Autoregressive (AR) modeling is invaluable in signal processing, in particular in speech and audio fields. Attempts in the literature can be found that regularize or constrain either the time-domain signal values or the AR coefficients, which is done for various reasons, including the incorporation of prior information or numerical stabilization. Although these attempts are appealing, an encompassing and generic modeling framework is still missing. We propose such a framework and the related optimization problem and algorithm. We discuss the computational demands of the algorithm and explore the effects of various improvements on its convergence speed. In the experimental part, we demonstrate the usefulness of our approach on the audio declipping problem. We compare its performance against the state-of-the-art methods and demonstrate the competitiveness of the proposed method, especially for mildly clipped signals. The evaluation is extended by considering a heuristic algorithm of generalized linear prediction (GLP), a strong competitor which has only been presented as a patent and is new in the scientific community.
Sasaki et al. (2018) presented an efficient audio declipping algorithm, based on the properties of Hankel-structure matrices constructed from time-domain signal blocks. We adapt their approach to solving the audio inpainting problem, where samples are missing in the signal. We analyze the algorithm and provide modifications, some of them leading to an improved performance. Overall, it turns out that the new algorithms perform reasonably well for speech signals but they are not competitive in the case of music signals.
We develop the analysis (cosparse) variant of the popular audio declipping algorithm of Siedenburg et al. (2014). Furthermore, we extend both the old and the new variants by the possibility of weighting the time-frequency coefficients. We examine the audio reconstruction performance of several combinations of weights and shrinkage operators. The weights are shown to improve the reconstruction quality in some cases; however, the best scores achieved by the non-weighted methods are not surpassed with the help of weights. Yet, the analysis Empirical Wiener (EW) shrinkage was able to reach the quality of a computationally more expensive competitor, the Persistent Empirical Wiener (PEW). Moreover, the proposed analysis variant incorporating PEW slightly outperforms the synthesis counterpart in terms of an auditorily motivated metric.
In this paper, we propose an audio declipping method that takes advantages of both sparse optimization and deep learning. Since sparsity-based audio declipping methods have been developed upon constrained optimization, they are adjustable and well-studied in theory. However, they always uniformly promote sparsity and ignore the individual properties of a signal. Deep neural network (DNN)-based methods can learn the properties of target signals and use them for audio declipping. Still, they cannot perform well if the training data have mismatches and/or constraints in the time domain are not imposed. In the proposed method, we use a DNN in an optimization algorithm. It is inspired by an idea called plug-and-play (PnP) and enables us to promote sparsity based on the learned information of data, considering constraints in the time domain. Our experiments confirmed that the proposed method is stable and robust to mismatches between training and test data.
Some audio declipping methods produce waveforms that do not fully respect the physical process of clipping, which is why we refer to them as inconsistent. This letter reports what effect on perception it has if the solution by inconsistent methods is forced consistent by postprocessing. We first propose a simple sample replacement method, then we identify its main weaknesses and propose an improved variant. The experiments show that the vast majority of inconsistent declipping methods significantly benefit from the proposed approach in terms of objective perceptual metrics. In particular, we show that the SS PEW method based on social sparsity combined with the proposed method performs comparable to top methods from the consistent class, but at a computational cost of one order of magnitude lower.
Dynamic range limitations in signal processing often lead to clipping, or saturation, in signals. The task of audio declipping is estimating the original audio signal, given its clipped measurements, and has attracted much interest in recent years. Audio declipping algorithms often make assumptions about the underlying signal, such as sparsity or low-rankness, and about the measurement system. In this paper, we provide an extensive review of audio declipping algorithms proposed in the literature. For each algorithm, we present assumptions that are made about the audio signal, the modeling domain, and the optimization algorithm. Furthermore, we provide an extensive numerical evaluation of popular declipping algorithms, on real audio data. We evaluate each algorithm in terms of the Signal-to-Distortion Ratio, and also using perceptual metrics of sound quality. The article is accompanied by a repository containing the evaluated methods.