Sparsity and cosparsity for audio declipping: a flexible non-convex approach

This work investigates the empirical performance of the sparse synthesis versus sparse analysis regularization for the ill-posed inverse problem of audio declipping. We develop a versatile non-convex heuristics which can be readily used with both data models. Based on this algorithm, we report that, in most cases, the two models perform almost similarly in terms of signal enhancement. However, the analysis version is shown to be amenable for real time audio processing, when certain analysis operators are considered. Both versions outperform state-of-the-art methods in the field, especially for the severely saturated signals

A Proper version of Synthesis-based Sparse Audio Declipper

Methods based on sparse representation have found great use in the recovery of audio signals degraded by clipping. The state of the art in declipping has been achieved by the SPADE algorithm by Kiti\'c et. al. (LVA/ICA2015). Our recent study (LVA/ICA2018) has shown that although the original S-SPADE can be improved such that it converges significantly faster than the A-SPADE, the restoration quality is significantly worse. In the present paper, we propose a new version of S-SPADE. Experiments show that the novel version of S-SPADE outperforms its old version in terms of restoration quality, and that it is comparable with the A-SPADE while being even slightly faster than A-SPADE

Revisiting Synthesis Model of Sparse Audio Declipper

The state of the art in audio declipping has currently been achieved by SPADE (SParse Audio DEclipper) algorithm by Kiti\'c et al. Until now, the synthesis/sparse variant, S-SPADE, has been considered significantly slower than its analysis/cosparse counterpart, A-SPADE. It turns out that the opposite is true: by exploiting a recent projection lemma, individual iterations of both algorithms can be made equally computationally expensive, while S-SPADE tends to require considerably fewer iterations to converge. In this paper, the two algorithms are compared across a range of parameters such as the window length, window overlap and redundancy of the transform. The experiments show that although S-SPADE typically converges faster, the average performance in terms of restoration quality is not superior to A-SPADE

Restoration of clipped audio signals

Ses işaretlerinde oluşan bozulmaların ortadan kaldırılması için yenileme işlemi yapılmaktadır. Bu bozulmalardan birisi olan kırpılmış ses işaretlerinin yenileme işleminde, işaretin bozulmamış bölgesindeki işaret parçası aracılığı ile işaretin bozulmaya uğramış bölgesinin özgün durumuna geri getirilmesi amaçlanmaktadır. İşaretin normal olarak verildiği ya da kayıt edildiği zaman ortamından farklı bir ortama dönüştürülmesi ve bu sayede temsil edilmesi için gerekli örnek sayısının azalması seyrek gösterim sayesinde mümkün olmaktadır. Bu çalışmada işaretin ayrık Fourier dönüşümü katsayılarının oluşturduğu seyrek gösterime dayanan bir yenileme yöntemi sunulmaktadır. Önerilen yöntemin başarımının değerlendirilmesi için farklı konuşma ve müzik işaretlerinden oluşan örnekler üzerinde çalışmalar yapılmıştır. Önerilen yöntemin işaretin daha yüksek oranda kırpılması durumunda karşılaştırılan diğer yöntemlere göre daha iyi işaret gürültü oranı başarımı elde ettiği gösterilmiştir.Restoration process is performed to remove degradations formed on the audio signals. In the restoration of clipped audio signals, which is one of these degradations, the degraded section is aimed to be restored to its original by the part of the undegraded section of the signal. The transformation of the signal from as normally given or recorded in the time domain to a different domain and thus reducing the number of samples required to be represented might be possible due to sparse representation. In this study, a restoration method is presented that relies on sparse representation of the discrete Fourier transform coefficients of the signal. In order to evaluate the performance of the proposed method, experiments were performed on various speech and music signal examples. It has been shown that the proposed method achieves better signal to noise ratio performance compared to the other methods in cases of higher clipping ratios

A new generalized projection and its application to acceleration of audio declipping

In convex optimization, it is often inevitable to work with projectors onto convex sets composed with a linear operator. Such a need arises from both the theory and applications, with signal processing being a prominent and broad field where convex optimization has been used recently. In this article, a novel projector is presented, which generalizes previous results in that it admits to work with a broader family of linear transforms when compared with the state of the art but, on the other hand, it is limited to box-type convex sets in the transformed domain. The new projector is described by an explicit formula, which makes it simple to implement and requires a low computational cost. The projector is interpreted within the framework of the so-called proximal splitting theory. The convenience of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two

Restoration of signals with limited instantaneous value for the multichannel audio signal

Tato diplomová práce se zabývá rekonstrukcí saturovaného vícekanálového audio signálu pomocí metod založených na řídké reprezentaci signálu. V první části práce je popsána teorie clippingu u audio signálů a teorie řídké reprezentace signálů. V této části je obsažena také krátká rešerše současných rekonstrukčních algoritmů. Následně jsou představeny dva rekonstrukční algoritmy, které byly v rámci práce naprogramovány v prostředí Matlab. První z nich je algoritmus SPADE, „state-of-the-art“ pro rekonstrukci monofonních signálů, a druhým je od něj odvozený algoritmus CASCADE, navržený pro vícekanálové signály. Ve třetí části práce jsou oba algoritmy otestovány a porovnány pomocí objektivních ukazatelů SDR a PEAQ a pomocí subjektivního poslechového testu MUSHRA.This master’s thesis deals with the restoration of clipped multichannel audio signals based on sparse representations. First, a general theory of clipping and theory of sparse representations of audio signals is described. A short overview of existing restoration methods is part of this thesis as well. Subsequently, two declipping algorithms are introduced and are also implemented in the Matlab environment as a part of the thesis. The first one, SPADE, is considered a state- of-the-art method for mono audio signals declipping and the second one, CASCADE, which is derived from SPADE, is designed for the restoration of multichannel signals. In the last part of the thesis, both algorithms are tested and the results are compared using the objective measures SDR and PEAQ, and also using the subjective listening test MUSHRA.