Search

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.

We propose a technique of signal acquisition using a combination of two devices with different sampling rates and quantization accuracies. Subsequent processing involving sparsity regularization enables us to reconstruct the signal at such a sampling frequency and with such a bit depth that was not possible using the two devices independently. Objective and subjective tests show the superiority of the proposed method in comparison with alternatives., Comment: Submitted to ICASSP 2025

The paper focuses on inpainting missing parts of an audio signal spectrogram. First, a recent successful approach based on an untrained neural network is revised and its several modifications are proposed, improving the signal-to-noise ratio of the restored audio. Second, the Janssen algorithm, the autoregression-based state-of-the-art for time-domain audio inpainting, is adapted for the time-frequency setting. This novel method, coined Janssen-TF, is compared to the neural network approach using both objective metrics and a subjective listening test, proving Janssen-TF to be superior in all the considered measures.

The paper presents an evaluation of popular audio inpainting methods based on autoregressive modeling, namely the extrapolation-based and Janssen methods. A novel variant of the Janssen method suitable for inpainting of gaps is also proposed. The main differences between the particular popular approaches are pointed out. In the experimental part, the importance of the choice of the AR model estimator is confirmed by objective metrics. Then, a mid-scale computational experiment is presented, and its results are confirmed by a listening test. All the experiments demonstrate the superiority of the new gap-wise Janssen method.

A method for perfusion imaging with DCE-MRI is developed based on two popular paradigms: the low-rank + sparse model for optimisation-based reconstruction, and the deep unfolding. A learnable algorithm derived from a proximal algorithm is designed with emphasis on simplicity and interpretability. The resulting deep network is trained and evaluated using a simulated measurement of a rat with a brain tumor, showing large performance gain over the classical low-rank + sparse baseline. Moreover, quantitative perfusion analysis is performed based on the reconstructed sequence, proving that even training based on a simple pixel-wise error can lead to significant improvement of the quality of the perfusion maps., Comment: This work has been submitted to the IEEE for possible publication

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.

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.

The paper deals with the hitherto neglected topic of audio dequantization. It reviews the state-of-the-art sparsity-based approaches and proposes several new methods. Convex as well as non-convex approaches are included, and all the presented formulations come in both the synthesis and analysis variants. In the experiments the methods are evaluated using the signal-to-distortion ratio (SDR) and PEMO-Q, a perceptually motivated metric.

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.

In their recent evaluation of time-frequency representations and structured sparsity approaches to audio inpainting, Lieb and Stark (2018) have used a particular mapping as a proximal operator. This operator serves as the fundamental part of an iterative numerical solver. However, their mapping is improperly justified. The present article proves that their mapping is indeed a proximal operator, and also derives its proper counterpart. Furthermore, it is rationalized that Lieb and Stark's operator can be understood as an approximation of the proper mapping. Surprisingly, in most cases, such an approximation (referred to as the approximal operator) is shown to provide even better numerical results in audio inpainting compared to its proper counterpart, while being computationally much more effective.

The paper presents a unified, flexible framework for the tasks of audio inpainting, declipping, and dequantization. The concept is further extended to cover analogous degradation models in a transformed domain, e.g. quantization of the signal's time-frequency coefficients. The task of reconstructing an audio signal from degraded observations in two different domains is formulated as an inverse problem, and several algorithmic solutions are developed. The viability of the presented concept is demonstrated on an example where audio reconstruction from partial and quantized observations of both the time-domain signal and its time-frequency coefficients is carried out.

The paper shows the potential of sparsity-based methods in restoring quantized signals. Following up on the study of Brauer et al. (IEEE ICASSP 2016), we significantly extend the range of the evaluation scenarios: we introduce the analysis (cosparse) model, we use more effective algorithms, we experiment with another time-frequency transform. The paper shows that the analysis-based model performs comparably to the synthesis-model, but the Gabor transform produces better results than the originally used cosine transform. Last but not least, we provide codes and data in a reproducible way.

We deal with the problem of sparsity-based audio inpainting, i.e. filling in the missing segments of audio. A consequence of the approaches based on mathematical optimization is the insufficient amplitude of the signal in the filled gaps. Remaining in the framework based on sparsity and convex optimization, we propose improvements to audio inpainting, aiming at compensating for such an energy loss. The new ideas are based on different types of weighting, both in the coefficient and the time domains. We show that our propositions improve the inpainting performance in terms of both the SNR and ODG.

A novel method for audio declipping based on sparsity is presented. The method incorporates psychoacoustic information by weighting the transform coefficients in the $\ell_1$ minimization. Weighting leads to an improved quality of restoration while retaining a low complexity of the algorithm. Three possible constructions of the weights are proposed, based on the absolute threshold of hearing, the global masking threshold and on a quadratic curve. Experiments compare the restoration quality according to the signal-to-distortion ratio (SDR) and PEMO-Q objective difference grade (ODG) and indicate that with correctly chosen weights, the presented method is able to compete, or even outperform, the current state of the art.

A novel sparsity-based algorithm for audio inpainting is proposed. It is an adaptation of the SPADE algorithm by Kiti\'c et al., originally developed for audio declipping, to the task of audio inpainting. The new SPAIN (SParse Audio INpainter) comes in synthesis and analysis variants. Experiments show that both A-SPAIN and S-SPAIN outperform other sparsity-based inpainting algorithms. Moreover, A-SPAIN performs on a par with the state-of-the-art method based on linear prediction in terms of the SNR, and, for larger gaps, SPAIN is even slightly better in terms of the PEMO-Q psychoacoustic criterion.

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.

Used in the paper is an overcomplete piecewise-polynomial image model incorporating sparsity. The paper shows that using such a model, the edges in the image can be resolved robustly with respect to noise. Two variants of the proposed approach are both shown to be superior to the use of the classic edge detecting kernels. The proposed method is in turn also suitable for image segmentation., Comment: appears at the ICSPCS 2018 conference https://dspcs-witsp.com/icspcs_2018/

This technical report shows and discusses in detail how Sparse Audio Declipper (SPADE) algorithms are derived from the signal model using the ADMM approach. The analysis version (A-SPADE) of Kiti\'c et. al. (LVA/ICA 2015) is derived and justified. The synthesis version (S-SPADE) of the same research team is shown to solve a different optimization task than intended. This issue is corrected in this report, leading to the new S-SPADE algorithm which is in line to A-SPADE.

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.