Cross-channel unlabeled sensing addresses the problem of recovering a multi-channel signal from measurements that were shuffled across channels. This work expands the cross-channel unlabeled sensing framework to signals that lie in a union of subspaces. The extension allows for handling more complex signal structures and broadens the framework to tasks like compressed sensing. These mismatches between samples and channels often arise in applications such as whole-brain calcium imaging of freely moving organisms or multi-target tracking. We improve over previous models by deriving tighter bounds on the required number of samples for unique reconstruction, while supporting more general signal types. The approach is validated through an application in whole-brain calcium imaging, where organism movements disrupt sample-to-neuron mappings. This demonstrates the utility of our framework in real-world settings with imprecise sample-channel associations, achieving accurate signal reconstruction.

In high-dimensional data analysis, such as financial index tracking or biomedical applications, it is crucial to select the few relevant variables while maintaining control over the false discovery rate (FDR). In these applications, strong dependencies often exist among the variables (e.g., stock returns), which can undermine the FDR control property of existing methods like the model-X knockoff method or the T-Rex selector. To address this issue, we have expanded the T-Rex framework to accommodate overlapping groups of highly correlated variables. This is achieved by integrating a nearest neighbors penalization mechanism into the framework, which provably controls the FDR at the user-defined target level. A real-world example of sparse index tracking demonstrates the proposed method’s ability to accurately track the S&P 500 index over the past 20 years based on a small number of stocks. An open-source implementation is provided within the R package TRexSelector on CRAN.

False discovery rate (FDR) control is a popular approach for maintaining the integrity of statistical analyses, especially in high-dimensional data settings, where multiple comparisons increase the risk of false positives. FDR control has been extensively researched for real-valued data. However, the complex data case, which is relevant for many signal processing applications, remains widely unexplored. We therefore present a fast and FDR-controlling variable selector for complex-valued high-dimensional data. The proposed Complex-Valued Terminating-Random Experiments (CT-Rex) selector controls a user-defined target FDR while maximizing the number of selected variables. This is achieved by optimally fusing the solutions of multiple early terminated complex-valued random experiments. We benchmark the performance in sparse complex regression simulation studies and showcase an example of FDR-controlled compressed-sensing-based single snapshot multi-source detection and direction of arrival (DOA) estimation. The proposed work applies to a wide range of research areas, such as DOA estimation, communications, mechanical engineering, and magnetic resonance imaging, bridging a critical gap in signal processing for complex-valued data.

We propose the Terminating-Random Experiments (T-Rex) selector, a fast variable selection method for high-dimensional data. The T-Rex selector controls a user-defined target false discovery rate (FDR) while maximizing the number of selected variables. This is achieved by fusing the solutions of multiple early terminated random experiments. The experiments are conducted on a combination of the original predictors and multiple sets of randomly generated dummy predictors. A finite sample proof based on martingale theory for the FDR control property is provided. Numerical simulations confirm that the FDR is controlled at the target level while allowing for high power. We prove that the dummies can be sampled from any univariate probability distribution with finite expectation and variance. The computational complexity of the proposed method is linear in the number of variables. The T-Rex selector outperforms state-of-the-art methods for FDR control in numerical experiments and on a simulated genome-wide association study (GWAS), while its sequential computation time is more than two orders of magnitude lower than that of the strongest benchmark methods. The open source R package TRexSelector containing the implementation of the T-Rex selector is available on CRAN.

Algorithms that ensure reproducible findings from large-scale, high-dimensional data are pivotal in numerous signal processing applications . In recent years, multivariate false discovery rate (FDR) controlling methods have emerged, providing guarantees even in high-dimensional settings where the number of variables surpasses the number of samples. However, these methods often fail to reliably control the FDR in the presence of highly dependent variable groups, a common characteristic in fields such as genomics and finance. To tackle this critical issue, we introduce a novel framework that accounts for general dependency structures. Our proposed dependency-aware T-Rex selector integrates hierarchical graphical models within the T-Rex framework to effectively harness the dependency structure among variables. Leveraging martingale theory, we prove that our variable penalization mechanism ensures FDR control. We further generalize the FDR-controlling framework by stating and proving a clear condition necessary for designing both graphical and non-graphical models that capture dependencies. Numerical experiments and a breast cancer survival analysis use-case demonstrate that the proposed method is the only one among the state-of-the-art benchmark methods that controls the FDR and reliably detects genes that have been previously identified to be related to breast cancer. An open-source implementation is available within the R package TRexSelector on CRAN.

Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection. Sparse PCA algorithms are usually expressed as a trade-off between explained variance and sparsity of the loading vectors (i.e., number of selected variables). As a high explained variance is not necessarily synonymous with relevant information, these methods are prone to select irrelevant variables. To overcome this issue, we propose an alternative formulation of sparse PCA driven by the false discovery rate (FDR). We then leverage the Terminating-Random Experiments (T-Rex) selector to automatically determine an FDR-controlled support of the loading vectors. A major advantage of the resulting T-Rex PCA is that no sparsity parameter tuning is required. Numerical experiments and a stock market data example demonstrate a significant performance improvement.

Mismatches between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple-target tracking or multi-person contactless vital sign monitoring may be severely affected by mismatched sample-channel assignments. To address this issue systematically, we frame it as a signal reconstruction problem where correspondences between samples and channels are lost. Assuming a sensing matrix for the signals, we show the problem’s equivalence to a highly structured unlabeled sensing problem and establish conditions for unique recovery. This is crucial since existing unlabeled sensing theory is inapplicable and results for reconstructing shuffled multi-channel signals do not yet exist. Our results extend to continuous-time sparse signals, and we derive conditions for reconstructing shuffled sparse signals. For the two-channel case, we provide a first reconstruction method, which combines sparse signal recovery with robust linear regression, outperforming existing unlabeled sensing methods in numerical experiments. Additionally, we showcase its effectiveness in a real-world application involving calcium imaging traces. Our theory marks a significant initial step in addressing this challenging signal reconstruction problem, with potential extensions to diverse signal representations encountered in real-world problems with imprecise measurement or channel assignment.

We address the problem of robust network localization in realistic mixed LOS/NLOS environments. We make use of the fact that the bias of range measurement errors is not only non-negative but also sparse when LOS dominates, which has been long overlooked in the existing literature. To exploit these two properties, we introduce a sparsity-promoting regularization term and relax the resulting optimization problem to a semi-definite programming (SDP) problem. The proposed method admits a neat mathematical formulation and is computationally cheap. Moreover, its global convergence is guaranteed and it achieves good robustness against NLOS measurements. In numerical results, the proposed method outperforms representative state-of-the-art SDP approaches, in terms of both localization accuracy and computational efficiency.

The problem of deciding whether a given set of data points forms one cluster or two clusters is investigated from a robust hypothesis testing perspective. It is assumed that a clustering algorithm exists that for both cases calculates cluster assignments and estimates of the corresponding probability density functions. Based on the latter, a statistical hypothesis test for the true number of clusters is formulated. In order to take falsely labeled data points into account, the clusters are then modeled as being contaminated with outliers. This leads to an uncertainty model for the cluster densities of the ε-contamination type, whose corresponding minimax optimal robust detector is well-known and can be implemented using least favorable densities. The performance of this detector under cluster overlap, cluster imbalance, and for different contamination ratios is evaluated numerically and is compared to that of a Bayesian cluster enumeration criterion. Significant performance improvements are shown in all cases.

Conventional approaches to matrix completion are sensitive to outliers and impulsive noise. This paper develops robust and computationally efficient M-estimation based matrix completion algorithms. By appropriately arranging the observed entries, and then applying alternating minimization, the robust matrix completion problem is converted into a set of regression M-estimation problems. Making use of differentiable loss functions, the proposed algorithm overcomes a weakness of the ℓp-loss (p ≤ 1), which easily gets stuck in an inferior point. We prove that our algorithm converges to a stationary point of the nonconvex problem. Huber's joint M-estimate of regression and scale can be used as a robust starting point for Tukey's redescending M-estimator of regression based on an auxiliary scale. Numerical experiments on synthetic and real-world data demonstrate the superiority to state-of-the-art approaches.

This paper is meant to share our experience on signal processing hands-on opportunities within the formal engineering education at Technische Universität Darmstadt. It is our strong belief that undergraduate students should be offered hands-on opportunities from the very beginning of their studies until their graduation. We describe our projects, lectures and seminars that we provide undergraduate students to gain hands-on experience inside signal processing along the time line of the curriculum. We further describe the variety of laboratories that we offer to expose students to state-of-the-art research and advanced equipment. Finally, we conclude by illustrating how we use competitions to motivate and challenge students with real-world problems.

The Bayesian information criterion is generic in the sense that it does not include information about the specific model selection problem at hand. Nevertheless, it has been widely used to estimate the number of data clusters in cluster analysis. We have recently derived a Bayesian cluster enumeration criterion from first principles which maximizes the posterior probability of the candidate models given observations. But, in the finite sample regime, the asymptotic assumptions made by the criterion, to arrive at a computationally simple penalty term, are violated. Hence, we propose a Bayesian cluster enumeration criterion whose penalty term is derived by removing the asymptotic assumptions. The proposed algorithm is a two-step approach which uses a model-based clustering algorithm such as the EM algorithm before applying the derived criterion. Simulation results demonstrate the superiority of our criterion over existing Bayesian cluster enumeration criteria.

We propose an improved version of the non-negative independent component analysis algorithm that uses a multiplicative update rule (M-NICA). We examine a challenging NICA application in a noise-embedded multi-speaker voice activity detection (VAD) setup. We present a novel approach that includes sparsity constraints to solve the energy separation problem with independent source signals. A sparse feature extraction step is performed to project the non-negative signals onto a dimension-reduced subspace and identify sparse principal components. Then, we maximize the signal decorrelation by employing a median measure of central tendency in the computation of the covariance matrix that contributes in robustness against outliers. Moreover, our approach supplies a straightforward multi-speaker VAD, for which no empirical thresholding or other ad-hoc decision rule is required. Instead, an active voice frame simply corresponds to a non-zero value of the separated energy signal. Numerical experiments using real data validate the superior performance of the proposed technique.

Today's wireless sensor networks provide the possibility to monitor physical environments via small low-cost wireless devices. Given the large amount of sensed data, efficient and robust classification becomes a critical task in many applications. Typically, the devices must operate under stringent power and communication constraints and the transmission of observations to a fusion center (FC) is, in many cases, infeasible or undesired. A challenging research question in such cases is the design of data clustering and classification rules when each sensor collects a set of unlabelled observations that are drawn from a known number of classes. We propose two robust distributed hybrid classification algorithms, i.e., the Diffusion K-Medians and the Communicationally Efficient Distributed K-Medians. An extensive performance analysis in comparison to a benchmark algorithm is provided that investigates the error rates in dependence of different parameters of a distributed sensor network, and also considers communication cost. Our proposed algorithms, which are insensitive to outliers and various parameters, are applicable to on-line classification problems and scale well w.r.t. the number of classes.

A novel algorithm for distributed labeling of speech sources is proposed. We consider a wireless sensor network comprising devices that are equipped with multiple microphones, which can “hear” a number of speech signals. The labeling task is performed in a decentralized fashion with a new two-step approach. The first step corresponds to the distributed extraction of proper source-specific features from the mixed signals. In the second step, these features are exploited via a distributed unsupervised learning technique. We present approaches that can be used in hierarchically organized or in non-hierarchically organized network configurations. Numerical examples using real data display the performance of the proposed technique.

The detection of abrupt changes in signals that are observed by wireless sensor networks (WSN), is an important research area with potential applications, e.g., in fault detection, prediction of natural catastrophic events, and speech segmentation. We consider the distributed robust detection of changes in the parameters of autoregressive (AR) models. Our method is robust on a single sensor level by suppressing the effect of outliers and impulsive noise via a robustified distance metric between a long-term and a short-term AR model. The new distributed change detector works without a fusion center and incorporates a weighting based on signal-to-noise-ratio (SNR) information, to ensure that every node will, at least, maintain its single node performance. A Monte-Carlo simulation study is provided which compares the proposed detector to a centralized version, in terms achievable detection rates and mean detection delay. Furthermore, an application example of distributed voice activity detection for a noisy speech signal is given.

Solving a linear inverse problem may include difficulties such as the presence of outliers and a mixing matrix with a large condition number. In such cases a regularized robust estimator is needed. We propose a new-type regularized robust estimator that is simultaneously highly robust against outliers, highly efficient in the presence of purely Gaussian noise, and also stable when the mixing matrix has a large condition number. We also propose an algorithm to compute the estimates, based on a regularized iterative reweighted least squares algorithm. A basic and a fast version of the algorithm are given. Finally, we test the performance of the proposed approach using numerical experiments and compare it with other estimators. Our estimator provides superior robustness, even up to 40% of outliers, while at the same time performing quite close to the optimal maximum likelihood estimator in the outlier-free case.

Testing the stationarity of stochastic processes is required in a variety of signal processing applications. When dealing with real-world problems, the presence of outliers and impulsive (heavy-tailed) noise causes classical stationarity tests to break down. In this work, a set of robust stationarity tests that are based on a sphericity statistic test (SST) in the frequency domain is proposed. Different possible approaches are investigated and compared to existing robust and non-robust stationarity tests in terms of the receiver operating characteristic (ROC). In addition to extensive simulations, a real-world data example of a malfunctioning window regulator motor, for which the dominant frequencies show a modulating character that results in a non-stationary signal, is investigated. Both for simulated and real-world data, the proposed methods significantly outperform existing approaches.

The bootstrap is a powerful computational tool for statistical inference that allows for the estimation of the distribution of an estimate without distributional assumptions on the underlying data, reliance on asymptotic results or theoretical derivations. On the other hand, robustness properties of the bootstrap in the presence of outliers are very poor, irrespective of the robustness of the underlying estimator. This motivates the need to robustify the bootstrap procedure itself. Improvements to two existing robust bootstrap methods are suggested and a novel approach for robustifying the bootstrap is introduced. The methods are compared in a simulation study and the proposed method is applied to robust geolocation.

Intracranial pressure (ICP) is an important physiological signal for patients with traumatic brain injuries. Accurate ICP forecasting enables active and early interventions for more effective control of ICP levels. To achieve high accuracy, most existing methods require a high sampling rate (100 Hz), which is infeasible for online medical applications. Therefore, we propose an online ICP forecasting method requiring only low rate signal sampling (0.1 Hz). Our ARIMA based forecasting method applies empirical mode decomposition (EMD) to remove non-stationarities from the ICP signal, and robust estimation to mitigate the influence of motion induced artifacts. Experimental performance assessment with simulated and clinically collected data demonstrate that the proposed method is more accurate compared to previously proposed and standard methods.

There has been much activity on model selection for multi-dimensional data in recent years under the assumption of a Gaussian noise distribution. However, methods which are optimal for Gaussian noise are very sensitive against brief sensor failures. We suggest two robust model order selection schemes for multi-dimensional data based on the MM-estimator of the covariance of the r-mode unfoldings of the complex valued data tensor. Simulation results are given for 2-D and 3-D uniform rectangular arrays based source enumeration, both for Gaussian noise and a brief sensor failure.

Corneal height data, typically measured with a videokeratoscope, is modeled as a set of Zernike polynomials. Accurate corneal modeling is important, e.g. prior to surgery. The measurements require a good quality of the pre-corneal tear film and sufficiently wide eyelid aperture, which is not always fulfilled in practice. This results in missing values or outliers in the corneal topography map. We suggest to treat this problem by a new two step model selection procedure and introduce a criterion based on r-estimation, which is simultaneously statistically robust and efficient. For this, we exploit the asymptotic equivalence of τ-estimation to M-estimation. The performance is evaluated using simulations, as well as real data.