Algorithms for solving tensor completion problem and its application for reconstruction of images

Sekulović, Una (author), Zalar, Aljaž (mentor), Pock, Thomas (comentor)

The tensor completion problem asks to complete a partially known tensor such that the rank of the completion is the smallest possible. In this thesis, we present the mathematical background of six algorithms used to solve this problem (HaLRTC, T-SVD, WangLRTC, TNN, TNN_DCT, SPC). We implement and compare them in the area of image reconstruction. Focusing on the area of image reconstruction, we study the robustness of the algorithms, quality of the reconstruction and convergence times. To obtain good performance, we also employ image preprocessing techniques to decompose the image into smaller low-rank subimages, known as patches.

• Language: English
• Keywords: image reconstruction, tensor completion problem, patch-based algorithms, singular value decomposition
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2024
• PID: 20.500.12556/RUL-163975
• COBISS.SI-ID: 215090691
• Publication date in RUL: 15.10.2024

Secondary language

• Language: Slovenian
• Title: Algoritmi za reševanje tenzorskih napolnitev in njihova uporaba za rekonstrukcijo slik

Abstract

Problem tenzorskih napolnitev je problem določitve neznanih vhodov delno določenega tenzorja tako, da je rang napolnitve najmanjši možen. V tem delu predstavljamo matematično ozadje šestih algoritmov, ki se uporabljajo za reševanje tega problema (HaLRTC, T-SVD, WangLRTC, TNN, TNN_DCT, SPC). Implementiramo jih v programu Matlab in primerjamo na področju rekonstrukcije slik. Preučujemo robustnost algoritmov, kakovost rekonstrukcije in čase konvergence. Za doseganje dobre učinkovitosti uporabljamo tudi tehnike predobdelave slike, tj., tehnike za redukcijo problema na več manjših podproblemov.

• Keywords: rekonstrukcija slike, problem tenzorskih napolnitev, tehnike zmanjševanja velikosti podatkov, razcep singularnih vrednosti