Sažimajuće očitavanje korištenjem spline funkcija

master's thesis

• Title (english): Compressive sensing using spline functions
• Author: Jelena Ivanković
• Mentor: Damir Seršić (mentor)
• Committee member: Damir Seršić (predsjednik povjerenstva)
• Committee member: Sven Lončarić (član povjerenstva)
• Committee member: Davor Petrinović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2018-02-22, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Electrical Engineering

Abstract

U ovom radu opisane su klasične jednodimenzionalne i dvodimenzionalne glatke interpolacijske polinomne funkcije konačnog reda, definirane po dijelovima na konačnom skupu intervala i periodičnih rubnih uvjeta.
Opisani su i osnovni principi sažimajućeg očitavanja te konstrukcija mjerne matrice korištenjem polinomnih funkcija navedenih svojstava. Dizajniran je sustav, sastavljen od matrice veza polinomnih funkcija na točkama intervala te mjerne matrice temeljene na istim funkcijama, koji predstavlja vezu diskretne i informacijama rijetke domene sažimajućeg očitavanja s kontinuiranom domenom koja spline funkcijama aproksimira sažete signale i omogućuje veće bogatstvo informacijama.
U MATLAB okruženju izrađeno je generiranje umjetnih primjera za provjeru učinkovitosti sustava.

Abstract (english)

This paper describes classic one and two dimensional smooth interpolating piecewise polynomial functions of finite order, defined on finite interval and with periodic boundary conditions.
Basics of compressive sensing theory are also described, as well as construction of measurement matrix using polynomial functions of aforementioned characteristics. Designed system, made of constructed matrix of polynomial connections at interval boundaries and of measurement matrix based on those same functions, represents connection between discreete domain of compressive sensing, with sparse information, and continuous domain which approximates those informations with spline functions and enables more information to be available.
Efficiency of designed system was checked in MATLAB environment by generation of synthetic measurement data.

• Keywords: uniformni periodični spline; sažimajuće očitavanje; chebyshevljevi polinomi; Gauss-Jordanova metoda eliminacije; nul-prostor; interpolacija; L1 norma; MATLAB
• Keywords (english): uniform periodic spline; compressive sensing; chebyshev polynomials; Gauss-Jordan elimination method; null-space; interpolation; L1 norm; MATLAB
• Language: croatian
• URN:NBN: urn:nbn:hr:168:682102
• Study programme: Title: Electrical Engineering and Information Technology; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka elektrotehnike i informacijske tehnologije (magistar/magistra inženjer/inženjerka elektrotehnike i informacijske tehnologije)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2019-03-13 21:00:25