Complex wavelet transform

The complex wavelet transform (CWT) is a complex-valued extension to the standard discrete wavelet transform (DWT). It is a two-dimensional wavelet transform which provides multiresolution, sparse representation, and useful characterization of the structure of an image. Further, it purveys a high degree of shift-invariance in its magnitude, which was investigated in.[1] However, a drawback to this transform is that it exhibits (where is the dimension of the signal being transformed) redundancy compared to a separable (DWT).

The use of complex wavelets in image processing was originally set up in 1995 by J.M. Lina and L. Gagnon[2] in the framework of the Daubechies orthogonal filters banks.[3] It was then generalized in 1997 by Nick Kingsbury[4][5][6] of Cambridge University.

In the area of computer vision, by exploiting the concept of visual contexts, one can quickly focus on candidate regions, where objects of interest may be found, and then compute additional features through the CWT for those regions only. These additional features, while not necessary for global regions, are useful in accurate detection and recognition of smaller objects. Similarly, the CWT may be applied to detect the activated voxels of cortex and additionally the temporal independent component analysis (tICA) may be utilized to extract the underlying independent sources whose number is determined by Bayesian information criterion [1][permanent dead link‍].

Dual-tree complex wavelet transform

The dual-tree complex wavelet transform (DTCWT) calculates the complex transform of a signal using two separate DWT decompositions (tree a and tree b). If the filters used in one are specifically designed different from those in the other it is possible for one DWT to produce the real coefficients and the other the imaginary.

Block diagram for a 3-level DTCWT

This redundancy of two provides extra information for analysis but at the expense of extra computational power. It also provides approximate shift-invariance (unlike the DWT) yet still allows perfect reconstruction of the signal.

The design of the filters is particularly important for the transform to occur correctly and the necessary characteristics are:

  • The low-pass filters in the two trees must differ by half a sample period
  • Reconstruction filters are the reverse of analysis
  • All filters from the same orthonormal set
  • Tree a filters are the reverse of tree b filters
  • Both trees have the same frequency response

See also

References

  1. ^ Barri, Adriaan; Dooms, Ann; Schelkens, Peter (2012). "The near shift-invariance of the dual-tree complex wavelet transform revisited". Journal of Mathematical Analysis and Applications. 389 (2): 1303–1314. arXiv:1304.7932. doi:10.1016/j.jmaa.2012.01.010. S2CID 119665123.
  2. ^ Lina, JM; Gagnon, L. (1995). Image enhancement with symmetric Daub echies wavelets (PDF). Wavelet Applications in Signal and Image Processing II. Vol. 2569. pp. 196–207. Archived from the original (PDF) on 2016-03-03.
  3. ^ Lina, JM (June 1997). "Image Processing with Complex Daubechies Wavelets". Journal of Mathematical Imaging and Vision. 7 (3): 211–22. doi:10.1023/A:1008274210946.
  4. ^ N. G. Kingsbury (September 1999). "Image processing with complex wavelets". Phil. Trans. Royal Society London. London.
  5. ^ Kingsbury, N G (May 2001). "Complex wavelets for shift invariant analysis and filtering of signals" (PDF). Applied and Computational Harmonic Analysis. 10 (3): 234–253. CiteSeerX 10.1.1.588.4232. doi:10.1006/acha.2000.0343.
  6. ^ Selesnick, Ivan W.; Baraniuk, Richard G.; Kingsbury, Nick G. (November 2005). "The Dual-Tree Complex Wavelet Transform" (PDF). IEEE Signal Processing Magazine. 22 (6): 123–151. Bibcode:2005ISPM...22..123S. doi:10.1109/MSP.2005.1550194. hdl:1911/20355. S2CID 833630.

Read other articles:

Gheorghe Gheorghiu-Dej

{for|the city in Romania formerly known as Gheorghe Gheorghiu-Dej|Onești}} Artikel ini membutuhkan rujukan tambahan agar kualitasnya dapat dipastikan. Mohon bantu kami mengembangkan artikel ini dengan cara menambahkan rujukan ke sumber tepercaya. Pernyataan tak bersumber bisa saja dipertentangkan dan dihapus.Cari sumber: Gheorghe Gheorghiu-Dej – berita · surat kabar · buku · cendekiawan · JSTOR (January 2013) Gheorghe Gheorghiu-Dej Pemimpin Partai Kom...

 

Museum Negara Malaysia

Muzium Negara Malaysia موزيوم نݢارا National Museum of Malaysia தேசிய அருங்காட்சியகம்Didirikan31 Agustus 1963Lokasi Kuala Lumpur, MalaysiaJenisSejarah MalaysiaSitus webwww.museum.gov.my Museum Negara Malaysia (Muzium Negara Malaysia) adalah museum nasional Malaysia yang terletak di luar Taman Tasik Perdana, Kuala Lumpur, Malaysia. Bangunan museum bercirikan istana Melayu tradisional negara bagian Terengganu. Desain gedung dipilih sendiri oleh...

 

Borsa Istanbul

Borsa İstanbulJenisBursa efekLokasiSarıyer, Istanbul, TurkiDidirikan26 Desember 1985 (1985-12-26) (sebagai İMKB) 5 April 2013Tokoh pentingTuncay Dinç (CEO)Mata uangLira TurkiEmiten tercatat371 [1]Kapitalisasi pasar$220.620 miliar (2014)[2][3]Volume$1.292 triliun(2012)IndeksBIST 30BIST 50BIST 100Situs webborsaistanbul.com Ekonomi Turki Sejarah ekonomi Turki Uang Lira Turki Bank Sentral Republik Turki Bursa Efek Istanbul Stock Exchange Perusahaan ...

Aluminium

13AlAluminiumSepotong aluminium berukuran 1×2 cm Garis spektrum aluminiumSifat umumNama, lambangaluminium, AlPengucapan/aluminium/[1] Penampilanmetalik abu-abu keperakanAluminium dalam tabel periodik 13Al Hidrogen Helium Lithium Berilium Boron Karbon Nitrogen Oksigen Fluor Neon Natrium Magnesium Aluminium Silikon Fosfor Sulfur Clor Argon Potasium Kalsium Skandium Titanium Vanadium Chromium Mangan Besi Cobalt Nikel Tembaga Seng Gallium Germanium Arsen Selen Bromin Kripton Rubidiu...

 

Associazione Calcio Napoli 1956-1957

Voce principale: Società Sportiva Calcio Napoli. AC NapoliStagione 1956-1957Sport calcio Squadra Napoli Allenatore Amedeo Amadei Presidente Achille Lauro Serie A11º Miglior marcatoreCampionato: Vinício (18) StadioArturo Collana 1955-1956 1957-1958 Si invita a seguire il modello di voce Questa voce raccoglie le informazioni riguardanti l'Associazione Calcio Napoli nelle competizioni ufficiali della stagione 1956-1957. Indice 1 Stagione 2 Divise 3 Rosa 4 Calciomercato 5 Risultati 5...

 

UTC+11:30

UTC+11:30Zona waktuPeta dunia dengan zona waktu berwarnaPerbedaan UTCUTCUTC+11:30Waktu kini05:45, 24 April 2024 UTC+11:30 [refresh]Meridian utama172,5 derajat TKelompok tanggal-waktuL* UTC+11:30: Biru (Desember), Jingga (Juni), Kuning (sepanjang tahun), Biru Muda - Wilayah lautan UTC+11:30 merupakan pengenal untuk perbedaan waktu dari UTC selama +11:30 jam. Waktu ini digunakan di: Sebagai waktu standar (sepanjang tahun) Oseania Australia - Waktu Standar Norfolk Pulau Norfolk Sejarah Pada tang...

Grand Junction, Colorado

Pemandangan udara Grand Junction Letak Grand Junction di County Mesa dan Colorado Grand Junction adalah kota otonom yang merupakan pusat pemerintahan dan kota terbesar di County Mesa, Colorado, Amerika Serikat.[1] Populasi Grand Junction adalah 65.560 jiwa pada Sensus Amerika Serikat tahun 2020, menjadikannya kota terpadat di Colorado barat dan kota Colorado terpadat ke-17 secara keseluruhan.[2] Komposisi ras di kota ini adalah 91,78% Kulit Putih, 0,60% Afrika Amerika, 0,94% P...

 

List of FA Cup winning managers

Arsène Wenger has won the tournament a record seven times The FA Cup is an association football competition contested between English clubs since 1872 and is the oldest football competition in the world.[1] Winning the competition was seen as an equal achievement to winning the league championship,[2] but the growing importance of the Premier League and UEFA Champions League has seen its importance diminish.[3] The role of the manager is to select the squad during th...

 

Dachau

Cet article concerne la ville allemande de Dachau. Pour le camp de concentration nazi, voir Camp de concentration de Dachau. Dachau Armoiries Administration Pays Allemagne Land Bavière District(Regierungsbezirk) Haute-Bavière Arrondissement(Landkreis) Dachau Bourgmestre(Bürgermeister) Florian Hartmann Code postal 85221 Code communal(Gemeindeschlüssel) 09 1 74 115 Indicatif téléphonique 08131 Immatriculation DAH Démographie Gentilé dachavien/ne Population 44 822 hab. (31...

Bongan, Kutai Barat

BonganKecamatanKantor kecamatan BonganNegara IndonesiaProvinsiKalimantan TimurKabupatenKutai BaratPopulasi • Total12,200 (2.021) jiwaKode Kemendagri64.07.12 Kode BPS6402010 Luas2.274,80 km²Desa/kelurahan16/- Bongan adalah sebuah kecamatan di Kabupaten Kutai Barat, Provinsi Kalimantan Timur, Indonesia. Batas wilayah Bongan mempunyai wilayah seluas 2274,7 km² dengan batas-batas sebagai berikut: Utara Kabupaten Kutai Kartanegara Timur Kabupaten Kutai Kartanegara Selatan K...

 

قرار مجلس الأمن التابع للأمم المتحدة رقم 378

قرار مجلس الأمن 378 الشرق الأوسطالشرق الأوسط التاريخ 23 أكتوبر 1975 اجتماع رقم 1851 الرمز S/RES/378  (الوثيقة) الموضوع مصر-إسرائيل ملخص التصويت 13 مصوت لصالحلا أحد مصوت ضدلا أحد ممتنع النتيجة اعتمد تكوين مجلس الأمن الأعضاء الدائمون  الصين فرنسا المملكة المتحدة الولاي�...

 

Nakbe

Artikel ini bukan mengenai Nakba. NakbeKuil di NakbeLokasi situsTampilkan peta MesoamericaNakbe (Guatemala)Tampilkan peta GuatemalaLokasiDepartemen Petén, GuatemalaWilayahCekungan PeténKoordinat17°40′58.08″N 89°49′59.16″W / 17.6828000°N 89.8331000°W / 17.6828000; -89.8331000JenisPemukimanSejarahPeriodePra-klasik awal sampai Pra-klasik AkhirBudayaPeradaban MayaCatatan situsKondisiDalam reruntuhan Nakbe adalah salah satu situs arkeologi Maya awal terbesar. ...

Armenian Church, Singapore

Armenian church For the general article about the Armenian Apostolic Church, see Armenian Apostolic Church. For other uses, see St. Gregory the Illuminator's Church (disambiguation). Armenian Church of Saint Gregory The IlluminatorReligionAffiliationArmenian Apostolic ChurchRiteArmenian RitePatronSt. Gregory the IlluminatorYear consecrated1836LocationLocation60 Hill Street, SingaporeCountrySingaporeShown within SingaporeGeographic coordinates1°17′35″N 103°50′57.5″E / ...

 

Richard Smallwood (footballer)

English association football player Richard Smallwood Smallwood in 2022Personal informationFull name Richard Smallwood[1]Date of birth (1990-12-29) 29 December 1990 (age 33)Place of birth Redcar, England[2]Height 5 ft 11 in (1.80 m)Position(s) MidfielderTeam informationCurrent team Bradford CityNumber 6Youth career000?–2010 MiddlesbroughSenior career*Years Team Apps (Gls)2010–2014 Middlesbrough 60 (3)2014 → Rotherham United (loan) 19 (0)2014–2017 Ro...

 

Church of St Mary and St Michael, Bonds

Church in Lancashire, EnglandChurch of St Mary and St Michael, BondsThe Church of St Mary and St Michael, Bonds,from the southwestChurch of St Mary and St Michael, BondsLocation in the Borough of Wyre53°53′51″N 2°46′16″W / 53.8975°N 2.7710°W / 53.8975; -2.7710OS grid referenceSD 494,449LocationBonds, LancashireCountryEnglandDenominationRoman CatholicWebsiteSt Mary and St Michael, BondsArchitectureFunctional statusActiveHeritage designationGrade IIDesignate...

Сферическая система координат

Сферическая система координат — трёхмерная система координат, в которой каждая точка пространства определяется тремя числами ( r , θ , φ ) {\displaystyle (r,\;\theta ,\;\varphi )} , где r {\displaystyle r}  — расстояние до начала координат (радиальное расстояние), а θ {\displaystyle \theta } и φ...

 

Amritsar

Metropolis in Punjab, India This article is about the city. For the district, see Amritsar district. Metropolis in Punjab, IndiaAmritsarMetropolisClockwise from top: The Golden Temple, Partition Museum, Jallianwala Bagh, Ram Bagh Palace, Gurdwara Baba Atal, Maharaja Ranjit Singh Chowk in Heritage StreetNicknames:  Nicknames The Holy CityAmbarsarSifti Da GharGuru NagariGolden City MapAmritsarLocation of the city center in PunjabShow map of PunjabAmritsarAmritsar (India)Show map of IndiaCo...

 

McGill Street (Montreal)

Not to be confused with McGill College Avenue. McGill StreetMcGill Street, looking north.Native namerue McGill (French)Length0.7 km (0.43 mi)LocationBetween Victoria Square and De la Commune StreetCoordinates45°30′01″N 73°33′28″W / 45.500401°N 73.557879°W / 45.500401; -73.557879Majorjunctions R-136 Ville-Marie Expressway (via service roads Viger Avenue and Saint Antoine Street) McGill Street in 1869. McGill Street (officially in French: rue M...

Agrianes

Ancient Paeonian tribeThis article is about the Thracian tribe. For the river in European Turkey, see Ergene. Paeonia, tribes and environs The Agrianes (Ancient Greek: Ἀγρίανες, Agrianes or Ἀγρίαι Agriai) or Agrianians, were a tribe whose country was centered at Upper Strymon, in present-day central Western Bulgaria as well as southeasternmost Serbia, at the time situated north of the Dentheletae. Per Strabo the source of the river Strymon was within Agrianes' territory. In th...

 

Equilibrio económico

Precio de equilibrio: P - precio Q - cantidad de un bien S - oferta D - demanda P0 - precio de equilibrio A - exceso de demanda - cuando P<P0 B - exceso de oferta - cuando P>P0 En economía, un equilibrio económico es un estado del mundo en el que las fuerzas económicas se encuentran equilibradas y en ausencia de influencias externas los valores de las variables económicas no cambian. Es el punto en el cual la cantidad demandada y la cantidad ofertada son iguales.[1]​ Un equili...