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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 inpainting algorithms
Kolbábková, Anežka ; Veselý, Vítězslav (oponent) ; Rajmic, Pavel (vedoucí práce)
The thesis deals with audio inpainting problem and sparse representation approaches to this problem. It focuses on some of recent approaches to solving audio inpainting problem with respect to sparse representation algorithms. It proposes solving audio inapinting problem based on sparse representation of signal and low rank structure in spectrogram of audio signal. Thesis also describes implementation in program Matlab and evaluation of the proposed method.
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Inpainting of Missing Audio Signal Samples
Mach, Václav ; Polec,, Jaroslav (oponent) ; Koldovský,, Zdeněk (oponent) ; Rajmic, Pavel (vedoucí práce)
Recently, sparse representations of signals became very popular in the field of signal processing. Sparse representation mean that the signal is represented exactly or very well approximated by a linear combination of only a few vectors from the specific representation system. This thesis deals with the utilization of sparse representations of signals for the process of audio restoration, either historical or recent records. Primarily old audio recordings suffer from defects like crackles or noise. Until now, short gaps in audio signals were repaired by interpolation techniques, especially autoregressive modeling. Few years ago, an algorithm termed the Audio Inpainting was introduced. This algorithm solves the missing audio signal samples inpainting using sparse representations through the greedy algorithm for sparse approximation. This thesis aims to compare the state-of-the-art interpolation methods with the Audio Inpainting. Besides this, l1-relaxation methods are utilized for sparse approximation, while both analysis and synthesis models are incorporated. Algorithms used for the sparse approximation are called the proximal algorithms. These algorithms treat the coefficients either separately or with relations to their neighbourhood (structured sparsity). Further, structured sparsity is used for audio denoising. In the experimental part of the thesis, parameters of each algorithm are evaluated in terms of optimal restoration efficiency vs. processing time efficiency. All of the algorithms described in the thesis are compared using objective evaluation methods Signal-to-Noise ratio (SNR) and PEMO-Q. Finally, the overall conclusion and discussion on the restoration results is presented.
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Doplňování chybějících dat ve zvukových signálech
Bartlová, Hana ; Veselý, Vítězslav (oponent) ; Rajmic, Pavel (vedoucí práce)
Tato práce se zabývá doplňováním chybějících dat do zvukových signálů. Na úvod jsou shrnuty základní poznatky využívané dále v textu. Před samotnou aplikační částí je představena řídká reprezentace signálů a některé algoritmy jejího hledání. V kapitole věnované doplňování dat je formulován problém a krátce popsány a srovnány dosavadní metody řešení. Poté je uveden nejnovější přístup řešení využívající harmonickou strukturu signálů a provedeny experimenty. Na závěr je odvozen algoritmus pro zajištění maximální efektivity výpočtu.
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Inpainting of Missing Audio Signal Samples
Mach, Václav ; Polec,, Jaroslav (oponent) ; Koldovský,, Zdeněk (oponent) ; Rajmic, Pavel (vedoucí práce)
Recently, sparse representations of signals became very popular in the field of signal processing. Sparse representation mean that the signal is represented exactly or very well approximated by a linear combination of only a few vectors from the specific representation system. This thesis deals with the utilization of sparse representations of signals for the process of audio restoration, either historical or recent records. Primarily old audio recordings suffer from defects like crackles or noise. Until now, short gaps in audio signals were repaired by interpolation techniques, especially autoregressive modeling. Few years ago, an algorithm termed the Audio Inpainting was introduced. This algorithm solves the missing audio signal samples inpainting using sparse representations through the greedy algorithm for sparse approximation. This thesis aims to compare the state-of-the-art interpolation methods with the Audio Inpainting. Besides this, l1-relaxation methods are utilized for sparse approximation, while both analysis and synthesis models are incorporated. Algorithms used for the sparse approximation are called the proximal algorithms. These algorithms treat the coefficients either separately or with relations to their neighbourhood (structured sparsity). Further, structured sparsity is used for audio denoising. In the experimental part of the thesis, parameters of each algorithm are evaluated in terms of optimal restoration efficiency vs. processing time efficiency. All of the algorithms described in the thesis are compared using objective evaluation methods Signal-to-Noise ratio (SNR) and PEMO-Q. Finally, the overall conclusion and discussion on the restoration results is presented.
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Doplňování chybějících dat ve zvukových signálech
Bartlová, Hana ; Veselý, Vítězslav (oponent) ; Rajmic, Pavel (vedoucí práce)
Tato práce se zabývá doplňováním chybějících dat do zvukových signálů. Na úvod jsou shrnuty základní poznatky využívané dále v textu. Před samotnou aplikační částí je představena řídká reprezentace signálů a některé algoritmy jejího hledání. V kapitole věnované doplňování dat je formulován problém a krátce popsány a srovnány dosavadní metody řešení. Poté je uveden nejnovější přístup řešení využívající harmonickou strukturu signálů a provedeny experimenty. Na závěr je odvozen algoritmus pro zajištění maximální efektivity výpočtu.
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Audio inpainting algorithms
Kolbábková, Anežka ; Veselý, Vítězslav (oponent) ; Rajmic, Pavel (vedoucí práce)
The thesis deals with audio inpainting problem and sparse representation approaches to this problem. It focuses on some of recent approaches to solving audio inpainting problem with respect to sparse representation algorithms. It proposes solving audio inapinting problem based on sparse representation of signal and low rank structure in spectrogram of audio signal. Thesis also describes implementation in program Matlab and evaluation of the proposed method.
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