Adaptivna valićna transformacija temeljena na kriteriju najmanje apsolutne pogreške

Sović Kržić, Ana

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doctoral thesis

Adaptivna valićna transformacija temeljena na kriteriju najmanje apsolutne pogreške

Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2012. urn:nbn:hr:168:654751

Sović Kržić, Ana

University of Zagreb
Faculty of Electrical Engineering and Computing
Department of Electronic Systems and Information Processing

Cite this document

APA 6th Edition

Sović Kržić, A. (2012). Adaptivna valićna transformacija temeljena na kriteriju najmanje apsolutne pogreške (Doctoral thesis). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:654751

MLA 8th Edition

Sović Kržić, Ana. "Adaptivna valićna transformacija temeljena na kriteriju najmanje apsolutne pogreške." Doctoral thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2012. https://urn.nsk.hr/urn:nbn:hr:168:654751

Chicago 17th Edition

Harvard

Sović Kržić, A. (2012). 'Adaptivna valićna transformacija temeljena na kriteriju najmanje apsolutne pogreške', Doctoral thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 23 September 2023, https://urn.nsk.hr/urn:nbn:hr:168:654751

Vancouver

Sović Kržić A. Adaptivna valićna transformacija temeljena na kriteriju najmanje apsolutne pogreške [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2012 [cited 2023 September 23] Available at: https://urn.nsk.hr/urn:nbn:hr:168:654751

IEEE

A. Sović Kržić, "Adaptivna valićna transformacija temeljena na kriteriju najmanje apsolutne pogreške", Doctoral thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2012. Available at: https://urn.nsk.hr/urn:nbn:hr:168:654751

Cite this item: https://urn.nsk.hr/urn:nbn:hr:168:654751

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Metadata

Title	Adaptivna valićna transformacija temeljena na kriteriju najmanje apsolutne pogreške
Title (english)	Adaptive wavelet transform based on least absolute error criterion
Author	Ana Sović Kržić
Mentor	Damir Seršić (mentor)
Committee member	Sven Lončarić (predsjednik povjerenstva)
Committee member	Branko Jeren (član povjerenstva)
Committee member	Viktor Sučić (član povjerenstva)
Granter	University of Zagreb Faculty of Electrical Engineering and Computing (Department of Electronic Systems and Information Processing) Zagreb
Defense date and country	2012-11-26, Croatia
Scientific / art field, discipline and subdiscipline	TECHNICAL SCIENCES Computing
Universal decimal classification (UDC)	004 - Computer science and technology. Computing. Data processing
Abstract	Rijedak zapis signala je važan za čitav niz primjena: kompresiju, potiskivanje šuma, rekonstrukciju signala, sažimajuće očitavanje, estimaciju, slijepu separaciju statistički zavisnih signala, izdvajanje značajki i mnoge druge. Kako bi se postigao rijedak zapis, u ovoj disertaciji je korišten kriterij najmanje apsolutne pogreške (NAP). Nova NAP metoda kretanja po bridovima u prostoru funkcije cilja rekurzivnom redukcijom dimenzionalnosti pokazuje prednosti za sustave s velikim brojem jednadžbi i manjim brojem nepoznanica u smislu brzine dostizanja globalnog minimuma. Nadalje, u disertaciji je predložena adaptivna valićna transformacija temeljena na kriteriju NAP, te je postignut rijedak zapis i gotovo nepristrana estimacija adaptivnih parametara za harmonijske signale. Isto tako, unaprijeđena je lokalna polinomijalna aproksimacija temeljena na presjeku intervala pouzdanosti koristeći NAP kriterij. Obje metode pokazuju bolje rezultate od postojećih u smislu očuvanja bridova te robusnosti na statistička odstupanja u signalu i različite distribucije šuma. Premda je koristeći NAP kriterij numerička složenost veća, u okviru disertacije je razvijena i brza NAP adaptacija u slučaju estimacije samo jednog parametra. Postignuti znanstveni doprinosi su: algoritam određivanja globalnog minimuma po kriteriju NAP, gotovo nepristrana adaptivna valićna transformacija temeljena na NAP kriteriju u cilju postizanja rijetkog zapisa signala, te pravilo presjeka intervala pouzdanosti temeljeno na NAP kriteriju u svrhu potiskivanja šuma uz očuvanje bridova signala i slika.
Abstract (english)	Sparsity of signal representation is a key of many applications, such as compression, denoising, signal reconstruction, compressive sensing, estimation, blind separation of statistically dependent signals, feature extraction and many others. In this dissertation, a concept of least absolute error (LAE) adaptation is proposed in purpose to achieve the sparse representation. Proposed method, that moves through edges of the LAE goal function using recursive reduction of dimensionality, has shown its advantages for systems with a lot of equations and a few of unknown parameters, in terms of the shortest calculation time. Furthermore, a novel, unbiased LAE adaptive wavelet transform is given. It is used for sparse representation of harmonic signals. Moreover, an improvement of the local polynomial approximation scheme based on the intersection of confidence intervals rule using the LAE criterion is presented. Proposed methods over perform state-of-the art competitors in terms of preserving edges and robustness to outliers or various noise distributions. In general, it is paid by increased numerical complexity. However, a fast LAE adaptive method is proposed when only one parameter is estimated. Achieved scientific contributions are: algorithm that finds global minimum of the LAE criterion, unbiased LAE adaptive wavelet transform for sparse signal representation, and intersection of confidence intervals rule using the LAE criterion for robust denoising with preserving edges.
Keywords
Keywords (english)
Language	croatian
URN:NBN	urn:nbn:hr:168:654751
Project	Number: 036-0362214-1987 Title: Modeliranje kompleksnih sustava Leader: Branko Jeren Jurisdiction: Croatia Funder: MZOS Funding stream: ZP
Study programme	Title: Electrical Engineering and Computing Study programme type: university Study level: postgraduate Academic / professional title: Doktor znanosti elektrotehnike i računarstva (Doktor znanosti elektrotehnike i računarstva)
Catalog URL	http://lib.fer.hr/cgi-bin/koha/opac-detail.pl?biblionumber=40758
Type of resource	Text
Extent	212 str ; 30 cm
File origin	Born digital
Access conditions	Closed access
Terms of use
Repository	FER Repository
Created on	2019-09-09 11:47:55