Modeling and robust estimation of a series of point sources in multidimensional imaging

doctoral thesis

• Title (croatian): Modeliranje i robusna estimacija niza točkastih izvora u višedimenzionalnom oslikavanju
• Author: Anita Gribl Koščević
• Mentor: Davor Petrinović (mentor)
• Committee member: Sven Lončarić (predsjednik povjerenstva)
• Committee member: Damir Seršić (član povjerenstva)
• Committee member: Azra Tafro (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; (Department of Electronic Systems and Information Processing); Zagreb
• Defense date and country: 2023-11-27, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing
• Universal decimal classification (UDC): 004 - Computer science and technology. Computing. Data processing

Abstract

The first part of the doctoral dissertation deals with the precise identification of overlapping stellar objects in astronomical images that can be approximated by 2D Gaussian profiles. A method for robust estimation of overlapped 2D Gaussian components was developed that outperforms existing methods and resolves overlap even beyond the resolution limit in certain cases. The second part of the doctoral dissertation deals with the parameter estimation of the multidimensional Gaussian profile. A fast method for estimating the Gaussian profile of an arbitrary dimension in the domain of the exponential function argument was proposed. For a given initial centroid position, the method provides an analytical solution for all other Gaussian profile parameters. The third part of the doctoral dissertation deals with the reconstruction of an unknown 2D distribution in low-dose 2D positron emission tomography (PET). In low-dose 2D PET, image reconstruction by using conventional methods does not resemble the original process due to an insufficient number of coincident events to describe the underlying process. As part of this research, a new method for data acquisition in low-dose PET was developed, where virtual response lines, i.e., coincident events, are artificially generated at the intersections of the original response lines, thereby artificially increasing the input dataset. The method is based on the relationship between spatial statistical properties of intersections of response lines and the process samples, which were derived and analyzed in detail within this dissertation.

Abstract (croatian)

Prvi dio doktorske disertacije bavi se preciznom identifikacijom preklopljenih zvjezdanih objekata na astronomskim slikama koji se mogu aproksimirati 2D Gaussovim profilima. Razvijena je metoda za robusnu procjenu preklopljenih 2D Gaussovih komponenti koja nadmašuje postojeće metode i rješava preklapanje čak i iznad granice rezolucije u određenim slučajevima. Drugi dio doktorske disertacije bavi se estimacijom parametara višedimenzionalnog Gaussovog profila. Predložena je brza metoda za estimaciju Gaussovog profila proizvoljne dimenzije u domeni argumenta eksponencijalne funkcije. Za zadani početni položaj težišta, metoda daje analitičko rješenje za sve ostale parametre Gaussovog profila. Treći dio doktorske disertacije bavi se rekonstrukcijom nepoznate 2D distribucije u niskodoznoj 2D pozitronskoj emisijskoj tomografiji (PET). U 2D PET-u s niskim dozama radioaktivnog sredstva, rekonstruirana slika dobivena korištenjem konvencionalnih metoda ne nalikuje izvornom procesu zbog nedovoljnog broja koincidentnih događaja za opis temeljnog procesa. U sklopu ovog istraživanja razvijena je nova metoda za prikupljanje podataka kod PET-a s niskim dozama, gdje se virtualne linije odziva, tj. koincidentni događaji, umjetno generiraju na sjecištima izvornih linija odziva čime se umjetno povećava ulazni skup podataka. Metoda se temelji na vezi prostornih statističkih svojstava sjecišta linija odziva i uzoraka temeljnog 2D procesa koji su izvedeni i detaljno analizirani u okviru ove disertacije.

• Keywords: astronomical imaging; modeling and detection of stellar objects; multidimensional Gaussian profile; parameter estimation; iteratively reweighted least squares method; robust statistics; low-dose 2D PET imaging; 2D PET image reconstruction
• Keywords (croatian): astronomske slike; modeliranje i detekcija zvjezdanih objekata; višedimenzionalni Gaussov profil; estimacija parametara; iterativna težinska metoda najmanjih kvadrata; robusna statistika; 2D PET oslikavanje s niskom dozom radioaktivnog sredstva; rekonstrukcija slike kod 2D PET-a
• Language: english
• URN:NBN: urn:nbn:hr:168:517303
• Promotion: 2023
• Study programme: Title: Computer Science; Study programme type: university; Study level: postgraduate; Academic / professional title: Doktor znanosti (Doktor znanosti)
• Type of resource: Text
• Extent: 158 str. : graf. prikazi u boji ; 30 cm
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-05-10 12:29:18