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master's thesis
Sažimajuće očitavanje signala
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:303523
Grozdanić, Karlo
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Grozdanić, K. (2023). Sažimajuće očitavanje signala (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:303523

Grozdanić, Karlo. "Sažimajuće očitavanje signala." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:303523

Grozdanić, Karlo. "Sažimajuće očitavanje signala." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:303523

Grozdanić, K. (2023). 'Sažimajuće očitavanje signala', Master's thesis, University of Zagreb, Faculty of Science, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:303523

Grozdanić K. Sažimajuće očitavanje signala [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:217:303523

K. Grozdanić, "Sažimajuće očitavanje signala", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:303523

Metadata
TitleSažimajuće očitavanje signala
Title (english)Summarizing signal reading
AuthorKarlo Grozdanić
MentorAzra Tafro (mentor)
Committee memberAzra Tafro (predsjednik povjerenstva)
Committee memberZvonko Iljazović (član povjerenstva)
Committee memberLjiljana Arambašić (član povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-03-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovome radu prezentiramo metodu sažimajućeg očitavanja koja nam omogućuje rekonstrukciju signala iz vrlo malog broja mjerenja, uz uvjet rijetkosti signala u nekoj bazi. Rekonstrukciju dobivamo preko problema minimizacije \(l_1\) norme, koja pod određenim uvjetima daje ista rješenja kao problem minimizacije \(l_0\) norme. U prvom poglavlju formuliran je problem sažimajućeg očitavanja i dana je usporedba s klasičnim pristupima sažimanju podataka. Uvedene su definicije i pojmovi koji se kasnije koriste. U drugom poglavlju detaljno je predstavljena teorija sažimajućeg očitavanja: pokazani su uvjeti pod kojima će postupak biti uspješan te su dane granice točnosti rekonstrukcije ovisno o parametrima mjerenja. U trećem poglavlju pokazali smo kako sažimajuće očitavanje radi u problemima rekonstrukcije slika, te smo uveli poboljšanja na sam postupak koja dovode do boljih rezultata rekonstrukcije.
Abstract (english)
In this paper, we investigate compressive sensing, a technique that allows for the reconstruction of a signal from a limited number of measurements, provided that the signal exibits sparsity in some orthonormal basis. The signal is reconstructed by solving a \(l_1\) minimization problem is solved, which in the right conditions, yields a solution that is equivalent to a \(l_0\) minimization problem. In the first chapter, we formulate the compressive sensing problem and give compare it to the standard approach for signal compression. Key definitions and concepts are introduced. In the second chapter, we present a comprehensive theory of compressive sensing, demonstrating the conditions under which the method is guaranteed to be successful, and we providing the bounds on the reconstruction error based on the measurement process. In the third chapter, we demonstrate the application of compressive sensing to image reconstruction and modifications that significantly improve the reconstruction accuracy.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:303523
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-03-27 08:17:12