In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters. Specifically, we show how a node-wise convolution for signals supported on a graph can be expressed as another node-wise convolution in a frequency domain graph, different from the original graph. This is achieved through a parameterization of the filter coefficients following a basis expansion model. After showing how the presented theorem is consistent with the already existing body of literature, we discuss its implications in terms of non-stationarity. Finally, we propose a data-driven algorithm based on subspace fitting to learn the frequency domain graph, which is then corroborated by experimental results on synthetic and real data.

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Four-dimensional ultrasound imaging of complex biological systems such as the brain is technically challenging because of the spatiotemporal sampling requirements. We present computational ultrasound imaging (cUSi), an imaging method that uses complex ultrasound fields that can be generated with simple hardware and a physical wave prediction model to alleviate the sampling constraints. cUSi allows for high-resolution four-dimensional imaging of brain hemodynamics in awake and anesthetized mice.

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We consider the problem of recovering complex-valued block sparse signals with unknown borders. Such signals arise naturally in numerous applications. Several algorithms have been developed to solve the problem of unknown block partitions. In pattern-coupled sparse Bayesian learning (PCSBL), each coefficient involves its own hyperparameter and those of its immediate neighbors to exploit the block sparsity. Extended block sparse Bayesian learning (EBSBL) assumes the block sparse signal consists of correlated and overlapping blocks to enforce block correlations. We propose a simpler alternative to EBSBL and reveal the underlying relationship between the proposed method and a particular case of EBSBL. The proposed algorithm uses the fact that immediate neighboring sparse coefficients are correlated. The proposed model is similar to classical sparse Bayesian learning (SBL). However, unlike the diagonal correlation matrix in conventional SBL, the unknown correlation matrix has a tridiagonal structure to capture the correlation with neighbors. Due to the entanglement of the elements in the inverse tridiagonal matrix, instead of a direct closed-form solution, an approximate solution is proposed. The alternative algorithm avoids the high dictionary coherence in EBSBL, reduces the unknowns of EBSBL, and is computationally more efficient. The sparse reconstruction performance of the algorithm is evaluated with both correlated and uncorrelated block sparse coefficients. Simulation results demonstrate that the proposed algorithm outperforms PCSBL and correlation-based methods such as EBSBL in terms of reconstruction quality. The numerical results also show that the proposed correlated SBL algorithm can deal with isolated zeros and nonzeros as well as block sparse patterns.

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Hearing impairment is a prevalent problem with daily challenges like impaired speech intelligibility and sound localisation. One of the shortcomings of spatial filtering in hearing aids is that speech intelligibility is often not optimised directly, meaning that different auditory processes contributing to intelligibility are often not considered. One example is the perceptual phenomenon known as spatial release from masking (SRM). This paper develops a signal model that explicitly considers SRM in the beamforming design, achieved by transforming the binaural intelligibility prediction model (BSIM) into a signal processing framework. The resulting extended signal model is used to analyse the performance of reference beamformers and design a novel beamformer that more closely considers how the auditory system perceives binaural sound. It can be shown that the binaural minimum variance distortionless response (BMVDR) beamformer is also an optimal solution for the extended, perceived model, suggesting that SRM does not play a significant role in intelligibility enhancement after optimal beamforming. However, the optimal beamformer is no longer unique in the extended signal model. The additional secondary degrees of freedom can be used to preserve binaural cues of interfering sources while still achieving the same perceived performance of the BMVDR beamformer, though with a possible high sensitivity to intelligibility model mismatch errors.

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Computational ultrasound imaging (cUSi) offers high-resolution 3D imaging with simpler hardware by relying on computational power. Central to cUSi is a large model matrix that stores all pulse-echo signals. For 3D imaging this matrix easily surpasses 1 terabyte, hindering in-memory storage and real-time processing. This paper presents a solution for cUSi through an aberrating layer by introducing a virtual array concept, which uses transfer functions to map data from the real to a virtual array, enabling the use of conventional reconstruction techniques like delay-and-sum (DAS). We demonstrate the mathematical similarity of this approach to using a full model matrix and validate it with promising imaging results.@en

A new method for joint ranging and Phase Offset (PO) estimation of multiple drones/aircrafts is proposed in this paper. The proposed method employs the superimposed uncoordinated Automatic Dependent Surveillance-Broadcast (ADS-B) packets broadcasted by drones/aircrafts for joint range and PO estimation. It jointly estimates range and PO prior to ADS-B packet decoding; thus, it can improve air safety when packet decoding is infeasible due to packet collision. Moreover, it enables coherent detection of ADS-B packets, which can result in more reliable multiple target tracking in aviation systems using cooperative sensors for detect and avoid (DAA). By minimizing the Kullback-Leibler Divergence (KLD) statistical distance measure, we show that the received complex baseband signal coming from K uncoordinated drones/aircrafts corrupted by Additive White Gaussian Noise (AWGN) at a single antenna receiver can be approximated by an independent and identically distributed (i.i.d.) Gaussian Mixture (GM) with 2^{K} mixture components in the two-dimensional (2D) plane. While direct joint Maximum Likelihood Estimation (MLE) of range and PO from the derived GM Probability Density Function (PDF) leads to an intractable maximization, our proposed method employs the Expectation-Maximization (EM) algorithm to estimate the modes of the 2D Gaussian mixture followed by a reordering estimation technique through combinatorial optimization to estimate range and PO. An extension to a multiple antenna receiver is also investigated in this article. While the proposed estimator can estimate the range of multiple drones/aircrafts with a single receive antenna, a larger number of drones/aircrafts can be supported with higher accuracy by the use of multiple antennas at the receiver. The effectiveness of the proposed estimator is supported by simulation results. We show that the proposed estimator can jointly estimate the range of multiple drones/aircrafts accurately.

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In this paper, we propose a new method for joint ranging and Phase Offset (PO) estimation of multiple transponder-equipped aviation vehicles (TEAVs), including Manned Aerial Vehicles (MAVs) and Unmanned Aerial Vehicles (UAVs). The proposed method employs the overlapping uncoordinated Automatic Dependent Surveillance-Broadcast (ADS-B) packets broadcasted by the TEAVs for joint range and PO estimation prior to ADS-B packet decoding; thus, it can improve air safety when packet decoding is infeasible due to packet collision. Moreover, it enables coherent detection of ADS-B packets, which can result in more reliable multiple target tracking in aviation systems using cooperative sensors for sense and avoid. By minimizing the Kullback-Leibler Divergence (KLD), we show that the received complex baseband signal, coming from K uncoordinated TEAVs, which is corrupted by Additive White Gaussian Noise (AWGN) at a single antenna receiver can be approximated by an independent and identically distributed (i.i.d.) Gaussian Mixture (GM) with 2^K mixture components in the two-dimensional plane. The proposed estimator employs the Expectation-Maximization (EM) algorithm to estimate the modes of the 2D Gaussian mixture followed by a reordering estimation technique to jointly estimate range and PO. Simulation results show that the proposed joint estimator outperforms excising methods, such as the time segmentation method and the blind adaptive beamforming.

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CANDECOMP/PARAFAC (CP) decomposition is the mostly used model to formulate the received tensor signal in a massive MIMO system, as the receiver generally sums the components from different paths or users. To achieve accurate and low-latency channel estimation, good and fast CP decomposition (CPD) algorithms are desired. The CP alternating least squares (CPALS) is the workhorse algorithm for calculating the CPD. However, its performance depends on the initializations, and good starting values can lead to more efficient solutions. Existing initialization strategies are decoupled from the CPALS and are not necessarily favorable for solving the CPD. This paper proposes a deep-learning-aided CPALS (DL-CPALS) method that uses a deep neural network (DNN) to generate favorable initializations. The proposed DL-CPALS integrates the DNN and CPALS to a model-based deep learning paradigm, where it trains the DNN to generate an initialization that facilitates fast and accurate CPD. Moreover, benefiting from the CP low-rankness, the proposed method is trained using noisy data and does not require paired clean data. The proposed DL-CPALS is applied to millimeter wave MIMO-OFDM channel estimation. Experimental results demonstrate the significant improvements of the proposed method in terms of both speed and accuracy for CPD and channel estimation.

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The main focus of this paper is an active sensing application that involves selecting transmit and receive sensors to optimize the Cramér-Rao bound (CRB) on target parameters. Although the CRB is non-convex in the transmit and receive selection, we demonstrate that it is convex in the virtual array weight vector, which describes the multiplicity of the virtual array elements. Based on this finding, we propose a novel algorithm that optimizes the virtual array weight vector first and then finds a matching transceiver array. This greatly enhances the efficiency of the transmit and receive sensor selection problem.

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Identifying overlapping communities from data is crucial for grasping the complex structure and dynamics of networks, amongst others in fields such as computational neuroscience. Research using fMRI has demonstrated that brain regions can change their functional network membership over time using temporal independent component analysis (tICA). However, reproducibility of such overlapping communities remains a challenge. Recently, several alternative approaches have been proposed to identify such overlapping communities. While results are promising, less is known about the model and assumptions that underlie these approaches. This paper shows that the bilinear model, combined with the assumption of quasi-stationary and uncorrelated sources, underlies novel methods for identifying overlapping brain networks. Furthermore, we propose a new algorithm, and through simulations, we investigate the robustness of our algorithm and several existing methods to solve the problem in noisy conditions with few available data samples. We conclude that quasi-stationary blind source separation-based techniques can have a promising advantage over tICA in terms of identifiability of overlapping communities and thus have the potential to contribute towards greater reproducibility of results.

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This paper proposes a super-resolution harmonic retrieval method for uncorrelated strictly non-circular signals, whose covariance and pseudo-covariance present Toeplitz and Hankel structures, respectively. Accordingly, the augmented covariance matrix constructed by the covariance and pseudo-covariance matrices is not only low rank but also jointly Toeplitz-Hankel structured. To efficiently exploit such a desired structure for high estimation accuracy, we develop a low-rank Toeplitz-Hankel covariance reconstruction (LRTHCR) solution employed over the augmented covariance matrix. Further, we design a fitting error constraint to flexibly implement the LRTHCR algorithm without knowing the noise statistics. In addition, performance analysis is provided for the proposed LRTHCR in practical settings. Simulation results reveal that the LRTHCR outperforms the benchmark methods in terms of lower estimation errors.@en

Integrated sidelobe level is a useful measure to quantify robustness of a waveform-filter pair to unknown range clutter and multiple closely located targets. Sidelobe suppression on receive will incur a loss in the signal to noise ratio after pulse compression. We derive a pulse compression filter that has the greatest integrated sidelobe suppression possible for a given acceptable signal to noise ratio loss. The solution is given in a closed form, which can be adjusted using a single parameter to chose between greater sidelobe or interference and noise suppression. We verify the derived filter using simulations, comparing it to other proposed mismatched filter designs. To expand the robustness of the filter, we additionally investigate noise uncertainty robustness. We derive two robustness measures for noise uncertainty and analyze the performance through simulation.@en

This article focuses on greedy approaches to select the most informative k sensors from N candidates to maximize the Fisher information, i.e., the determinant of the Fisher information matrix (FIM), which indicates the volume of the information ellipsoid (VIE) constructed by the FIM. However, it is a critical issue for conventional greedy approaches to quantify the Fisher information properly when the FIM of the selected subset is rank-deficient in the first (n-1) steps, where n is the problem dimension. In this work, we propose a new metric, i.e., the Fisher information intensity (FII), to quantify the Fisher information contained in the subset S with respect to that in the ground set N specifically in the subspace spanned by the vectors associated with S. Based on the FII, we propose to optimize the ratio between VIEs corresponding to S and N. This volume ratio is composed of a nonzero (i.e., the FII) and a zero part. Moreover, the volume ratio can be easily calculated based on a change of basis. A cost function is developed based on the volume ratio and proven monotone submodular. A greedy algorithm and its fast version are proposed accordingly to guarantee a near-optimal solution with a complexity of O Nkn-3 and O Nkn2, respectively. Numerical results demonstrate the superiority of the proposed algorithms under various measurement settings.

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Fitting a polynomial to observed data is an ubiquitous task in many signal processing and machine learning tasks, such as interpolation and prediction. In that context, input and output pairs are available and the goal is to find the coefficients of the polynomial. However, in many applications, the input may be partially known or not known at all, rendering conventional regression approaches not applicable. In this paper, we formally state the (potentially partial) blind regression problem, illustrate some of its theoretical properties, and propose an algorithmic approach to solve it. As a case-study, we apply our methods to a jitter-correction problem and corroborate its performance.@en

In this paper, we show the mathematical equivalence of two popular modulation schemes: OSDM and OTFS. The former is mainly used in underwater acoustic communications, while the latter scheme is a promising modulation technique in radio-frequency communications. Although literature suggests a link between the two modulation schemes by connecting them to related modulation schemes like V-OFDM and A-OFDM, to the best of the authors’ knowledge, a direct mathematical comparison between the schemes has not been presented yet. The main purpose of this paper is therefore to show the mathematical equivalence of the two schemes. In addition, by combining the knowledge of acoustic and radio-frequency communications, we give insight in the performance of OSDM/OTFS in terms of intersymbol interference (ISI) and intercarrier interference (ICI) by analyzing its signal structure.@en

We consider the scenario of finding the transfer function of an aberrating layer in front of a receiving ultrasound (US) array, assuming a separate non-aberrated transmit source. We propose a method for blindly estimating this transfer function without exact knowledge of the ultrasound sources or acoustic contrast image, and without directly measuring the transfer function using a separate controlled calibration experiment. Instead, the measurement data of many unknown random images is collected, such as from blood flow, and its second-order statistics are exploited. A measurement model is formulated that explicitly defines the layer's transfer function. A covariance domain problem is then defined to eliminate the image variable, and it is solved for the layer's transfer function using manifold-based optimization. The proposed approach and calibration algorithm are evaluated on a range of challenging and realistic simulations using the k-Wave toolbox. Our results show that, given a sufficiently efficient parameterization of the layer's transfer function, and by jointly estimating the transfer function at multiple frequencies, the proposed algorithm is able to obtain an accurate estimate. Subsequent simulated imaging experiments using the obtained transfer function also show increased imaging performance in various aberrating layers, including a skull layer.

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Sensor selection is a useful method to help reduce computational, hardware, and power requirements while maintaining acceptable performance. Although minimizing the Cramér-Rao bound has been adopted previously for sparse sensing, it did not consider multiple targets and unknown target directions. We propose to tackle the sensor selection problem for direction of arrival estimation using the worst-case Cramér-Rao bound of two uncorrelated equal power sources on planar arrays. We cast the problem as a convex semi-definite program and retrieve the binary selection by randomized rounding. We illustrate the proposed method through numerical examples related to planar arrays. We show that our method selects a combination of edge and center elements, which contrasts with solutions obtained by minimizing the single-target Cramér-Rao bound.@en

We consider the problem of recovering block-sparse signals with unknown boundaries. Such signals arise naturally in various applications. Recent literature introduced a pattern-coupled or clustered Gaussian prior, in which each coefficient involves its own hyperparameter as well as its immediate neighbors' hyperparameters. Some methods use a hierarchical distribution making the solution vulnerable to the parameter choice. Besides, these methods mainly rely on the expectation-maximization (EM) algorithm and either require a suboptimal solution or an approximation of the hyperparameters. To address these difficulties, we propose to solve the pattern coupling problem via fixed point iterations instead of the EM algorithm. The proposed algorithm does not require any further assumptions on the hyperparameters and provides a simple update rule for the hyperparameters. Although the fixed point iterations method is an empirical strategy, it provides a fast convergence rate. The proposed algorithm is tested on a simple direction of arrival (DOA) and amplitude estimation problem. From our simulations, we see that the proposed method achieves similar reconstruction results with the state-of-the-art; however, the proposed method is faster than the existing counterparts.@en

The edge flow reconstruction task consists of retreiving edge flow signals from corrupted or incomplete measurements. This is typically solved by a regularized optimization problem on higher-order networks such as simplicial complexes and the corresponding regularizers are chosen based on prior knowledge. Tailoring this prior to the setting of interest can be challenging or it may not even be possible. Thus, we consider to learn this prior knowledge via a model-based deep learning approach. We propose a new regularized optimization problem for the simplicial edge flow reconstruction task, the simplicial ElasticNet, which combines the advantages of the 1 and 2 norms. We solve the simplicial ElasticNet problem via the multi-block alternating direction method of multipliers (ADMM) algorithm and provide conditions on its convergence. By unrolling the ADMM iterative steps, we develop a model-based neural network with a low requirement on the number of training data. This unrolling network replaces the fixed parameters in the iterative algorithm by learnable weights, thus exploiting the neural network s learning capability while preserving the iterative algorithm s interpretability. We enhance this unrolling network via simplicial convolutional filters to aggregate information from the edge flow neighbors, ultimately, improving the network learning expressivity. Extensive experiments on real-world and synthetic datasets validate the proposed approaches and show considerable improvements over both baselines and traditional non-model-based neural networks.

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Graph-based learning and estimation are fundamental problems in various applications involving power, social, and brain networks, to name a few. While learning pair-wise interactions in network data is a well-studied problem, discovering higher-order interactions among subsets of nodes is still not yet fully explored. To this end, encompassing and leveraging (non)linear structural equation models as well as vector autoregressions, this paper proposes autoregressive graph Volterra models (AGVMs) that can capture not only the connectivity between nodes but also higher-order interactions presented in the networked data. The proposed overarching model inherits the identifiability and expressibility of the Volterra series. Furthermore, two tailored algorithms based on the proposed AGVM are put forth for topology identification and link prediction in distribution grids and social networks, respectively. Real-data experiments on different real-world collaboration networks highlight the impact of higher-order interactions in our approach, yielding discernible differences relative to existing methods.@en