Sažimajuće očitavanje

master's thesis

• Title (english): Compressed sensing
• Author: Mario Marjanović
• Mentor: Ivica Nakić (mentor)
• Committee member: Ivica Nakić (predsjednik povjerenstva)
• Committee member: Marko Erceg (član povjerenstva)
• Committee member: Marko Radulović (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-09-29, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu dan je uvod u sažimajuće očitavanje gdje su objašnjeni osnovni pojmovi, rezultati i neke najpoznatije primjene ovog aktualnog, brzo rastućeg područja matematike. Pokazano je kakvi uvjeti moraju biti zadovoljeni ako želimo računati egzaktno rješenje problema i zašto zapravo rijetko računamo egzaktno rješenje. Analizirane su dvije najzastpuljenije familije algoritama za aproksimiranje rješenja, dani su i neki konkretni primjeri algoritama te navedene neke njihove prednosti i nedostatci. Posebni naglasak stavljen je na algoritme Orthogonal Matching Pursuit (OMP) i Prošireni Lagrangeov Multiplikator (PLM) koji su naknadno implementirani i čije perfromanse su uspoređene za problem prepoznavanja lica. Detaljnije je obrađena primjena sažimajućeg očitavanja u problemu klasifikacije, specifično u sustavima za prepoznavanje lica. Opisano je kako problem prepoznavanja lica postaviti kao klasični problem sažimajućeg očitavanja. Na kraju rada, opisana je aplikacija koja implementira sustav za prepoznavanje lica baziranom na sažimajućem očitavanju. Za treniranje i testiranje sustava korištena je extended Yale B baza podataka lica, a sama aplikacija napisana je u programskom jeziku Java koristeći biblioteku ND4J za brze matrične operacije.

Abstract (english)

This paper gives an introduction to compressed sensing where the basic terms, results and some of the most famous applications of this rapidly growing field of mathematics are explained. It is shown which conditions must be met if we want to calculate the exact solution to the problem and why we rarely calculate the exact solution. The two most common families of algorithms for approximating solutions are analyzed, some specific examples of algorithms are given, and some of their advantages and disadvantages are listed. Special emphasis was placed on the Orthogonal Matching Pursuit (OMP) and Augmented Lagrange Multiplier (ALM) algorithms, which were subsequently implemented and whose performances were compared for the face recognition problem. The application of compressed sensing in the problem of classification, specific to facial recognition systems, is treated in more detail. It is described how the problem of face recognition is posed as a classic problem of compressed sensing. At the end of the paper, an application that implements a face recognition system based on summarizing reading is described. The extended Yale B face database is used for training and testing the system, and the application itself is written in the Java programming language using the ND4J library for faster matrix operations.

• Keywords: Orthogonal Matching Pursuit (OMP); Prošireni Lagrangeov Multiplikator (PLM); sustavi za prepoznavanje lica; extended Yale B baza podataka lica; programski jeziku Java; biblioteka ND4J za brze matrične operacije
• Keywords (english): Orthogonal Matching Pursuit (OMP); Augmented Lagrange Multiplier (ALM); facial recognition systems; extended Yale B face database; Java programming language; ND4J library for faster matrix operations
• Language: croatian
• URN:NBN: urn:nbn:hr:217:272465
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-11-02 12:08:20