R, Kleimenova N G, Gromova L I Geomagn. Aeron. 57 559 (2017)
  70. Proskuryakov A Y, Kropotov Y A Procedia Engineering 201 789 (2017)
  71. Yasin A S, Pavlov A N, Hramov A E J. Commun. Technol. Electron. 62 236 (2017)
  72. Yaseen A S, Pavlova O N, Pavlov A N Tech. Phys. Lett. 43 641 (2017)
  73. Tapiador F J, Behrangi A et al JGR Atmospheres 121 2161 (2016)
  74. Ismailov M, Guliyeva F, Nasibov Yu Journal Of Function Spaces 2016 1 (2016)
  75. Kartashevskiy I 2016 Third International Scientific-Practical Conference Problems of Infocommunications Science and Technology (PIC S&T), (2016) p. 11
  76. Yasin A S, Pavlov A N, Hramov A E J. Commun. Technol. Electron. 61 145 (2016)
  77. Yasin A S, Pavlova O N, Pavlov A N Tech. Phys. Lett. 42 865 (2016)
  78. Simankina T, Romanovich M et al MATEC Web Of Conferences 53 01054 (2016)
  79. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 1 (2015) p. 1
  80. Yaseen A S, Pavlov A N Tech. Phys. Lett. 41 680 (2015)
  81. Bilalov B, Guliyeva F Complex Anal. Oper. Theory 9 1609 (2015)
  82. Chugai O N, Abashin S L et al Inorg Mater 51 972 (2015)
  83. Ivanov V V, Bondar T N Geomagn. Aeron. 55 389 (2015)
  84. Hramov A E, Koronovskii A A et al Wavelets in Neuroscience Springer Series In Synergetics Chapter 2 (2015) p. 15
  85. Lyamets Yu Ya, Voronov P I, Romanov Yu V Therm. Eng. 61 1015 (2014)
  86. Pavlov A N, Semyachkina-Glushkovskaya O V et al Physiol. Meas. 35 1983 (2014)
  87. Suleimanov B A, Dyshin O A Applied Mathematics And Computation 219 7036 (2013)
  88. Efimov A I, Lukanina L A et al J. Commun. Technol. Electron. 58 429 (2013)
  89. Uspenskii Yu A, Ivanov O V et al Bull. Lebedev Phys. Inst. 40 132 (2013)
  90. Ivanov V V, Bondar’ T N Geomagn. Aeron. 52 664 (2012)
  91. Pavlov A N, Hramov A E et al Uspekhi Fizicheskikh Nauk 182 905 (2012)
  92. Efimov A I, Lukanina L A et al J. Commun. Technol. Electron. 56 1407 (2011)
  93. Sazhina O S, Sazhin M V J. Exp. Theor. Phys. 113 798 (2011)
  94. Dremin I M, Eyyubova G Kh et al Indian J Phys 85 39 (2011)
  95. Pavlov A N, Filatova A E, Hramov A E J. Commun. Technol. Electron. 56 1098 (2011)
  96. Kirillov A, Kirillova O, Kirillov S 2011 3rd International Conference on Advanced Computer Control, (2011) p. 138
  97. Sazhina O S, Sazhin M V Moscow Univ. Phys. 66 588 (2011)
  98. PAVLOV ALEXEY N, PAVLOVA OLGA N et al Fluct. Noise Lett. 09 259 (2010)
  99. Skorbun A D, Ogorodnikov B I Russ. Meteorol. Hydrol. 35 536 (2010)
  100. But A V, Mygal V P, Phomin A S Semiconductors 43 581 (2009)
  101. Makhortih S A, Semechkin R A Bull Exp Biol Med 147 493 (2009)
  102. Abbasov E M, Dyshin O A, Suleimanov B A Comput. Math. And Math. Phys. 49 1554 (2009)
  103. Abraamyan Kh U, Friesen A V et al Phys. Rev. C 80 (3) (2009)
  104. Abbasov E M, Dyshin O A, Suleimanov B A Comput. Math. And Math. Phys. 48 251 (2008)
  105. Ardagna C A, Bernardoni E et al 2008 2nd IEEE International Conference on Digital Ecosystems and Technologies, (2008) p. 274
  106. Dolgal A S, Simanov A A Dokl. Earth Sc. 418 118 (2008)
  107. Dremin I M, Leonidov A V Bull. Lebedev Phys. Inst. 35 1 (2008)
  108. Korotkikh V L, Eyyubova G Kh Moscow Univ. Phys. 63 20 (2008)
  109. Jones B J T Lecture Notes In Physics Vol. Data Analysis in CosmologyThe Sea of Wavelets665 Chapter 1 (2008) p. 3
  110. Abbasov E M, Dyshin O A, Suleimanov B A Comput. Math. And Math. Phys. 48 2194 (2008)
  111. Dremin I M, Eyyubova G Kh et al J. Phys. G: Nucl. Part. Phys. 35 095106 (2008)
  112. Ivanov V V, Bondar’ T N Geomagn. Aeron. 48 680 (2008)
  113. Bolmont J, Jacholkowska A et al ApJ 676 532 (2008)
  114. Fedorets I D, Ratkevich S S Phys. Atom. Nuclei 71 1325 (2008)
  115. Pavlov A N, Anishchenko V S Uspekhi Fizicheskikh Nauk 177 859 (2007)
  116. Ryabinkov A I, Kaminker A D, Varshalovich D A 376 1838 (2007)
  117. Novikov L V Instrum Exp Tech 50 61 (2007)
  118. Bityutskaya L A, Distler V V et al Phys. Solid State 49 1382 (2007)
  119. Ovchinnikov P E, Semin Yu A Radiophys Quantum Electron 50 317 (2007)
  120. Hennen B, Rotariu I, Steinbuch M 2007 American Control Conference, (2007) p. 570
  121. Lagutkin V N, Radchenko Yu V J. Commun. Technol. Electron. 52 28 (2007)
  122. Kolodyazhny V M, Rvachov V A Cybern Syst Anal 43 893 (2007)
  123. Zakharov V I, Zienko A S Moscow Univ. Phys. 62 108 (2007)
  124. Novikov L V J. Commun. Technol. Electron. 51 663 (2006)
  125. Sharov S A, Dolenko S A, Persiantsev I G Pattern Recognit. Image Anal. 16 65 (2006)
  126. Distler V V, Bityutskaya L A et al Dokl. Earth Sc. 407 335 (2006)
  127. Sharov S A, Orlov Yu V, Persiantsev I G Pattern Recognit. Image Anal. 16 68 (2006)
  128. Dremin I M Nuclear Physics A 767 233 (2006)
  129. Voloshin V I, Korchinskii V M Kosm. Nauka Tehnol. 12 15 (2006)
  130. Visheratin K N, Kamenogradskii N E et al Izv. Atmos. Ocean. Phys. 42 184 (2006)
  131. Balashov Yu A, Glaznev V N Geochem. Int. 44 109 (2006)
  132. Mygal V P, Phomin A S Tech. Phys. Lett. 32 484 (2006)
  133. Kharintsev S S, Galimullin D Z et al Spectrochimica Acta Part A: Molecular And Biomolecular Spectroscopy 65 292 (2006)
  134. Novikov L V J. Commun. Technol. Electron. 51 1261 (2006)
  135. EFIMOV V G Nondestructive Testing And Evaluation 21 27 (2006)
  136. Zakharov Yu P, Antonov V M et al Plasma Phys. Rep. 32 183 (2006)
  137. Sidorenko A V, Solonovich N A J. Commun. Technol. Electron. 51 446 (2006)
  138. Oshurko V B Tech. Phys. Lett. 32 691 (2006)
  139. Kravchenko V F, Lazorenko O V et al Dokl. Math. 74 767 (2006)
  140. Lazorenko O V, Lazorenko S V, Chernogor L F Kosm. Nauka Tehnol. 11 22 (2005)
  141. Kharintsev S S, Kamalova D I et al Spectrochimica Acta Part A: Molecular And Biomolecular Spectroscopy 61 149 (2005)
  142. Rushchitsky J J, Cattani C, Terletskaya E V Int Appl Mech 41 374 (2005)
  143. Istomin I A, Istomin I A i dr Teor. Mat. Fiz. 142 148 (2005) [Istomin I A, Kotlyarov O L, Loskutov A Yu Theor Math Phys 142 128 (2005)]
  144. Amosov G G, Man’ko V I Theor Math Phys 142 306 (2005)
  145. Dremin I M Phys. Atom. Nuclei 68 508 (2005)
  146. Ivanov L M, Mel’nichenko O V Phys Oceanogr 15 92 (2005)
  147. Chukalina M V, Dubrovskii Yu V, Funke H 30 930 (2004)
  148. Voloshin V I, Korchinskii V M, Negoda A A Kosm. Nauka Tehnol. 10 178 (2004)
  149. Fedorov M V, Chuev G N et al Phys. Rev. E 70 (5) (2004)
  150. Abramochkin E G, Volostnikov V G Uspekhi Fizicheskikh Nauk 174 1273 (2004)
  151. Voloshin V I, Bushuev Y I et al Kosm. Nauka Tehnol. 10 187 (2004)
  152. Dremin I M Phys. Atom. Nuclei 67 41 (2004)
  153. Ellis J, Mavromatos N E et al A&A 402 409 (2003)
  154. Ivanov A A, Krasil’nikov A D, Pravdin M I Jetp Lett. 78 695 (2003)
  155. Ivanov O, Nechitailo V, Dremin I Handbook of Scaling Methods in Aquatic Ecology (2003) p. 279
  156. Rotanova N M, Bondar T N, Kovalevskaya E V Russ. J. Earth Sci. 5 375 (2003)
  157. Belozerova T S, Frick P G, Henner V K Phys. Atom. Nuclei 66 1269 (2003)
  158. Dremin I M Uspekhi Fizicheskikh Nauk 172 551 (2002)
  159. Medvinskii A B, Petrovskii S V et al Uspekhi Fizicheskikh Nauk 172 31 (2002)
  160. Dremin I M, Furletov V I et al Control Engineering Practice 10 599 (2002)
  161. Dremin I M Surveys In High Energy Physics 16 141 (2001)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions