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Modern Optimization Methods for Interpolation of Missing Sections in Audio Signals
Mokrý, Ondřej ; Kowalski, Matthieu (oponent) ; Koldovský, Zbyněk (oponent) ; Rajmic, Pavel (vedoucí práce)
Damage to audio signals is in practice common, yet undesirable. Information loss can occur due to improper recording (low sample rate or dynamic range), transmission error (sample dropout), media damage, or because of noise. The removal of such disturbances is possible using inverse problems. Specifically, this work focuses on the situation where sections of an audio signal of length in the order of tens of milliseconds are completely lost, and the goal is to interpolate the missing samples based on the unimpaired context and a suitable signal model. The first part of the dissertation is devoted to convex and non-convex optimization methods, which are designed to find a solution to the interpolation problem based on the assumption of sparsity of the time-frequency spectrum. The general background and some algorithms are taken from the literature and adapted to the interpolation problem, many modifications and experimental approaches are original. The second part of the thesis focuses on the use of non-negative matrix factorization, with which a probabilistic model of the signal spectrogram can be constructed and used for the interpolation of the signal. This model is then used as the basis for a successful reconstruction algorithm, to which two alternative methods are derived in the present thesis. Finally, an extensive experimental validation of the methods on a group of musical signals is conducted. Using objective indicators of the quality of the interpolated signal, it is shown, that in each class of methods, the proposed modifications lead to a noticeable improvement in quality or convergence over the baseline methods. In particular, within the studied range of impairments, algorithms using factorization compete with the current best methods for interpolating missing sections of the audio signal.
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Audio Signal Declipping and Dequantization Using Sparsity-Based Methods
Záviška, Pavel ; Šroubek,, Filip (oponent) ; Koldovský,, Zbyněk (oponent) ; Rajmic, Pavel (vedoucí práce)
Audio signals are susceptible to various types of quality degradation, with clipping being one of the most common and problematic distortions. This Thesis addresses the restoration of audio signals corrupted by nonlinear distortions and presents the contribution in the field of sparsity-based audio restoration algorithms, with the main focus on audio declipping and dequantization. The first part of the Thesis deals with the problem of audio declipping and presents several sparsity-based approaches, containing both the original research and adopted algorithms, which have been reimplemented or modified. The performance of the algorithms is evaluated using the Signal-to-Distortion ratio, as well as perceptually motivated metrics of sound quality. Then, attention is paid on incorporating psychoacoustic information into declipping by weighting the transform coefficients. Three possible constructions of the weights are presented and it is shown that with correctly chosen weights, it is possible to significantly improve the performance of the algorithms, which achieve state-of-the-art restoration quality with low computational complexity. Special focus is also paid on declipping methods that allow a deviation in the reliable part. In that direction, the Thesis studies the perceptual effects of plain replacement of the reliable samples, then identifies its main weaknesses and introduces methods to compensate the discovered negative effects. It is shown that using this technique, it is possible to enhance the performance of such declipping algorithms without a significant increase in computational complexity. Finally, selected declipping algorithms are adopted to the problem of audio dequantization. The Thesis is accompanied by repositories containing implementations of the presented methods.
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Inverzní problémy v úlohách přenosu tepla s fázovými změnami
Kamarýt, Petr ; Mauder, Tomáš (oponent) ; Klimeš, Lubomír (vedoucí práce)
Tato diplomová práce se zabývá inverzními problémy v úlohách přenosu tepla se změnou fáze. V první kapitole jsou popsány mechanizmy přenosu tepla včetně modelování materiálu se změnou fáze. Druhá kapitola se věnuje výpočtovému řešení úloh přenosu tepla. Ve třetí je formulována inverzní úloha pro neznámou okrajovou podmínku. Čtvrtá kapitola popisuje autorem implementované metody pro řešení přímých a inverzních úloh přenosu tepla. Inverzní úlohy jsou řešeny sekvenční metodou a pomocí umělých neuronových sítí. Byly zvoleny dva průběhy hustoty tepelného toku: spojitý, po částech lineární a nespojitý, po částech konstantní. Obě metody dosahují pro obě úlohy srovnatelných výsledků. V případě nespojité hustoty tepelného toku jsou výsledky horší než v případě spojitého průběhu.
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Inverzní problémy v úlohách přenosu tepla s fázovými změnami
Kamarýt, Petr ; Mauder, Tomáš (oponent) ; Klimeš, Lubomír (vedoucí práce)
Tato diplomová práce se zabývá inverzními problémy v úlohách přenosu tepla se změnou fáze. V první kapitole jsou popsány mechanizmy přenosu tepla včetně modelování materiálu se změnou fáze. Druhá kapitola se věnuje výpočtovému řešení úloh přenosu tepla. Ve třetí je formulována inverzní úloha pro neznámou okrajovou podmínku. Čtvrtá kapitola popisuje autorem implementované metody pro řešení přímých a inverzních úloh přenosu tepla. Inverzní úlohy jsou řešeny sekvenční metodou a pomocí umělých neuronových sítí. Byly zvoleny dva průběhy hustoty tepelného toku: spojitý, po částech lineární a nespojitý, po částech konstantní. Obě metody dosahují pro obě úlohy srovnatelných výsledků. V případě nespojité hustoty tepelného toku jsou výsledky horší než v případě spojitého průběhu.
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Audio Signal Declipping and Dequantization Using Sparsity-Based Methods
Záviška, Pavel ; Šroubek,, Filip (oponent) ; Koldovský,, Zbyněk (oponent) ; Rajmic, Pavel (vedoucí práce)
Audio signals are susceptible to various types of quality degradation, with clipping being one of the most common and problematic distortions. This Thesis addresses the restoration of audio signals corrupted by nonlinear distortions and presents the contribution in the field of sparsity-based audio restoration algorithms, with the main focus on audio declipping and dequantization. The first part of the Thesis deals with the problem of audio declipping and presents several sparsity-based approaches, containing both the original research and adopted algorithms, which have been reimplemented or modified. The performance of the algorithms is evaluated using the Signal-to-Distortion ratio, as well as perceptually motivated metrics of sound quality. Then, attention is paid on incorporating psychoacoustic information into declipping by weighting the transform coefficients. Three possible constructions of the weights are presented and it is shown that with correctly chosen weights, it is possible to significantly improve the performance of the algorithms, which achieve state-of-the-art restoration quality with low computational complexity. Special focus is also paid on declipping methods that allow a deviation in the reliable part. In that direction, the Thesis studies the perceptual effects of plain replacement of the reliable samples, then identifies its main weaknesses and introduces methods to compensate the discovered negative effects. It is shown that using this technique, it is possible to enhance the performance of such declipping algorithms without a significant increase in computational complexity. Finally, selected declipping algorithms are adopted to the problem of audio dequantization. The Thesis is accompanied by repositories containing implementations of the presented methods.
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Mathematical modelling and computational methods in applied sciences and engineering - Modelling 2019
Blaheta, Radim ; Starý, Jiří ; Sysala, Stanislav
Modelling 2019 is an international conference on Mathematical Modelling and Computational Methods in Applied Sciences and Engineering held in\nOlomouc, Czech Republic, in September 16 - 20, 2019. It aims to be a forum for an exchange of ideas, insights and experiences in different areas\nof mathematical modelling. It includes the fundamental formulation and analysis of mathematical models, the development of numerical methods and exploitation of capabilities of the contemporary high-performance computers or applications of mathematical modelling.\nThis conference belongs to a series of conferences previously held in Roznov in 2014 and 2009, in Pilsen in 2005 and 2001, and in Prague in 1998 and 1994. During the period of 25 years, the focus of the conference has been substantially enlarged. Besides the topics aiming at the development\nof numerical methods and analysis of mathematical models described by the partial differential equations, the conference relates to the inverse\nproblems, quantification of uncertainties in the input data, machine learning and exploitation of high-performance computing systems of petaflops and pre-exaflops performance. Increased attention is devoted to challenging industrial problems and collaboration with industry.
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