Adaptive wavelet transform with application in signal denoising

doctoral thesis

• Title (english): Adaptivna valićna transformacija s primjenom na uklanjanje šuma iz signala
• Author: Mladen Tomić
• Mentor: Damir Seršić (mentor)
• Committee member: Sven Lončarić (predsjednik povjerenstva)
• Committee member: Viktor Sučić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2010-02-26, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Electrical Engineering
• Universal decimal classification (UDC): 621.3 - Electrical engineering

Abstract

We propose an adaptive lifting scheme with a goal of improving the wavelet transform performance about edges in a signal. The adaptive algorithm is based on the statistical method of intersection of confidence intervals (ICI) rule. It is used on a point-by-point basis, and on each scale. As a final result, longer and smoother wavelets are used in smooth signal regions, while shorter wavelets are used in higher frequency regions. The approach allows for efficient reconstruction of edges or, in general, higher signal frequencies. Additionally, a method for automated sensitivity parameter $\Gamma$ value selection was proposed, as its proper value is a prerequisite for high transform efficiency. The adaptive algorithm was also tested in a real-world application of fluoroscopic image sequences denoising, in which edge preservation is an essential requirement. The proposed adaptive edge preserving lifting scheme and accompanying parameter $\Gamma$ selection method were shown to represent a well performing model of the second generation wavelets, i.e., wavelets which inherit all the benefits and good properties of the classical wavelet transforms, while in the same time introducing additional advantages and features.

Abstract (english)

Predložena je adaptivna shema podizanja čiji je cilj poboljšavanje učinkovitosti valićne transformacije u okolini rubova unutar signala. Adaptivni je algoritam baziran na stastističkoj metodi pravilo presjeka intervala pouzdanosti (Intersection of Confidence Intervals -- ICI). Metoda se koristi na svakom nivou razlaganja i u svakoj točki signala. Kao konačni rezultat, dulji i glatki valići koriste se za glatke dijelove signala, dok se kraći valići koriste u dijelovima signala u kojima su prisutne više frekvencije. Takav pristup omogućava učinkovitu rekonstrukciju rubova unutar signala odnosno, općenito, visokih frekvencija. Dodatno, predložena je i metoda za automatsko određivanje vrijednosti parametra osjetljivosti transformacije, Γ, čiji je dobar odabir preduvjet za njenu visoku učinkovitost. Adaptivni je algoritam testiran i na primjeni uklanjanja šuma iz stvarnih fluoroskopskih nizova slika, pri čemu je očuvanje rubova unutar slike ključan zahtjev. Predložena adaptivna shema podizanja sa svojstvom očuvanja rubova unutar signala, te pripadajuća metoda odabira Γ parametra, učinkovita su realizacija valića druge generacije, odnosno valića koji zadržavaju sve prednosti i dobre značajke klasičnih valića, ali u isto vrijeme donose i nove mogućnosti te poboljšanja učinkovitosti.

• Keywords: wavelet transform; adaptive lifting scheme; second generation wavelets; local polynomial approximation; intersection of confidence intervals; signal denoising; fluoroscopic imaging
• Keywords (english): valićna transformacija; adaptivna shema podizanja; valići druge generacije; lokalna aproksimacija polinomima; presjek intervala pouzdanosti; uklanjanje šuma iz signala; fluoroskopske snimke
• Language: english
• URN:NBN: urn:nbn:hr:168:089406
• Promotion: 2010
• Study programme: Title: Doctoral study programme "Electrical Engineering and Computing"; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti, po-dručje tehničkih znanosti (doktor/doktorica znanosti, po-dručje tehničkih znanosti)
• Type of resource: Text
• Extent: i, 149 str. : graf. prikazi
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-03-18 09:45:09