Inverzni problemi velikih dimenzija kod obrade slika

master's thesis

• Author: Goran Jeličić
• Mentor: Nela Bosner (mentor)
• Committee member: Nela Bosner (predsjednik povjerenstva)
• Committee member: Goranka Nogo (član povjerenstva)
• Committee member: Ana Prlić (član povjerenstva)
• Committee member: Maja Resman (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Inverzni problemi velikih dimenzija pojavljuju se u različitim primjenama u sklopu obrade slika. Zbog numeričke osjetljivosti rješavanja takvih problema, efikasne metode regularizacije su potrebne kako bi se izračunala suvisla rješenja. Ovaj rad dao bi pregled nekoliko uobičajenih matematičkih modela, uključujući linearni model, separabilan nelinearan model, i općeniti nelinearan model. Razmotriti će se tehnike regularizacije i implementacije problema velikih dimenzija, sa posebnim fokusom na algoritme koje mogu iskoristiti specifičnu strukturu problema. Mogućnosti i potencijal opisanih algoritama ilustrirat će se primjerima iz dekonvolucije slika, slijepe dekonvolucije slika sa više okvira i tomosinteze. Na kraju bi se teorija ilustrirala konkretnim primjerima izraženim u MATLAB okruženju.

Abstract (english)

Large-scale inverse problems occur in a variety of applications in image processing. Due to the numerical sensitivity of solving such problems, effective regularization methods are needed in order to calculate it coherent solutions. This thesis gives an overview of a few common mathematical models, including linear model, separable nonlinear model, and generalize nonlinear model. Regularization and implementation techniques are considered, with a particular focus on algorithms that can take advantage of the specific problem structure. The possibilities and potential of described algorithms are illustrated with examples from image deconvolution, blind frame deconvolution, and tomosynthesis. Finally, the theory is illustrated with concrete examples expressed in the MATLAB environment.

• Keywords: obrada slika; metode regularizacije; MATLAB
• Keywords (english): image processing; regularization methods; MATLAB
• Language: croatian
• URN:NBN: urn:nbn:hr:217:457738
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-02-05 10:42:20