Adaptivna valićna transformacija temeljena na kriteriju najmanje apsolutne pogreške

doctoral thesis

• 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: kriterij najmanje apsolutne pogreške; norma; medijan; potiskivanje šuma; očuvanje bridova; adaptivna valićna transformacija; nepristrana estimacija; presjek intervala pouzdanosti; relativni presjek intervala pouzdanosti
• Keywords (english): least absolute error criterion; norm; median; denoising; edge-preserving; adaptive wavelet transform; unbiased estimation; intersection of confidence intervals; relative intersection of confidence intervals
• 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
• Repository: FER Repository
• Created on: 2019-09-09 11:47:55