A common assumption in matrix completion (MC) and tensor completion (TC) is that the missing locations are sampled randomly. However, in real-world scenarios, the unobserved elements are often not arbitrarily located, and may concentrate within entire rows or columns. We refer to this missing mechanism as structural missingness, and traditional MC and TC schemes suffer from drastic degradation under these circumstances. This work addresses the challenge of restoring structural missingness by introducing a novel framework for simultaneously reconstructing multiple matrices, called multi-matrix completion (MMC). In MMC, tri-factorization across matrices captures the correlation between matrices, and Tikhonov regularization on each matrix exploits its correlation. This design enables MMC to efficiently handle both random and structural missingness. In addition, MMC is not affected by the smoothness along matrices which makes it suitable for a wider variety of data compared to Fourier transform based TC methods. The alternating direction method of multipliers is utilized to solve the resultant optimization problem. The global convergence of the algorithm is supported by comprehensive theoretical analyses. We demonstrate the versatility of MMC through extensive experiments in image and video restoration, and showcase its superior performance in comparison to traditional MC and TC methods.

A nonparametric variant of the Kiefer-Weiss problem is proposed and solved. The objective is to minimize a weighted sum of the error probabilities of a binary sequential test subject to a constraint on its maximum expected sample size. This maximum is taken over all possible probability distributions on the given sequence space. First, it is shown that the nonparametric Kiefer-Weiss problem can be reduced to an optimal stopping problem. Then, the optimal stopping policy is derived under the assumption that at most k uses of randomization are permitted during any run of the test. The solution to the original problem is then obtained by letting k go to infinity. The optimal cost function is shown to be the solution of a nonlinear Bellman equation. The corresponding optimal stopping policy is shown to be based on a two-dimensional test statistic, with one component tracking the likelihood ratio and the other one tracking the expected remaining sample size. Critically, the stopping policy uses randomization to increase the remaining expected sample size for some runs, while stopping early for others. The optimal randomization rule is shown to be determined by a function that maps the likelihood ratio to an integer-valued sample size. Two approximations of this function are proposed that can be evaluated easily in practice. The results are illustrated with two numerical examples of nonparametric Kiefer-Weiss tests, one for a shift in the success probability of a Bernoulli distribution, and one for a shift in the mean of a normal distribution.

We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data given the parameter of interest, is subject to uncertainty. Both, a Bayesian formulation and a Neyman-Pearson-like formulation, are considered. It is shown that the optimal policy induces an f-similarity that must be maximized to identify the least favorable distributions. Besides the general results, the implementation is investigated using a band-type uncertainty model. For designing the minimax procedures, existing algorithms are modified to increase convergence speed while maintaining numerical stability. The proposed theory is supplemented by numerical results for both formulations.

The detection of interesting or anomalous signal behavior using sensor networks plays a key role in many applications. In this work, we model the sensor network as a graph, with each vertex representing a sensor and a signal over time associated with each vertex. The objective is to identify the true state of the signal at each point in the joint spatio-temporal domain. We propose a step-up empirical Bayes multiple hypothesis testing approach to make decisions based on local summary statistics. To this end, we establish consistent estimates of the prior probability of the null hypothesis as well as the probability models under the alternative, which are obtained using a bandlimited generalized graph signal model. Asymptotic control of the false discovery rate is proven. Numerical experiments validate the effectiveness of our approach compared to existing methods.

In this paper, we design Graph Neural Networks (GNNs) with attention mechanisms to tackle an important yet challenging nonlinear regression problem: massive network localization. We first review our previous network localization method based on Graph Convolutional Network (GCN), which can exhibit state-of-the-art localization accuracy, even under severe Non-Line-of-Sight (NLOS) conditions, by carefully preselecting a constant threshold for determining adjacency. As an extension, we propose a specially designed Attentional GNN (AGNN) model to resolve the sensitive thresholding issue of the GCN-based method and enhance the underlying model capacity. The AGNN comprises an Adjacency Learning Module (ALM) and Multiple Graph Attention Layers (MGALs), employing distinct attention architectures to systematically address the demerits of the GCN-based method, rendering it more practical for real-world applications. Comprehensive analyses are conducted to explain the superior performance of these methods, including a theoretical analysis of the AGNN's dynamic attention property and computational complexity, along with a systematic discussion of their robust characteristic against NLOS measurements. Extensive experimental results demonstrate the effectiveness of the GCN-based and AGNN-based network localization methods. Notably, integrating attention mechanisms into the AGNN yields substantial improvements in localization accuracy, approaching the fundamental lower bound and showing approximately 37% to 53% reduction in localization error compared to the vanilla GCN-based method across various NLOS noise configurations. Both methods outperform all competing approaches by far in terms of localization accuracy, robustness, and computational time, especially for considerably large network sizes.

We propose the Cyclic-Volatility Influence Function (CV-IF) Bootstrap - a resampling methodology that unifies pe-riodic and stochastic components in time series. The framework addresses challenges in modeling signals with deterministic periodicity coupled with stochastic variability. Two implementations of the framework are presented: GARCH-IF, applied to heating consumption data, and Gated Sin-IF, applied to solar production data. By using an empirical influence function to weight residuals and correct for both seasonality and volatility, our method provides improved inference and uncertainty quantification compared to standard bootstrap techniques.

Vital sign monitoring plays a critical role in healthcare and well-being, as parameters such as respiration and heart rate offer valuable insights into an individual's physiological state. While wearable devices allow for continuous measurement, their use in settings like in-home elderly care is often hindered by discomfort or user noncompliance. As a result, contactless solutions based on radar sensing have garnered increasing attention. This is due to their unobtrusive design and preservation of privacy advantages compared to camera-based systems. However, a single radar perspective can fail to capture breathing-induced chest movements reliably, particularly when the subject's orientation is unfavorable. To address this limitation, we integrate a reconfigurable intelligent surface (RIS) that provides an additional sensing path, thereby enhancing the robustness of respiratory monitoring. We present a novel model for multi-path vital sign sensing that leverages both the direct radar path and an RIS-reflected path. We further discuss the potential benefits and improved performance our approach offers in continuous, privacy-preserving vital sign monitoring.

This paper presents a novel loss function referred to as hybrid ordinary-Welsch (HOW) and a new sparsity-inducing regularizer associated with HOW. We theoretically show that the regularizer is quasiconvex and that the corresponding Moreau envelope is convex. Moreover, the closed-form solution to its Moreau envelope, namely, the proximity operator, is derived. Compared with nonconvex regularizers like the lp-norm with 0

We consider the multiple hypothesis testing (MHT) problem over the joint domain formed by a graph and a measure space. On each sample point of this joint domain, we assign a hypothesis test and a corresponding p-value. The goal is to make decisions for all hypotheses simultaneously, using all available p-values. In practice, this problem resembles the detection problem over a sensor network during a period of time. To solve this problem, we extend the traditional two-groups model such that the prior probability of the null hypothesis and the alternative distribution of p-values can be inhomogeneous over the joint domain. We model the inhomogeneity via a generalized graph signal. This more flexible statistical model yields a more powerful detection strategy by leveraging the information from the joint domain.

The block diagonal structure of an affinity matrix is a commonly desired property in cluster analysis because it represents clusters of feature vectors by non-zero coefficients that are concentrated in blocks. However, recovering a block diagonal affinity matrix is challenging in real-world applications, in which the data may be subject to outliers and heavy-tailed noise that obscure the hidden cluster structure. To address this issue, we first analyze the effect of different fundamental outlier types in graph-based cluster analysis. A key idea that simplifies the analysis is to introduce a vector that represents a block diagonal matrix as a piece-wise linear function of the similarity coefficients that form the affinity matrix. We reformulate the problem as a robust piece-wise linear fitting problem and propose a Fast and Robust Sparsity-Aware Block Diagonal Representation (FRS-BDR) method, which jointly estimates cluster memberships and the number of blocks. Comprehensive experiments on a variety of real-world applications demonstrate the effectiveness of FRS-BDR in terms of clustering accuracy, robustness against corrupted features, computation time and cluster enumeration performance.

To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the thresholding functions of these nonconvex regularizers may not have closed-form expressions and thus iterations are needed, which increases the computational loads. To solve this issue, we devise a framework to generate sparsity-inducing regularizers with closed-form thresholding functions. These regularizers are applied to low-tubal-rank tensor completion, and efficient algorithms based on the alternating direction method of multipliers are developed. Furthermore, convergence of our methods is analyzed and it is proved that the generated sequences are bounded and any limit point is a stationary point. Experimental results using synthetic and real-world datasets show that the proposed algorithms outperform the state-of-the-art methods in terms of restoration performance.

We propose two robust seasonal bootstrap techniques, based on our prior work, the Complex Seasonal Circular Block Bootstrap (XSCBB). These robustifications are implemented through two methods, the Block Robust Empirical Standardised Influence Function (BRESIF or Block RESIF) and the Block Average XSCBB (BA-XSCBB) methods. The BRESIF-XSCBB method employs an adaptive weighting function to adjust the XSCBB technique for time series with heavy-tailed distributions or extreme values. Conversely, the Block-Average/Median XSCBB strategy seeks to reduce the influence of outliers by incorporating either the block average or median to restore the seasonal characteristics. Through simulation studies, we showcase the efficacy of these methods in enhancing the XSCBB's performance when outliers are present. Our results indicate that these robustified versions of XSCBB not only pre-serve the original method's capacity to detect complex seasonal patterns but also significantly enhance resilience and accuracy in challenging data scenarios.

We propose the Block-Toeplitz Bootstrap method, which we have named the Blitz-Boot, and apply it to improve the estimation of Direction of Arrival (DOA) and frequency estimation in compressed sensing applications. This method employs a joint frequency-DOA estimation approach based on the Finite Rate of Innovation (FRI) principle. Empirical results reveal that Blitz-Boot enhances this estimation process. We present accuracy metrics for various block lengths and across different Signal to Noise Ratios (SNRs), demonstrating that the Blitz-Boot method notably improves performance, especially in environments characterized by lower SNRs. Furthermore, we provide a performance comparison with the Cramér-Rao Lower Bound, underscoring the efficacy of our proposed method.

Dual-function radar and communications (DFRC) systems based on multiple-input multiple-output (MIMO) arrays have received considerable attention in recent years due to their excellent ability to alleviate spectrum congestion. The MIMO DFRC systems enable high-resolution detection of multiple targets while communicating with multiple users simultaneously. However, MIMO arrays require numerous radio frequency (RF) units and suffer a strong mutual coupling among antennas, resulting in significant system overhead and performance degradation, respectively. In light of this, this paper investigates the joint optimization of transmit precoding and antenna selection for MIMO DFRC systems, aiming to improve the angular ambiguity function with a guaranteed communication quality of service (QoS) using a small number of antennas. To address the resultant non-convex optimization problem, both the indirect and direct precoding methods are proposed. In the former, the waveform covariance and antenna selection vector are first jointly optimized via a promoted sparsity along the covariance diagonal, followed by the precoding matrix indirectly derived from the optimal covariance. In the latter, the precoding matrix is directly optimized via an imposed group sparsity under the communication QoS and power constraints. Simulation results demonstrate that the proposed sparse MIMO DFRC system with fewer active antennas can achieve comparable dual-functional performance to that of the full array system.

The MALTA family of Depleted Monolithic Active Pixel Sensors (DMAPS) is produced using Tower 180 nm CMOS technology, specifically targeting radiation-hard applications in the HL-LHC and beyond. Several process modifications have resulted in radiation hardness up to ${3 \times 10^{15}~1 ~\text{MeV}~\text{n}_{\text{eq}} /\text{cm}^2}$ and time resolution below 2 ns, with uniform charge collection efficiency across the chip formed of $512 \times 224$ pixels with a size of $36.4 \times 36.4~\mu\text{m}^2$. This is achieved when adopting high-resistivity Czochralski substrates with backside metallisation to obtain a good propagation of the bias voltage. This contribution will show the most recent results obtained on MALTA2 chip demonstrators, including signal efficiency, noise occupancy and time resolution, at different levels of irradiation as well as the performance of the MALTA telescope permanently installed at the SPS at CERN and used in the test beam campaign in 2021-2023.

The large number and scale of natural and man-made disasters have led to an urgent demand for technologies that enhance the safety and efficiency of search and rescue teams. Semi-autonomous rescue robots are beneficial, especially when searching inaccessible terrains, or dangerous environments, such as collapsed infrastructures. For search and rescue missions in degraded visual conditions or non-line of sight scenarios, radar-based approaches may contribute to acquire valuable, and otherwise unavailable information. This article presents a complete signal processing chain for radar-based multi-person detection, 2D-MUSIC localization and breathing frequency estimation. The proposed method shows promising results on a challenging emergency response dataset that we collected using a semi-autonomous robot equipped with a commercially available through-wall radar system. The dataset is composed of 62 scenarios of various difficulty levels with up to five persons captured in different postures, angles and ranges including wooden and stone obstacles that block the radar line of sight. Ground truth data for reference locations, respiration, electrocardiogram, and acceleration signals are included. The full emergency response benchmark data set as well as all codes to reproduce our results, are publicly available at https://doi.org/10.21227/4bzd-jm32.

MALTA2 is the latest full-scale prototype of the MALTA family of Depleted Monolithic Active Pixel Sensors (DMAPS) produced in Tower Semiconductor 180 nm CMOS technology. In order to comply with the requirements of High Energy Physics (HEP) experiments, various process modifications and front-end changes have been implemented to achieve low power consumption, reduce Random Telegraph Signal (RTS) noise, and optimise the charge collection geometry. Compared to its predecessors, MALTA2 targets the use of a high-resistivity, thick Czochralski (Cz) substrates in order to demonstrate radiation hardness in terms of detection efficiency and timing resolution up to 3E15 1 MeV neq/cm2 with backside metallisation to achieve good propagation of the bias voltage. This manuscript shows the results that were obtained with non-irradiated and irradiated MALTA2 samples on Cz substrates from the CERN SPS test beam campaign from 2021-2023 using the MALTA telescope.

Synthetic aperture radar (SAR) images are inherently affected by speckle noise. Deep learning-based methods have shown good potential in image denoising task. Most deep learning methods for denoising focus on additive Gaussian noise removal. However, SAR images are usually contaminated by non-Gaussian multiplicative speckle noise. In this paper, we propose a novel deep unrolling network named SAR-DURNet to deal with the SAR image despeckling problem. We establish optimization problem of speckle noise removal by using the priori of noise distribution, which can be sovled by half-quadratic splitting (HQS) method with iterative steps. We unroll the iterative process into a trainable deep unrolling network(SAR-DURNet). The parameters of the SAR-DURNet are trained end-to-end with simulated SAR image dataset. Experimental results on simulated test data and real SAR data show that the proposed approach has superior results in terms of quantitative performance metrics and the preservation of intricate visual details, compared to several well-known SAR image despeckling methods.

The instantaneous velocity of any moving object can be decomposed into two orthogonal components with reference to the observing radar, namely, radial velocity along the radar line of sight (LoS) and transversal velocity perpendicular to the LoS. It has been shown that the measurement of transversal velocity can significantly improve the performance of both radar target tracking and classification. Furthermore, the precision of transversal velocity estimation is proportional to the baseline length using static interferometry. However, the large baseline is impractical in applications, such as automotive radar with restrictions on the packaging size. This letter proposes synthetic interferometry exploiting radar motions. A large virtual baseline can be synthesized by moving the side-looking radar and synchronizing the received signals at two locations, thus improving the accuracy of transversal velocity measurement. We derive the conditions of time synchronization for successful interferometry in terms of the maximum moving distance and the maximum observation time. Both simulations and experiments have been conducted to validate the feasibility and effectiveness of the proposed synthetic interferometry.

We propose the Complex Seasonal Circular Block Bootstrap (XSCBB), a variation of seasonal (circular) block bootstrap that caters for multiple seasonality components in a time series. Electricity consumption (load) prediction is important to balance the supply and load demand, to plan facilities construction and maintenance, to plan distribution, and avoid outages or excess loss. We apply the XSCBB method parametrically to calculate the prediction interval of future electricity consumption given a relatively small amount of historical sample points using the composite ARMA(p, q) - GARCH(r, s) model.