arXiv subjects

Mads Græsbøll Christensen

Publications and source records attributed to Mads Græsbøll Christensen.

At least 19 recordsLinked to original sources

arXiv2026

A Study of the Scale Invariant Signal to Distortion Ratio in Speech Separation with Noisy References

This paper examines the implications of using the Scale-Invariant Signal-to-Distortion Ratio (SI-SDR) as both evaluation and training objective in supervised speech separation, when the training references contain noise, as is the case with the de facto benchmark WSJ0-2Mix. A derivation of the SI-SDR with noisy references reveals that noise limits the achievable SI-SDR, or leads to undesired noise in the separated outputs. To address this, a method is proposed to enhance references and augment the mixtures with WHAM!, aiming to train models that avoid learning noisy references. Two models trained on these enhanced datasets are evaluated with the non-intrusive NISQA.v2 metric. Results show reduced noise in separated speech but suggest that processing references may introduce artefacts, limiting overall quality gains. Negative correlation is found between SI-SDR and perceived noisiness across models on the WSJ0-2Mix and Libri2Mix test sets, underlining the conclusion from the derivation.

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arXiv2026

Online Single-Channel Audio-Based Sound Speed Estimation for Robust Multi-Channel Audio Control

Robust spatial audio control relies on accurate acoustic propagation models, yet environmental variations, especially changes in the speed of sound, cause systematic mismatches that degrade performance. Existing methods either assume known sound speed, require multiple microphones, or rely on separate calibration, making them impractical for systems with minimal sensing. We propose an online sound speed estimator that operates during general multichannel audio playback and requires only a single observation microphone. The method exploits the structured effect of sound speed on the reproduced signal and estimates it by minimizing the mismatch between the measured audio and a parametric acoustic model. Simulations show accurate tracking of sound speed for diverse input signals and improved spatial control performance when the estimates are used to compensate propagation errors in a sound zone control framework.

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arXiv2025

Learning-based A Posteriori Speech Presence Probability Estimation and Applications

The a posteriori speech presence probability (SPP) is the fundamental component of noise power spectral density (PSD) estimation, which can contribute to speech enhancement and speech recognition systems. Most existing SPP estimators can estimate SPP accurately from the background noise. Nevertheless, numerous challenges persist, including the difficulty of accurately estimating SPP from non-stationary noise with statistics-based methods and the high latency associated with deep learning-based approaches. This paper presents an improved SPP estimation approach based on deep learning to achieve higher SPP estimation accuracy, especially in non-stationary noise conditions. To promote the information extraction performance of the DNN, the global information of the observed signal and the local information of the decoupled frequency bins from the observed signal are connected as hybrid global-local information. The global information is extracted by one encoder. Then, one decoder and two fully connected layers are used to estimate SPP from the information of residual connection. To evaluate the performance of our proposed SPP estimator, the noise PSD estimation and speech enhancement tasks are performed. In contrast to existing minimum mean-square error (MMSE)-based noise PSD estimation approaches, the noise PSD is estimated by the sub-optimal MMSE based on the current frame SPP estimate without smoothing. Directed by the noise PSD estimate, a standard speech enhancement framework, the log spectral amplitude estimator, is employed to extract clean speech from the observed signal. From the experimental results, we can confirm that our proposed SPP estimator can achieve high noise PSD estimation accuracy and speech enhancement performance while requiring low model complexity.

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arXiv2025

Robust Fixed-Filter Sound Zone Control with Audio-Based Position Tracking

Performance of sound zone control (SZC) systems deployed in practical scenarios are highly sensitive to the location of the listener(s) and can degrade significantly when listener(s) are moving. This paper presents a robust SZC system that adapts to dynamic changes such as moving listeners and varying zone locations using a dictionary-based approach. The proposed system continuously monitors the environment and updates the fixed control filters by tracking the listener position using audio signals only. To test the effectiveness of the proposed SZC method, simulation studies are carried out using practically measured impulse responses. These studies show that SZC, when incorporated with the proposed audio-only position tracking scheme, achieves optimal performance when all listener positions are available in the dictionary. Moreover, even when not all listener positions are included in the dictionary, the method still provides good performance improvement compared to a traditional fixed filter SZC scheme.

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arXiv2024

Provable Privacy Advantages of Decentralized Federated Learning via Distributed Optimization

Federated learning (FL) emerged as a paradigm designed to improve data privacy by enabling data to reside at its source, thus embedding privacy as a core consideration in FL architectures, whether centralized or decentralized. Contrasting with recent findings by Pasquini et al., which suggest that decentralized FL does not empirically offer any additional privacy or security benefits over centralized models, our study provides compelling evidence to the contrary. We demonstrate that decentralized FL, when deploying distributed optimization, provides enhanced privacy protection - both theoretically and empirically - compared to centralized approaches. The challenge of quantifying privacy loss through iterative processes has traditionally constrained the theoretical exploration of FL protocols. We overcome this by conducting a pioneering in-depth information-theoretical privacy analysis for both frameworks. Our analysis, considering both eavesdropping and passive adversary models, successfully establishes bounds on privacy leakage. We show information theoretically that the privacy loss in decentralized FL is upper bounded by the loss in centralized FL. Compared to the centralized case where local gradients of individual participants are directly revealed, a key distinction of optimization-based decentralized FL is that the relevant information includes differences of local gradients over successive iterations and the aggregated sum of different nodes' gradients over the network. This information complicates the adversary's attempt to infer private data. To bridge our theoretical insights with practical applications, we present detailed case studies involving logistic regression and deep neural networks. These examples demonstrate that while privacy leakage remains comparable in simpler models, complex models like deep neural networks exhibit lower privacy risks under decentralized FL.

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arXiv2024

Sound Zone Control Robust To Sound Speed Change

Sound zone control (SZC) implemented using static optimal filters is significantly affected by various perturbations in the acoustic environment, an important one being the fluctuation in the speed of sound, which is in turn influenced by changes in temperature and humidity (TH). This issue arises because control algorithms typically use pre-recorded, static impulse responses (IRs) to design the optimal control filters. The IRs, however, may change with time due to TH changes, which renders the derived control filters to become non-optimal. To address this challenge, we propose a straightforward model called sinc interpolation-compression/expansion-resampling (SICER), which adjusts the IRs to account for both sound speed reduction and increase. Using the proposed technique, IRs measured at a certain TH can be corrected for any TH change and control filters can be re-derived without the need of re-measuring the new IRs (which is impractical when SZC is deployed). We integrate the proposed SICER IR correction method with the recently introduced variable span trade-off (VAST) framework for SZC, and propose a SICER-corrected VAST method that is resilient to sound speed variations. Simulation studies show that the proposed SICER-corrected VAST approach significantly improves acoustic contrast and reduces signal distortion in the presence of sound speed changes.

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arXiv2023

A Two-Stage Deep Representation Learning-Based Speech Enhancement Method Using Variational Autoencoder and Adversarial Training

This paper focuses on leveraging deep representation learning (DRL) for speech enhancement (SE). In general, the performance of the deep neural network (DNN) is heavily dependent on the learning of data representation. However, the DRL's importance is often ignored in many DNN-based SE algorithms. To obtain a higher quality enhanced speech, we propose a two-stage DRL-based SE method through adversarial training. In the first stage, we disentangle different latent variables because disentangled representations can help DNN generate a better enhanced speech. Specifically, we use the $β$-variational autoencoder (VAE) algorithm to obtain the speech and noise posterior estimations and related representations from the observed signal. However, since the posteriors and representations are intractable and we can only apply a conditional assumption to estimate them, it is difficult to ensure that these estimations are always pretty accurate, which may potentially degrade the final accuracy of the signal estimation. To further improve the quality of enhanced speech, in the second stage, we introduce adversarial training to reduce the effect of the inaccurate posterior towards signal reconstruction and improve the signal estimation accuracy, making our algorithm more robust for the potentially inaccurate posterior estimations. As a result, better SE performance can be achieved. The experimental results indicate that the proposed strategy can help similar DNN-based SE algorithms achieve higher short-time objective intelligibility (STOI), perceptual evaluation of speech quality (PESQ), and scale-invariant signal-to-distortion ratio (SI-SDR) scores. Moreover, the proposed algorithm can also outperform recent competitive SE algorithms.

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arXiv2023

Frequency bin-wise single channel speech presence probability estimation using multiple DNNs

In this work, we propose a frequency bin-wise method to estimate the single-channel speech presence probability (SPP) with multiple deep neural networks (DNNs) in the short-time Fourier transform domain. Since all frequency bins are typically considered simultaneously as input features for conventional DNN-based SPP estimators, high model complexity is inevitable. To reduce the model complexity and the requirements on the training data, we take a single frequency bin and some of its neighboring frequency bins into account to train separate gate recurrent units. In addition, the noisy speech and the a posteriori probability SPP representation are used to train our model. The experiments were performed on the Deep Noise Suppression challenge dataset. The experimental results show that the speech detection accuracy can be improved when we employ the frequency bin-wise model. Finally, we also demonstrate that our proposed method outperforms most of the state-of-the-art SPP estimation methods in terms of speech detection accuracy and model complexity.

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arXiv2022

Privacy-Preserving Distributed Expectation Maximization for Gaussian Mixture Model using Subspace Perturbation

Privacy has become a major concern in machine learning. In fact, the federated learning is motivated by the privacy concern as it does not allow to transmit the private data but only intermediate updates. However, federated learning does not always guarantee privacy-preservation as the intermediate updates may also reveal sensitive information. In this paper, we give an explicit information-theoretical analysis of a federated expectation maximization algorithm for Gaussian mixture model and prove that the intermediate updates can cause severe privacy leakage. To address the privacy issue, we propose a fully decentralized privacy-preserving solution, which is able to securely compute the updates in each maximization step. Additionally, we consider two different types of security attacks: the honest-but-curious and eavesdropping adversary models. Numerical validation shows that the proposed approach has superior performance compared to the existing approach in terms of both the accuracy and privacy level.

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arXiv2022

Space Alternating Variational Estimation Based Sparse Bayesian Learning for Complex-value Sparse Signal Recovery Using Adaptive Laplace Priors

Due to its self-regularizing nature and its ability to quantify uncertainty, the Bayesian approach has achieved excellent recovery performance across a wide range of sparse signal recovery applications. However, most existing methods are based on the real-value signal model, with the complex-value signal model rarely considered. Motivated by the adaptive least absolute shrinkage and selection operator (LASSO) and the sparse Bayesian learning (SBL) framework, a hierarchical model with adaptive Laplace priors is proposed in this paper for recovery of complex sparse signals. Moreover, the space alternating approach is integrated into the algorithm to reduce the computational complexity of the proposed method. In experiments, the proposed algorithm is studied for complex Gaussian random dictionaries and different types of complex signals. These experiments show that the proposed algorithm offers better recovery performance for different types of complex signals than state-of-the-art methods.

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arXiv2022

A deep representation learning speech enhancement method using $β$-VAE

In previous work, we proposed a variational autoencoder-based (VAE) Bayesian permutation training speech enhancement (SE) method (PVAE) which indicated that the SE performance of the traditional deep neural network-based (DNN) method could be improved by deep representation learning (DRL). Based on our previous work, we in this paper propose to use $β$-VAE to further improve PVAE's ability of representation learning. More specifically, our $β$-VAE can improve PVAE's capacity of disentangling different latent variables from the observed signal without the trade-off problem between disentanglement and signal reconstruction. This trade-off problem widely exists in previous $β$-VAE algorithms. Unlike the previous $β$-VAE algorithms, the proposed $β$-VAE strategy can also be used to optimize the DNN's structure. This means that the proposed method can not only improve PVAE's SE performance but also reduce the number of PVAE training parameters. The experimental results show that the proposed method can acquire better speech and noise latent representation than PVAE. Meanwhile, it also obtains a higher scale-invariant signal-to-distortion ratio, speech quality, and speech intelligibility.

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arXiv2022

A Bayesian Permutation training deep representation learning method for speech enhancement with variational autoencoder

Recently, variational autoencoder (VAE), a deep representation learning (DRL) model, has been used to perform speech enhancement (SE). However, to the best of our knowledge, current VAE-based SE methods only apply VAE to the model speech signal, while noise is modeled using the traditional non-negative matrix factorization (NMF) model. One of the most important reasons for using NMF is that these VAE-based methods cannot disentangle the speech and noise latent variables from the observed signal. Based on Bayesian theory, this paper derives a novel variational lower bound for VAE, which ensures that VAE can be trained in supervision, and can disentangle speech and noise latent variables from the observed signal. This means that the proposed method can apply the VAE to model both speech and noise signals, which is totally different from the previous VAE-based SE works. More specifically, the proposed DRL method can learn to impose speech and noise signal priors to different sets of latent variables for SE. The experimental results show that the proposed method can not only disentangle speech and noise latent variables from the observed signal but also obtain a higher scale-invariant signal-to-distortion ratio and speech quality score than the similar deep neural network-based (DNN) SE method.

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arXiv2021

Communication efficient privacy-preserving distributed optimization using adaptive differential quantization

Privacy issues and communication cost are both major concerns in distributed optimization. There is often a trade-off between them because the encryption methods required for privacy-preservation often incur expensive communication bandwidth. To address this issue, we, in this paper, propose a quantization-based approach to achieve both communication efficient and privacy-preserving solutions in the context of distributed optimization. By deploying an adaptive differential quantization scheme, we allow each node in the network to achieve its optimum solution with a low communication cost while keeping its private data unrevealed. Additionally, the proposed approach is general and can be applied in various distributed optimization methods, such as the primal-dual method of multipliers (PDMM) and the alternating direction method of multipliers (ADMM). Moveover, we consider two widely used adversary models: passive and eavesdropping. Finally, we investigate the properties of the proposed approach using different applications and demonstrate its superior performance in terms of several parameters including accuracy, privacy, and communication cost.

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arXiv2021

Speech Decomposition Based on a Hybrid Speech Model and Optimal Segmentation

In a hybrid speech model, both voiced and unvoiced components can coexist in a segment. Often, the voiced speech is regarded as the deterministic component, and the unvoiced speech and additive noise are the stochastic components. Typically, the speech signal is considered stationary within fixed segments of 20-40 ms, but the degree of stationarity varies over time. For decomposing noisy speech into its voiced and unvoiced components, a fixed segmentation may be too crude, and we here propose to adapt the segment length according to the signal local characteristics. The segmentation relies on parameter estimates of a hybrid speech model and the maximum a posteriori (MAP) and log-likelihood criteria as rules for model selection among the possible segment lengths, for voiced and unvoiced speech, respectively. Given the optimal segmentation markers and the estimated statistics, both components are estimated using linear filtering. A codebook-based approach differentiates between unvoiced speech and noise. A better extraction of the components is possible by taking into account the adaptive segmentation, compared to a fixed one. Also, a lower distortion for voiced speech and higher segSNR for both components is possible, as compared to other decomposition methods.

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arXiv2020

Privacy-Preserving Distributed Processing: Metrics, Bounds, and Algorithms

Privacy-preserving distributed processing has recently attracted considerable attention. It aims to design solutions for conducting signal processing tasks over networks in a decentralized fashion without violating privacy. Many algorithms can be adopted to solve this problem such as differential privacy, secure multiparty computation, and the recently proposed distributed optimization based subspace perturbation. However, how these algorithms relate to each other is not fully explored yet. In this paper, we therefore first propose information-theoretic metrics based on mutual information. Using the proposed metrics, we are able to compare and relate a number of existing well-known algorithms. We then derive a lower bound on individual privacy that gives insights on the nature of the problem. To validate the above claims, we investigate a concrete example and compare a number of state-of-the-art approaches in terms of different aspects such as output utility, individual privacy and algorithm robustness against the number of corrupted parties, using not only theoretical analysis but also numerical validation. Finally, we discuss and provide principles for designing appropriate algorithms for different applications.

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arXiv2020

Signal-Adaptive and Perceptually Optimized Sound Zones with Variable Span Trade-Off Filters

Creating sound zones has been an active research field since the idea was first proposed. So far, most sound zone control methods rely on either an optimization of physical metrics such as acoustic contrast and signal distortion or a mode decomposition of the desired sound field. By using these types of methods, approximately 15 dB of acoustic contrast between the reproduced sound field in the target zone and its leakage to other zone(s) has been reported in practical set-ups, but this is typically not high enough to satisfy the people inside the zones. In this paper, we propose a sound zone control method shaping the leakage errors so that they are as inaudible as possible for a given acoustic contrast. The shaping of the leakage errors is performed by taking the time-varying input signal characteristics and the human auditory system into account when the loudspeaker control filters are calculated. We show how this shaping can be performed using variable span trade-off filters, and we show theoretically how these filters can be used for trading signal distortion in the target zone for acoustic contrast. The proposed method is evaluated based on physical metrics such as acoustic contrast and perceptual metrics such as STOI. The computational complexity and processing time of the proposed method for different system set-ups are also investigated. Lastly, the results of a MUSHRA listening test are reported. The test results show that the proposed method provides more than 20% perceptual improvement compared to existing sound zone control methods.

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arXiv2020

A Speech Enhancement Algorithm based on Non-negative Hidden Markov Model and Kullback-Leibler Divergence

In this paper, we propose a novel supervised single-channel speech enhancement method combing the the Kullback-Leibler divergence-based non-negative matrix factorization (NMF) and hidden Markov model (NMF-HMM). With the application of HMM, the temporal dynamics information of speech signals can be taken into account. In the training stage, the sum of Poisson, leading to the KL divergence measure, is used as the observation model for each state of HMM. This ensures that a computationally efficient multiplicative update can be used for the parameter update of the proposed model. In the online enhancement stage, we propose a novel minimum mean-square error (MMSE) estimator for the proposed NMF-HMM. This estimator can be implemented using parallel computing, saving the time complexity. The performance of the proposed algorithm is verified by objective measures. The experimental results show that the proposed strategy achieves better speech enhancement performance than state-of-the-art speech enhancement methods. More specifically, compared with the traditional NMF-based speech enhancement methods, our proposed algorithm achieves a 5\% improvement for short-time objective intelligibility (STOI) and 0.18 improvement for perceptual evaluation of speech quality (PESQ).

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arXiv2020

Privacy-Preserving Distributed Optimization via Subspace Perturbation: A General Framework

As the modern world becomes increasingly digitized and interconnected, distributed signal processing has proven to be effective in processing its large volume of data. However, a main challenge limiting the broad use of distributed signal processing techniques is the issue of privacy in handling sensitive data. To address this privacy issue, we propose a novel yet general subspace perturbation method for privacy-preserving distributed optimization, which allows each node to obtain the desired solution while protecting its private data. In particular, we show that the dual variables introduced in each distributed optimizer will not converge in a certain subspace determined by the graph topology. Additionally, the optimization variable is ensured to converge to the desired solution, because it is orthogonal to this non-convergent subspace. We therefore propose to insert noise in the non-convergent subspace through the dual variable such that the private data are protected, and the accuracy of the desired solution is completely unaffected. Moreover, the proposed method is shown to be secure under two widely-used adversary models: passive and eavesdropping. Furthermore, we consider several distributed optimizers such as ADMM and PDMM to demonstrate the general applicability of the proposed method. Finally, we test the performance through a set of applications. Numerical tests indicate that the proposed method is superior to existing methods in terms of several parameters like estimated accuracy, privacy level, communication cost and convergence rate.

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