arXiv subjects

Richard Heusdens

Publications and source records attributed to Richard Heusdens.

At least 19 recordsLinked to original sources

arXiv2026

A two-step approach for speech enhancement in low-SNR scenarios using cyclostationary beamforming and DNNs

Deep Neural Networks (DNNs) often struggle to suppress noise at low signal-to-noise ratios (SNRs). This paper addresses speech enhancement in scenarios dominated by harmonic noise and proposes a framework that integrates cyclostationarity-aware preprocessing with lightweight DNN-based denoising. A cyclic minimum power distortionless response (cMPDR) spectral beamformer is used as a preprocessing block. It exploits the spectral correlations of cyclostationary noise to suppress harmonic components prior to learning-based enhancement and does not require modifications to the DNN architecture. The proposed pipeline is evaluated in a single-channel setting using two DNN architectures: a simple and lightweight convolutional recurrent neural network (CRNN), and a state-of-the-art model, namely ultra-low complexity network (ULCNet). Experiments on synthetic data and real-world recordings dominated by rotating machinery noise demonstrate consistent improvements over end-to-end DNN baselines, particularly at low SNRs. Remarkably, a parameter-efficient CRNN with cMPDR preprocessing surpasses the performance of the larger ULCNet operating on raw or Wiener-filtered inputs. These results indicate that explicitly incorporating cyclostationarity as a signal prior is more effective than increasing model capacity alone for suppressing harmonic interference.

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arXiv2026

When Is Distributed Nonlinear Aggregation Private? Optimality and Information-Theoretical Bounds

Nonlinear aggregation is central to modern distributed systems, yet its privacy behavior is far less understood than that of linear aggregation. Unlike linear aggregation where mature mechanisms can often suppress information leakage, nonlinear operators impose inherent structural limits on what privacy guarantees are theoretically achievable when the aggregate must be computed exactly. This paper develops a unified information-theoretic framework to characterize privacy leakage in distributed nonlinear aggregation under a joint adversary that combines passive (honest-but-curious) corruption and eavesdropping over communication channels. We cover two broad classes of nonlinear aggregates: order-based operators (maximum/minimum and top-$K$) and robust aggregation (median/quantiles and trimmed mean). We first derive fundamental lower bounds on leakage that hold without sacrificing accuracy, thereby identifying the minimum unavoidable information revealed by the computation and the transcript. We then propose simple yet effective privacy-preserving distributed algorithms, and show that with appropriate randomized initialization and parameter choices, our proposed approaches can attach the derived optimal bounds for the considered operators. Extensive experiments validate the tightness of the bounds and demonstrate that network topology and key algorithmic parameters (including the stepsize) govern the observed leakage in line with the theoretical analysis, yielding actionable guidelines for privacy-preserving nonlinear aggregation.

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arXiv2025

Cyclic MPDR Beamforming for Suppression of Almost-Cyclostationary Acoustic Interference

Conventional acoustic beamformers typically assume short-time stationarity and process frequency bins independently, ignoring inter-frequency correlations. This is suboptimal for almost-periodic noise sources such as engines, fans, and musical instruments: these signals are better modeled as (almost) cyclostationary (ACS) processes with statistically correlated spectral components. This paper introduces the cyclic minimum power distortionless response (cMPDR) beamformer, which extends the conventional MPDR to jointly exploit spatial and spectral correlations. Building on frequency-shifted (FRESH) filtering, it suppresses noise components that are coherent across harmonically related frequencies, reducing residual noise beyond what spatial filtering alone can achieve. To address inharmonicity, where partials deviate from exact integer multiples of a fundamental frequency, we estimate resonant frequencies from a periodogram and derive frequency shifts from their pairwise spacing. Theoretical analysis yields closed-form expressions for residual noise and proves that output power decreases monotonically with the number of cyclic components. Experiments on synthetic harmonic noise and real UAV motor recordings confirm these findings: in low-SNR scenarios, the cMPDR achieves up to 5 dB improvement in SI-SDR over the MPDR, yields consistent STOI gains, and remains effective with a single microphone. When spectral correlation is absent, the method reduces to conventional MPDR and does not degrade performance. These results suggest that cyclic processing is a viable direction for acoustic noise reduction that deserves further investigation. Code and audio samples are available at https://github.com/Screeen/cMPDR.

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arXiv2025

Harmonics to the Rescue: Why Voiced Speech is Not a Wss Process

Speech processing algorithms often rely on statistical knowledge of the underlying process. Despite many years of research, however, the debate on the most appropriate statistical model for speech still continues. Speech is commonly modeled as a wide-sense stationary (WSS) process. However, the use of the WSS model for spectrally correlated processes is fundamentally wrong, as WSS implies spectral uncorrelation. In this paper, we demonstrate that voiced speech can be more accurately represented as a cyclostationary (CS) process. By employing the CS rather than the WSS model for processes that are inherently correlated across frequency, it is possible to improve the estimation of cross-power spectral densities (PSDs), source separation, and beamforming. We illustrate how the correlation between harmonic frequencies of CS processes can enhance system identification, and validate our findings using both simulated and real speech data.

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arXiv2025

Cyclic Multichannel Wiener Filter for Acoustic Beamforming

Acoustic beamforming models typically assume wide-sense stationarity of speech signals within short time frames. However, voiced speech is better modeled as a cyclostationary (CS) process, a random process whose mean and autocorrelation are $T_1$-periodic, where $\alpha_1=1/T_1$ corresponds to the fundamental frequency of vowels. Higher harmonic frequencies are found at integer multiples of the fundamental. This work introduces a cyclic multichannel Wiener filter (cMWF) for speech enhancement derived from a cyclostationary model. This beamformer exploits spectral correlation across the harmonic frequencies of the signal to further reduce the mean-squared error (MSE) between the target and the processed input. The proposed cMWF is optimal in the MSE sense and reduces to the MWF when the target is wide-sense stationary. Experiments on simulated data demonstrate considerable improvements in scale-invariant signal-to-distortion ratio (SI-SDR) on synthetic data but also indicate high sensitivity to the accuracy of the estimated fundamental frequency $\alpha_1$, which limits effectiveness on real data.

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arXiv2025

Optimal Privacy-Preserving Distributed Median Consensus

Distributed median consensus has emerged as a critical paradigm in multi-agent systems due to the inherent robustness of the median against outliers and anomalies in measurement. Despite the sensitivity of the data involved, the development of privacy-preserving mechanisms for median consensus remains underexplored. In this work, we present the first rigorous analysis of privacy in distributed median consensus, focusing on an $L_1$-norm minimization framework. We establish necessary and sufficient conditions under which exact consensus and perfect privacy-defined as zero information leakage-can be achieved simultaneously. Our information-theoretic analysis provides provable guarantees against passive and eavesdropping adversaries, ensuring that private data remain concealed. Extensive numerical experiments validate our theoretical results, demonstrating the practical feasibility of achieving both accuracy and privacy in distributed median consensus.

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arXiv2024

Re-Evaluating Privacy in Centralized and Decentralized Learning: An Information-Theoretical and Empirical Study

Decentralized Federated Learning (DFL) has garnered attention for its robustness and scalability compared to Centralized Federated Learning (CFL). While DFL is commonly believed to offer privacy advantages due to the decentralized control of sensitive data, recent work by Pasquini et, al. challenges this view, demonstrating that DFL does not inherently improve privacy against empirical attacks under certain assumptions. For investigating fully this issue, a formal theoretical framework is required. Our study offers a novel perspective by conducting a rigorous information-theoretical analysis of privacy leakage in FL using mutual information. We further investigate the effectiveness of privacy-enhancing techniques like Secure Aggregation (SA) in both CFL and DFL. Our simulations and real-world experiments show that DFL generally offers stronger privacy preservation than CFL in practical scenarios where a fully trusted server is not available. We address discrepancies in previous research by highlighting limitations in their assumptions about graph topology and privacy attacks, which inadequately capture information leakage in FL.

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arXiv2024

Privacy-Preserving Distributed Maximum Consensus Without Accuracy Loss

In distributed networks, calculating the maximum element is a fundamental task in data analysis, known as the distributed maximum consensus problem. However, the sensitive nature of the data involved makes privacy protection essential. Despite its importance, privacy in distributed maximum consensus has received limited attention in the literature. Traditional privacy-preserving methods typically add noise to updates, degrading the accuracy of the final result. To overcome these limitations, we propose a novel distributed optimization-based approach that preserves privacy without sacrificing accuracy. Our method introduces virtual nodes to form an augmented graph and leverages a carefully designed initialization process to ensure the privacy of honest participants, even when all their neighboring nodes are dishonest. Through a comprehensive information-theoretical analysis, we derive a sufficient condition to protect private data against both passive and eavesdropping adversaries. Extensive experiments validate the effectiveness of our approach, demonstrating that it not only preserves perfect privacy but also maintains accuracy, outperforming existing noise-based methods that typically suffer from accuracy loss.

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arXiv2024

AttentionX: Exploiting Consensus Discrepancy In Attention from A Distributed Optimization Perspective

In this paper, we extend the standard Attention in transformer by exploiting the consensus discrepancy from a distributed optimization perspective, referred to as AttentionX. It is noted that the primal-dual method of multipliers (PDMM) \cite{Zhang16PDMM} is designed to iteratively solve a broad class of distributed optimization problems over a pear-to-pear (P2P) network, where neighbouring nodes gradually reach consensus as specified by predefined linear edge-constraints in the optimization process. In particular, at each iteration of PDMM, each node in a network first performs information-gathering from neighbours and then performs local information-fusion. From a high-level point of view, the $KQ$-softmax-based weighted summation of $V$-representations in Attention corresponds information-gathering from neighbours while the feature-processing via the feed-forward network (FFN) in transformer corresponds to local information fusion. PDMM exploits the Lagrangian multipliers to capture the historical consensus discrepancy in the form of residual errors of the linear edge-constraints, which plays a crucial role for the algorithm to converge. Inspired by PDMM, we propose AttentionX to incorporate the consensus discrepancy in the output update-expression of the standard Attention. The consensus discrepancy in AttentionX refers to the difference between the weighted summation of $V$-representations and scaled $V$-representions themselves. Experiments on ViT and nanoGPT show promising performance.

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arXiv2024

Wideband Relative Transfer Function (RTF) Estimation Exploiting Frequency Correlations

This article focuses on estimating relative transfer functions (RTFs) for beamforming applications. Traditional methods often assume that spectra are uncorrelated, an assumption that is often violated in practical scenarios due to factors such as time-domain windowing or the non-stationary nature of signals, as observed in speech. To overcome these limitations, we propose an RTF estimation technique that leverages spectral and spatial correlations through subspace analysis. Additionally, we derive Cram\'er--Rao bounds (CRBs) for the RTF estimation task, providing theoretical insights into the achievable estimation accuracy. These bounds reveal that channel estimation can be performed more accurately if the noise or the target signal exhibits spectral correlations. Experiments with both real and synthetic data show that our technique outperforms the narrowband maximum-likelihood estimator, known as covariance whitening (CW), when the target exhibits spectral correlations. Although the proposed algorithm generally achieves accuracy close to the theoretical bound, there is potential for further improvement, especially in scenarios with highly spectrally correlated noise. While channel estimation has various applications, we demonstrate the method using a minimum variance distortionless (MVDR) beamformer for multichannel speech enhancement. A free Python implementation is also provided.

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arXiv2024

Adaptive Differentially Quantized Subspace Perturbation (ADQSP): A Unified Framework for Privacy-Preserving Distributed Average Consensus

Privacy-preserving distributed average consensus has received significant attention recently due to its wide applicability. Based on the achieved performances, existing approaches can be broadly classified into perfect accuracy-prioritized approaches such as secure multiparty computation (SMPC), and worst-case privacy-prioritized approaches such as differential privacy (DP). Methods of the first class achieve perfect output accuracy but reveal some private information, while methods from the second class provide privacy against the strongest adversary at the cost of a loss of accuracy. In this paper, we propose a general approach named adaptive differentially quantized subspace perturbation (ADQSP) which combines quantization schemes with so-called subspace perturbation. Although not relying on cryptographic primitives, the proposed approach enjoys the benefits of both accuracy-prioritized and privacy-prioritized methods and is able to unify them. More specifically, we show that by varying a single quantization parameter the proposed method can vary between SMPC-type performances and DP-type performances. Our results show the potential of exploiting traditional distributed signal processing tools for providing cryptographic guarantees. In addition to a comprehensive theoretical analysis, numerical validations are conducted to substantiate our results.

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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

Distributed Nonlinear Conic Optimisation with partially separable Structure

In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and fixed-point theory, the primal-dual method of multipliers (PDMM), originally designed for equality constraint optimisation and recently extended to include linear inequality constraints, to accommodate for cone constraints. The resulting algorithm can be used to implement a variety of optimisation problems, including the important class of semidefinite programs with partially separable structure, in a fully distributed fashion. We derive update equations by applying the Peaceman-Rachford splitting algorithm to the monotonic inclusion related to the lifted dual problem. The cone constraints are implemented by a reflection method in the lifted dual domain where auxiliary variables are reflected with respect to the intersection of the polar cone and a subspace relating the dual and lifted dual domain. Convergence results for both synchronous and stochastic update schemes are provided and an application of the proposed algorithm is demonstrated to implement an approximate algorithm for maximum cut problems based on semidefinite programming in a fully distributed fashion.

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arXiv2024

Optimal Pilot Design for OTFS in Linear Time-Varying Channels

This paper investigates the positioning of the pilot symbols, as well as the power distribution between the pilot and the communication symbols in the orthogonal time frequency space (OTFS) modulation scheme. We analyze the pilot placements that minimize the mean squared error (MSE) in estimating the channel taps. This allows us to identify two new pilot allocations for OTFS. In addition, we optimize the average channel capacity by adjusting the power balance. We show that this leads to a significant increase in average capacity. The results provide valuable guidance for designing the OTFS parameters to achieve maximum capacity. Numerical simulations are performed to validate the findings.

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arXiv2024

Distributed Optimisation with Linear Equality and Inequality Constraints using PDMM

In this paper, we consider the problem of distributed optimisation of a separable convex cost function over a graph, where every edge and node in the graph could carry both linear equality and/or inequality constraints. We show how to modify the primal-dual method of multipliers (PDMM), originally designed for linear equality constraints, such that it can handle inequality constraints as well. The proposed algorithm does not need any slack variables, which is similar to the recent work [1] which extends the alternating direction method of multipliers (ADMM) for addressing decomposable optimisation with linear equality and inequality constraints. Using convex analysis, monotone operator theory and fixed-point theory, we show how to derive the update equations of the modified PDMM algorithm by applying Peaceman-Rachford splitting to the monotonic inclusion related to the lifted dual problem. To incorporate the inequality constraints, we impose a non-negativity constraint on the associated dual variables. This additional constraint results in the introduction of a reflection operator to model the data exchange in the network, instead of a permutation operator as derived for equality constraint PDMM. Convergence for both synchronous and stochastic update schemes of PDMM are provided. The latter includes asynchronous update schemes and update schemes with transmission losses. Experiments show that PDMM converges notably faster than extended ADMM of [1].

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arXiv2023

Topology-Dependent Privacy Bound For Decentralized Federated Learning

Decentralized Federated Learning (FL) has attracted significant attention due to its enhanced robustness and scalability compared to its centralized counterpart. It pivots on peer-to-peer communication rather than depending on a central server for model aggregation. While prior research has delved into various factors of decentralized FL such as aggregation methods and privacy-preserving techniques, one crucial aspect affecting privacy is relatively unexplored: the underlying graph topology. In this paper, we fill the gap by deriving a stringent privacy bound for decentralized FL under the condition that the accuracy is not compromised, highlighting the pivotal role of graph topology. Specifically, we demonstrate that the minimum privacy loss at each model aggregation step is dependent on the size of what we term as 'honest components', the maximally connected subgraphs once all untrustworthy participants are excluded from the networks, which is closely tied to network robustness. Our analysis suggests that attack-resilient networks will provide a superior privacy guarantee. We further validate this by studying both Poisson and power law networks, showing that the latter, being less robust against attacks, indeed reveals more privacy. In addition to a theoretical analysis, we consolidate our findings by examining two distinct privacy attacks: membership inference and gradient inversion.

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arXiv2023

Privacy-Preserving Distributed Optimisation using Stochastic PDMM

Privacy-preserving distributed processing has received considerable attention recently. The main purpose of these algorithms is to solve certain signal processing tasks over a network in a decentralised fashion without revealing private/secret data to the outside world. Because of the iterative nature of these distributed algorithms, computationally complex approaches such as (homomorphic) encryption are undesired. Recently, an information theoretic method called subspace perturbation has been introduced for synchronous update schemes. The main idea is to exploit a certain structure in the update equations for noise insertion such that the private data is protected without compromising the algorithm's accuracy. This structure, however, is absent in asynchronous update schemes. In this paper we will investigate such asynchronous schemes and derive a lower bound on the noise variance after random initialisation of the algorithm. This bound shows that the privacy level of asynchronous schemes is always better than or at least equal to that of synchronous schemes. Computer simulations are conducted to consolidate our theoretical results.

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arXiv2023

Sensor Selection using the Two-Target Cramér-Rao Bound for Angle of Arrival Estimation

Sensor selection is a useful method to help reduce data throughput, as well as computational, power, and hardware requirements, while still maintaining acceptable performance. Although minimizing the Cramér-Rao bound has been adopted previously for sparse sensing, it did not consider multiple targets and unknown source models. We propose to tackle the sensor selection problem for angle of arrival estimation using the worst-case Cramér-Rao bound of two uncorrelated sources. We cast the problem as a convex semi-definite program and retrieve the binary selection by randomized rounding. Through numerical examples related to a linear array, we illustrate the proposed method and show that it leads to the selection of elements at the edges plus the center of the linear array.

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