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Brain-Computer Interfaces (BCIs) help people with severe speech and motor disabilities communicate and interact with their environment using neural activity. This work focuses on the Rapid Serial Visual Presentation (RSVP) paradigm of BCIs using noninvasive electroencephalography (EEG). The RSVP typing task is a recursive task with multiple sequences, where users see only a subset of symbols in each sequence. Extensive research has been conducted to improve classification in the RSVP typing task, achieving fast classification. However, these methods struggle to achieve high accuracy and do not consider the typing mechanism in the learning procedure. They apply binary target and non-target classification without including recursive training. To improve performance in the classification of symbols while controlling the classification speed, we incorporate the typing setup into training by proposing a Partially Observable Markov Decision Process (POMDP) approach. To the best of our knowledge, this is the first work to formulate the RSVP typing task as a POMDP for recursive classification. Experiments show that the proposed approach, MarkovType, results in a more accurate typing system compared to competitors. Additionally, our experiments demonstrate that while there is a trade-off between accuracy and speed, MarkovType achieves the optimal balance between these factors compared to other methods., Comment: 9 pages, 4 figures

Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when parts of the system's states are not measured, specifically when the dynamics generating the non-measured states are unknown. Inspired by state estimation theory and Physics Informed Neural ODEs, we present a sequential optimization framework in which dynamics governing unmeasured processes can be learned. We demonstrate the performance of the proposed approach leveraging numerical simulations and a real dataset extracted from an electro-mechanical positioning system. We show how the underlying equations fit into our formalism and demonstrate the improved performance of the proposed method when compared with baselines.

One of the main challenges of federated learning (FL) is handling non-independent and identically distributed (non-IID) client data, which may occur in practice due to unbalanced datasets and use of different data sources across clients. Knowledge sharing and model personalization are key strategies for addressing this issue. Clustered federated learning is a class of FL methods that groups clients that observe similarly distributed data into clusters, such that every client is typically associated with one data distribution and participates in training a model for that distribution along their cluster peers. In this paper, we present a unified Bayesian framework for clustered FL which associates clients to clusters. Then we propose several practical algorithms to handle the, otherwise growing, data associations in a way that trades off performance and computational complexity. This work provides insights on client-cluster associations and enables client knowledge sharing in new ways. The proposed framework circumvents the need for unique client-cluster associations, which is seen to increase the performance of the resulting models in a variety of experiments.

The Kalman filter (KF) and its variants are among the most celebrated algorithms in signal processing. These methods are used for state estimation of dynamic systems by relying on mathematical representations in the form of simple state-space (SS) models, which may be crude and inaccurate descriptions of the underlying dynamics. Emerging data-centric artificial intelligence (AI) techniques tackle these tasks using deep neural networks (DNNs), which are model-agnostic. Recent developments illustrate the possibility of fusing DNNs with classic Kalman-type filtering, obtaining systems that learn to track in partially known dynamics. This article provides a tutorial-style overview of design approaches for incorporating AI in aiding KF-type algorithms. We review both generic and dedicated DNN architectures suitable for state estimation, and provide a systematic presentation of techniques for fusing AI tools with KFs and for leveraging partial SS modeling and data, categorizing design approaches into task-oriented and SS model-oriented. The usefulness of each approach in preserving the individual strengths of model-based KFs and data-driven DNNs is investigated in a qualitative and quantitative study, whose code is publicly available, illustrating the gains of hybrid model-based/data-driven designs. We also discuss existing challenges and future research directions that arise from fusing AI and Kalman-type algorithms., Comment: Submitted to IEEE Signal Processing Magazine

Approaches based on Koopman operators have shown great promise in forecasting time series data generated by complex nonlinear dynamical systems (NLDS). Although such approaches are able to capture the latent state representation of a NLDS, they still face difficulty in long term forecasting when applied to real world data. Specifically many real-world NLDS exhibit time-varying behavior, leading to nonstationarity that is hard to capture with such models. Furthermore they lack a systematic data-driven approach to perform data assimilation, that is, exploiting noisy measurements on the fly in the forecasting task. To alleviate the above issues, we propose a Koopman operator-based approach (named KODA - Koopman Operator with Data Assimilation) that integrates forecasting and data assimilation in NLDS. In particular we use a Fourier domain filter to disentangle the data into a physical component whose dynamics can be accurately represented by a Koopman operator, and residual dynamics that represents the local or time varying behavior that are captured by a flexible and learnable recursive model. We carefully design an architecture and training criterion that ensures this decomposition lead to stable and long-term forecasts. Moreover, we introduce a course correction strategy to perform data assimilation with new measurements at inference time. The proposed approach is completely data-driven and can be learned end-to-end. Through extensive experimental comparisons we show that KODA outperforms existing state of the art methods on multiple time series benchmarks such as electricity, temperature, weather, lorenz 63 and duffing oscillator demonstrating its superior performance and efficacy along the three tasks a) forecasting, b) data assimilation and c) state prediction.

This paper presents a radar target tracking framework for addressing main-beam range deception jamming attacks using random finite sets (RFSs). Our system handles false alarms and detections with false range information through multiple hypothesis tracking (MHT) to resolve data association uncertainties. We focus on range gate pull-off (RGPO) attacks, where the attacker adds positive delays to the radar pulse, thereby mimicking the target trajectory while appearing at a larger distance from the radar. The proposed framework incorporates knowledge about the spatial behavior of the attack into the assumed RFS clutter model and uses only position information without relying on additional signal features. We present an adaptive solution that estimates the jammer-induced biases to improve tracking accuracy as well as a simpler non-adaptive version that performs well when accurate priors on the jamming range are available. Furthermore, an expression for RGPO attack detection is derived, where the adaptive solution offers superior performance. The presented strategies provide tracking resilience against multiple RGPO attacks in terms of position estimation accuracy and jamming detection without degrading tracking performance in the absence of jamming., Comment: 12 pages, 7 figures

Continuously optimizing sensor placement is essential for precise target localization in various military and civilian applications. While information theory has shown promise in optimizing sensor placement, many studies oversimplify sensor measurement models or neglect dynamic constraints of mobile sensors. To address these challenges, we employ a range measurement model that incorporates radar parameters and radar-target distance, coupled with Model Predictive Path Integral (MPPI) control to manage complex environmental obstacles and dynamic constraints. We compare the proposed approach against stationary radars or simplified range measurement models based on the root mean squared error (RMSE) of the Cubature Kalman Filter (CKF) estimator for the targets' state. Additionally, we visualize the evolving geometry of radars and targets over time, highlighting areas of highest measurement information gain, demonstrating the strengths of the approach. The proposed strategy outperforms stationary radars and simplified range measurement models in target localization, achieving a 38-74% reduction in mean RMSE and a 33-79% reduction in the upper tail of the 90% Highest Density Interval (HDI) over 500 Monte Carl (MC) trials across all time steps. Code will be made publicly available upon acceptance., Comment: Submitted to IEEE Aerospace and Electronic Systems

Radar Automated Target Recognition (RATR) for Unmanned Aerial Vehicles (UAVs) involves transmitting Electromagnetic Waves (EMWs) and performing target type recognition on the received radar echo, crucial for defense and aerospace applications. Previous studies highlighted the advantages of multistatic radar configurations over monostatic ones in RATR. However, fusion methods in multistatic radar configurations often suboptimally combine classification vectors from individual radars probabilistically. To address this, we propose a fully Bayesian RATR framework employing Optimal Bayesian Fusion (OBF) to aggregate classification probability vectors from multiple radars. OBF, based on expected 0-1 loss, updates a Recursive Bayesian Classification (RBC) posterior distribution for target UAV type, conditioned on historical observations across multiple time steps. We evaluate the approach using simulated random walk trajectories for seven drones, correlating target aspect angles to Radar Cross Section (RCS) measurements in an anechoic chamber. Comparing against single radar Automated Target Recognition (ATR) systems and suboptimal fusion methods, our empirical results demonstrate that the OBF method integrated with RBC significantly enhances classification accuracy compared to other fusion methods and single radar configurations., Comment: Accepted to IEEE Transactions on Aerospace and Electronic Systems

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based solutions face important challenges when dealing with spatio-temporal PDEs over long time scales. Specifically, the current theory of NOs does not present a systematic framework to perform data assimilation and efficiently correct the evolution of PDE solutions over time based on sparsely sampled noisy measurements. In this paper, we propose a learning-based state-space approach to compute the solution operators to infinite-dimensional semilinear PDEs. Exploiting the structure of semilinear PDEs and the theory of nonlinear observers in function spaces, we develop a flexible recursive method that allows for both prediction and data assimilation by combining prediction and correction operations. The proposed framework is capable of producing fast and accurate predictions over long time horizons, dealing with irregularly sampled noisy measurements to correct the solution, and benefits from the decoupling between the spatial and temporal dynamics of this class of PDEs. We show through experiments on the Kuramoto-Sivashinsky, Navier-Stokes and Korteweg-de Vries equations that the proposed model is robust to noise and can leverage arbitrary amounts of measurements to correct its prediction over a long time horizon with little computational overhead., Comment: ICLR 2024

Curvature estimation methods are important as they capture salient features for various applications in image processing, especially within medical domains where tortuosity of vascular structures is of significant interest. Existing methods based on centerline or skeleton curvature fail to capture curvature gradients across a rotating tubular structure. This paper presents a Tubular Curvature Filter method that locally calculates the acceleration of bundles of curves that traverse along the tubular object parallel to the centerline. This is achieved by examining the directional rate of change in the eigenvectors of the Hessian matrix of a tubular intensity function in space. This method implicitly calculates the local tubular curvature without the need to explicitly segment the tubular object. Experimental results demonstrate that the Tubular Curvature Filter method provides accurate estimates of local curvature at any point inside tubular structures., Comment: 11 pages, 5 figures

Although considerable effort has been dedicated to improving the solution to the hyperspectral unmixing problem, non-idealities such as complex radiation scattering and endmember variability negatively impact the performance of most existing algorithms and can be very challenging to address. Recently, deep learning-based frameworks have been explored for hyperspectral umixing due to their flexibility and powerful representation capabilities. However, such techniques either do not address the non-idealities of the unmixing problem, or rely on black-box models which are not interpretable. In this paper, we propose a new interpretable deep learning method for hyperspectral unmixing that accounts for nonlinearity and endmember variability. The proposed method leverages a probabilistic variational deep-learning framework, where disentanglement learning is employed to properly separate the abundances and endmembers. The model is learned end-to-end using stochastic backpropagation, and trained using a self-supervised strategy which leverages benefits from semi-supervised learning techniques. Furthermore, the model is carefully designed to provide a high degree of interpretability. This includes modeling the abundances as a Dirichlet distribution, the endmembers using low-dimensional deep latent variable representations, and using two-stream neural networks composed of additive piecewise-linear/nonlinear components. Experimental results on synthetic and real datasets illustrate the performance of the proposed method compared to state-of-the-art algorithms.

Objective: The objective of the study is to efficiently increase the expressivity of surface electromyography-based (sEMG) gesture recognition systems. Approach: We use a problem transformation approach, in which actions were subset into two biomechanically independent components - a set of wrist directions and a set of finger modifiers. To maintain fast calibration time, we train models for each component using only individual gestures, and extrapolate to the full product space of combination gestures by generating synthetic data. We collected a supervised dataset with high-confidence ground truth labels in which subjects performed combination gestures while holding a joystick, and conducted experiments to analyze the impact of model architectures, classifier algorithms, and synthetic data generation strategies on the performance of the proposed approach. Main Results: We found that a problem transformation approach using a parallel model architecture in combination with a non-linear classifier, along with restricted synthetic data generation, shows promise in increasing the expressivity of sEMG-based gestures with a short calibration time. Significance: sEMG-based gesture recognition has applications in human-computer interaction, virtual reality, and the control of robotic and prosthetic devices. Existing approaches require exhaustive model calibration. The proposed approach increases expressivity without requiring users to demonstrate all combination gesture classes. Our results may be extended to larger gesture vocabularies and more complicated model architectures., Comment: 14 pages, 12 figures

We designed and tested a system for real-time control of a user interface by extracting surface electromyographic (sEMG) activity from eight electrodes in a wrist-band configuration. sEMG data were streamed into a machine-learning algorithm that classified hand gestures in real-time. After an initial model calibration, participants were presented with one of three types of feedback during a human-learning stage: veridical feedback, in which predicted probabilities from the gesture classification algorithm were displayed without alteration, modified feedback, in which we applied a hidden augmentation of error to these probabilities, and no feedback. User performance was then evaluated in a series of minigames, in which subjects were required to use eight gestures to manipulate their game avatar to complete a task. Experimental results indicated that, relative to baseline, the modified feedback condition led to significantly improved accuracy and improved gesture class separation. These findings suggest that real-time feedback in a gamified user interface with manipulation of feedback may enable intuitive, rapid, and accurate task acquisition for sEMG-based gesture recognition applications., Comment: 10 pages, 10 figures. V2: Fix latex characters in author name. V3: Add published DOI and Copyright notice

Plastic waste entering the riverine harms local ecosystems leading to negative ecological and economic impacts. Large parcels of plastic waste are transported from inland to oceans leading to a global scale problem of floating debris fields. In this context, efficient and automatized monitoring of mismanaged plastic waste is paramount. To address this problem, we analyze the feasibility of macro-plastic litter detection using computational imaging approaches in river-like scenarios. We enable near-real-time tracking of partially submerged plastics by using snapshot Visible-Shortwave Infrared hyperspectral imaging. Our experiments indicate that imaging strategies associated with machine learning classification approaches can lead to high detection accuracy even in challenging scenarios, especially when leveraging hyperspectral data and nonlinear classifiers. All code, data, and models are available online: https://github.com/RIVeR-Lab/hyperspectral_macro_plastic_detection.

Jamming signals can jeopardize the operation of GNSS receivers until denying its operation. Given their ubiquity, jamming mitigation and localization techniques are of crucial importance, for which jammer classification is of help. Data-driven models have been proven useful in detecting these threats, while their training using crowdsourced data still poses challenges when it comes to private data sharing. This article investigates the use of federated learning to train jamming signal classifiers locally on each device, with model updates aggregated and averaged at the central server. This allows for privacy-preserving training procedures that do not require centralized data storage or access to client local data. The used framework FedAvg is assessed on a dataset consisting of spectrogram images of simulated interfered GNSS signal. Six different jammer types are effectively classified with comparable results to a fully centralized solution that requires vast amounts of data communication and involves privacy-preserving concerns.

Multitemporal hyperspectral unmixing (MTHU) is a fundamental tool in the analysis of hyperspectral image sequences. It reveals the dynamical evolution of the materials (endmembers) and of their proportions (abundances) in a given scene. However, adequately accounting for the spatial and temporal variability of the endmembers in MTHU is challenging, and has not been fully addressed so far in unsupervised frameworks. In this work, we propose an unsupervised MTHU algorithm based on variational recurrent neural networks. First, a stochastic model is proposed to represent both the dynamical evolution of the endmembers and their abundances, as well as the mixing process. Moreover, a new model based on a low-dimensional parametrization is used to represent spatial and temporal endmember variability, significantly reducing the amount of variables to be estimated. We propose to formulate MTHU as a Bayesian inference problem. However, the solution to this problem does not have an analytical solution due to the nonlinearity and non-Gaussianity of the model. Thus, we propose a solution based on deep variational inference, in which the posterior distribution of the estimated abundances and endmembers is represented by using a combination of recurrent neural networks and a physically motivated model. The parameters of the model are learned using stochastic backpropagation. Experimental results show that the proposed method outperforms state of the art MTHU algorithms.

A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also includes the prior model information. In reality, however, the true model generating the data is either unknown or simplified when deriving estimators, which motivates the works to derive estimation bounds under modeling mismatch situations. This paper provides a derivation of a Bayesian Cram\'{e}r-Rao bound under model misspecification, defining important concepts such as pseudotrue parameter that were not clearly identified in previous works. The general result is particularized in linear and Gaussian problems, where closed-forms are available and results are used to validate the results., Comment: Accepted by ICASSP 2023

Real-time satellite imaging has a central role in monitoring, detecting and estimating the intensity of key natural phenomena such as floods, earthquakes, etc. One important constraint of satellite imaging is the trade-off between spatial/spectral resolution and their revisiting time, a consequence of design and physical constraints imposed by satellite orbit among other technical limitations. In this paper, we focus on fusing multi-temporal, multi-spectral images where data acquired from different instruments with different spatial resolutions is used. We leverage the spatial relationship between images at multiple modalities to generate high-resolution image sequences at higher revisiting rates. To achieve this goal, we formulate the fusion method as a recursive state estimation problem and study its performance in filtering and smoothing contexts. Furthermore, a calibration strategy is proposed to estimate the time-varying temporal dynamics of the image sequence using only a small amount of historical image data. Differently from the training process in traditional machine learning algorithms, which usually require large datasets and computation times, the parameters of the temporal dynamical model are calibrated based on an analytical expression that uses only two of the images in the historical dataset. A distributed version of the Bayesian filtering and smoothing strategies is also proposed to reduce its computational complexity. To evaluate the proposed methodology we consider a water mapping task where real data acquired by the Landsat and MODIS instruments are fused generating high spatial-temporal resolution image estimates. Our experiments show that the proposed methodology outperforms the competing methods in both estimation accuracy and water mapping tasks., Comment: arXiv admin note: substantial text overlap with arXiv:2204.12566

Despite the extensive body of literature focused on remote sensing applications for land cover mapping and the availability of high-resolution satellite imagery, methods for continuously updating classification maps in real-time remain limited, especially when training data is scarce. This paper introduces the Recursive Bayesian Classifier (RBC), which converts any instantaneous classifier into a robust online method through a probabilistic framework that is resilient to non-informative image variations. Three experiments are conducted using Sentinel-2 data: water mapping of the Oroville Dam in California and the Charles River basin in Massachusetts, and deforestation detection in the Amazon. RBC is applied to a Gaussian Mixture Model (GMM), Logistic Regression (LR), and our proposed Spectral Index Classifier (SIC). Results show that RBC significantly enhances classifier robustness in multitemporal settings under challenging conditions, such as cloud cover and cyanobacterial blooms. Specifically, balanced classification accuracy improves by up to 26.95% for SIC, 12.4% for GMM, and 13.81% for LR in water mapping, and by 15.25%, 14.17%, and 14.7% in deforestation detection. Moreover, without additional training data, RBC improves the performance of the state-of-the-art DeepWaterMap and WatNet algorithms by up to 9.62% and 11.03%. These benefits are provided by RBC while requiring minimal supervision and maintaining a low computational cost that remains constant for each time step regardless of the time-series length., Comment: Without supplemental results: 31 pages, 16 figures, 5 tables. With supplemental results: 35 pages, 20 figures, 5 tables

Monitoring interferences to satellite-based navigation systems is of paramount importance in order to reliably operate critical infrastructures, navigation systems, and a variety of applications relying on satellite-based positioning. This paper investigates the use of crowdsourced data to achieve such detection and monitoring at a central node that receives the data from an arbitrary number of agents in an area of interest. Under ideal conditions, the pathloss model is used to compute the Cram\'er-Rao Bound of accuracy as well as the corresponding maximum likelihood estimator. However, in real scenarios where obstructions and reflections are common, the signal propagation is far more complex than the pathloss model can explain. We propose to augment the pathloss model with a data-driven component, able to explain the complexities of the propagation channel. The paper shows a general methodology to jointly estimate the interference location and the parameters of the augmented model, showing superior performances in complex scenarios such as those encountered in urban environments., Comment: 5 pages, 6 figures

The integration of data and knowledge from several sources is known as data fusion. When data is only available in a distributed fashion or when different sensors are used to infer a quantity of interest, data fusion becomes essential. In Bayesian settings, a priori information of the unknown quantities is available and, possibly, present among the different distributed estimators. When the local estimates are fused, the prior knowledge used to construct several local posteriors might be overused unless the fusion node accounts for this and corrects it. In this paper, we analyze the effects of shared priors in Bayesian data fusion contexts. Depending on different common fusion rules, our analysis helps to understand the performance behavior as a function of the number of collaborative agents and as a consequence of different types of priors. The analysis is performed by using two divergences which are common in Bayesian inference, and the generality of the results allows to analyze very generic distributions. These theoretical results are corroborated through experiments in a variety of estimation and classification problems, including linear and nonlinear models, and federated learning schemes.

Subspace clustering algorithms are used for understanding the cluster structure that explains the dataset well. These methods are extensively used for data-exploration tasks in various areas of Natural Sciences. However, most of these methods fail to handle unwanted biases in datasets. For datasets where a data sample represents multiple attributes, naively applying any clustering approach can result in undesired output. To this end, we propose a novel framework for jointly removing unwanted attributes (biases) while learning to cluster data points in individual subspaces. Assuming we have information about the bias, we regularize the clustering method by adversarially learning to minimize the mutual information between the data and the unwanted attributes. Our experimental result on synthetic and real-world datasets demonstrate the effectiveness of our approach.

We study the problem of inferring user intent from noninvasive electroencephalography (EEG) to restore communication for people with severe speech and physical impairments (SSPI). The focus of this work is improving the estimation of posterior symbol probabilities in a typing task. At each iteration of the typing procedure, a subset of symbols is chosen for the next query based on the current probability estimate. Evidence about the user's response is collected from event-related potentials (ERP) in order to update symbol probabilities, until one symbol exceeds a predefined confidence threshold. We provide a graphical model describing this task, and derive a recursive Bayesian update rule based on a discriminative probability over label vectors for each query, which we approximate using a neural network classifier. We evaluate the proposed method in a simulated typing task and show that it outperforms previous approaches based on generative modeling., Comment: 5 pages, 2 figures

Quantum Monte-Carlo simulations of hybrid quantum-classical models such as the double exchange Hamiltonian require calculating the density of states of the quantum degrees of freedom at every step. Unfortunately, the computational complexity of exact diagonalization grows $ \mathcal{O} (N^3)$ as a function of the system's size $ N $, making it prohibitively expensive for any realistic system. We consider leveraging data-driven methods, namely neural networks, to replace the exact diagonalization step in order to speed up sample generation. We explore a model that learns the free energy for each spin configuration and a second one that learns the Hamiltonian's eigenvalues. We implement data augmentation by taking advantage of the Hamiltonian's symmetries to artificially enlarge our training set and benchmark the different models by evaluating several thermodynamic quantities. While all models considered here perform exceedingly well in the one-dimensional case, only the neural network that outputs the eigenvalues is able to capture the right behavior in two dimensions. The simplicity of the architecture we use in conjunction with the model agnostic form of the neural networks can enable fast sample generation without the need of a researcher's intervention., Comment: 8 pages, 5 figures

Orthogonal Frequency Division Multiplexing (OFDM)-based waveforms are used for communication links in many current and emerging Internet of Things (IoT) applications, including the latest WiFi standards. For such OFDM-based transceivers, many core physical layer functions related to channel estimation, demapping, and decoding are implemented for specific choices of channel types and modulation schemes, among others. To decouple hard-wired choices from the receiver chain and thereby enhance the flexibility of IoT deployment in many novel scenarios without changing the underlying hardware, we explore a novel, modular Machine Learning (ML)-based receiver chain design. Here, ML blocks replace the individual processing blocks of an OFDM receiver, and we specifically describe this swapping for the legacy channel estimation, symbol demapping, and decoding blocks with Neural Networks (NNs). A unique aspect of this modular design is providing flexible allocation of processing functions to the legacy or ML blocks, allowing them to interchangeably coexist. Furthermore, we study the implementation cost-benefits of the proposed NNs in resource-constrained IoT devices through pruning and quantization, as well as emulation of these compressed NNs within Field Programmable Gate Arrays (FPGAs). Our evaluations demonstrate that the proposed modular NN-based receiver improves bit error rate of the traditional non-ML receiver by averagely 61% and 10% for the simulated and over-the-air datasets, respectively. We further show complexity-performance tradeoffs by presenting computational complexity comparisons between the traditional algorithms and the proposed compressed NNs.

Satellite imaging has a central role in monitoring, detecting and estimating the intensity of key natural phenomena. One important feature of satellite images is the trade-off between spatial/spectral resolution and their revisiting time, a consequence of design and physical constraints imposed by satellite orbit among other technical limitations. In this paper, we focus on fusing multi-temporal, multi-spectral images where data acquired from different instruments with different spatial resolutions is used. We leverage the spatial relationship between images at multiple modalities to generate high-resolution image sequences at higher revisiting rates. To achieve this goal, we formulate the fusion method as a recursive state estimation problem and study its performance in filtering and smoothing contexts. The proposed strategy clearly outperforms competing methodologies, which is shown in the paper for real data acquired by the Landsat and MODIS instruments., Comment: Published in IEEE AeroConf 2022

In this paper we present a hybrid neural network augmented physics-based modeling (APBM) framework for Bayesian nonlinear latent space estimation. The proposed APBM strategy allows for model adaptation when new operation conditions come into play or the physics-based model is insufficient (or incomplete) to properly describe the latent phenomenon. One advantage of the APBMs and our estimation procedure is the capability of maintaining the physical interpretability of estimated states. Furthermore, we propose a constraint filtering approach to control the neural network contributions to the overall model. We also exploit assumed density filtering techniques and cubature integration rules to present a flexible estimation strategy that can easily deal with nonlinear models and high-dimensional latent spaces. Finally, we demonstrate the efficacy of our methodology by leveraging a target tracking scenario with nonlinear and incomplete measurement and acceleration models, respectively.

Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we propose to combine neural networks with physics-based models. Specifically, we demonstrate how we can approximate missing ordinary differential equations (ODEs) coupled with known ODEs using Bayesian filtering techniques to train the model parameters and simultaneously estimate dynamic state variables. As a study case we leverage a well-understood model for blood circulation in the human retina and replace one of its core ODEs with a neural network approximation, representing the case where we have incomplete knowledge of the physiological state dynamics. Results demonstrate that state dynamics corresponding to the missing ODEs can be approximated well using a neural network trained using a recursive Bayesian filtering approach in a fashion coupled with the known state dynamic differential equations. This demonstrates that dynamics and impact of missing state variables can be captured through joint state estimation and model parameter estimation within a recursive Bayesian state estimation (RBSE) framework. Results also indicate that this RBSE approach to training the NN parameters yields better outcomes (measurement/state estimation accuracy) than training the neural network with backpropagation through time in the same setting.

Localization and tracking of objects using data-driven methods is a popular topic due to the complexity in characterizing the physics of wireless channel propagation models. In these modeling approaches, data needs to be gathered to accurately train models, at the same time that user's privacy is maintained. An appealing scheme to cooperatively achieve these goals is known as Federated Learning (FL). A challenge in FL schemes is the presence of non-independent and identically distributed (non-IID) data, caused by unevenly exploration of different areas. In this paper, we consider the use of recent FL schemes to train a set of personalized models that are then optimally fused through Bayesian rules, which makes it appropriate in the context of indoor localization.

Autoencoder (AEC) networks have recently emerged as a promising approach to perform unsupervised hyperspectral unmixing (HU) by associating the latent representations with the abundances, the decoder with the mixing model and the encoder with its inverse. AECs are especially appealing for nonlinear HU since they lead to unsupervised and model-free algorithms. However, existing approaches fail to explore the fact that the encoder should invert the mixing process, which might reduce their robustness. In this paper, we propose a model-based AEC for nonlinear HU by considering the mixing model a nonlinear fluctuation over a linear mixture. Differently from previous works, we show that this restriction naturally imposes a particular structure to both the encoder and to the decoder networks. This introduces prior information in the AEC without reducing the flexibility of the mixing model. Simulations with synthetic and real data indicate that the proposed strategy improves nonlinear HU.

Multitemporal spectral unmixing (SU) is a powerful tool to process hyperspectral image (HI) sequences due to its ability to reveal the evolution of materials over time and space in a scene. However, significant spectral variability is often observed between collection of images due to variations in acquisition or seasonal conditions. This characteristic has to be considered in the design of SU algorithms. Because of its good performance, the multiple endmember spectral mixture analysis algorithm (MESMA) has been recently used to perform SU in multitemporal scenarios arising in several practical applications. However, MESMA does not consider the relationship between the different HIs, and its computational complexity is extremely high for large spectral libraries. In this work, we propose an efficient multitemporal SU method that exploits the high temporal correlation between the abundances to provide more accurate results at a lower computational complexity. We propose to solve the complex general multitemporal SU problem by separately addressing the endmember selection and the abundance estimation problems. This leads to a simpler solution without sacrificing the accuracy of the results. We also propose a strategy to detect and address abrupt abundance variations in time. Theoretical results demonstrate how the proposed method compares to MESMA in terms of quality, and how effective it is in detecting abundance changes. This analysis provides valuable insight into the conditions under which the algorithm succeeds. Simulation results show that the proposed method achieves state-of-the-art performance at a smaller computational cost.

The spectral signatures of the materials contained in hyperspectral images, also called endmembers (EM), can be significantly affected by variations in atmospheric, illumination or environmental conditions typically occurring within an image. Traditional spectral unmixing (SU) algorithms neglect the spectral variability of the endmembers, what propagates significant mismodeling errors throughout the whole unmixing process and compromises the quality of its results. Therefore, large efforts have been recently dedicated to mitigate the effects of spectral variability in SU. This resulted in the development of algorithms that incorporate different strategies to allow the EMs to vary within a hyperspectral image, using, for instance, sets of spectral signatures known a priori, Bayesian, parametric, or local EM models. Each of these approaches has different characteristics and underlying motivations. This paper presents a comprehensive literature review contextualizing both classic and recent approaches to solve this problem. We give a detailed evaluation of the sources of spectral variability and their effect in image spectra. Furthermore, we propose a new taxonomy that organizes existing works according to a practitioner's point of view, based on the necessary amount of supervision and on the computational cost they require. We also review methods used to construct spectral libraries (which are required by many SU techniques) based on the observed hyperspectral image, as well as algorithms for library augmentation and reduction. Finally, we conclude the paper with some discussions and an outline of possible future directions for the field., Comment: Published at the IEEE Geoscience and Remote Sensing Magazine

The recent evolution of hyperspectral imaging technology and the proliferation of new emerging applications presses for the processing of multiple temporal hyperspectral images. In this work, we propose a novel spectral unmixing (SU) strategy using physically motivated parametric endmember representations to account for temporal spectral variability. By representing the multitemporal mixing process using a state-space formulation, we are able to exploit the Bayesian filtering machinery to estimate the endmember variability coefficients. Moreover, by assuming that the temporal variability of the abundances is small over short intervals, an efficient implementation of the expectation maximization (EM) algorithm is employed to estimate the abundances and the other model parameters. Simulation results indicate that the proposed strategy outperforms state-of-the-art multitemporal SU algorithms.

Multiple Endmember Spectral Mixture Analysis (MESMA) is one of the leading approaches to perform spectral unmixing (SU) considering variability of the endmembers (EMs). It represents each EM in the image using libraries of spectral signatures acquired a priori. However, existing spectral libraries are often small and unable to properly capture the variability of each EM in practical scenes, which compromises the performance of MESMA. In this paper, we propose a library augmentation strategy to increase the diversity of existing spectral libraries, thus improving their ability to represent the materials in real images. First, we leverage the power of deep generative models to learn the statistical distribution of the EMs based on the spectral signatures available in the existing libraries. Afterwards, new samples can be drawn from the learned EM distributions and used to augment the spectral libraries, improving the overall quality of the SU process. Experimental results using synthetic and real data attest the superior performance of the proposed method even under library mismatch conditions.

Introducing spatial prior information in hyperspectral imaging (HSI) analysis has led to an overall improvement of the performance of many HSI methods applied for denoising, classification, and unmixing. Extending such methodologies to nonlinear settings is not always straightforward, specially for unmixing problems where the consideration of spatial relationships between neighboring pixels might comprise intricate interactions between their fractional abundances and nonlinear contributions. In this paper, we consider a multiscale regularization strategy for nonlinear spectral unmixing with kernels. The proposed methodology splits the unmixing problem into two sub-problems at two different spatial scales: a coarse scale containing low-dimensional structures, and the original fine scale. The coarse spatial domain is defined using superpixels that result from a multiscale transformation. Spectral unmixing is then formulated as the solution of quadratically constrained optimization problems, which are solved efficiently by exploring their strong duality and a reformulation of their dual cost functions in the form of root-finding problems. Furthermore, we employ a theory-based statistical framework to devise a consistent strategy to estimate all required parameters, including both the regularization parameters of the algorithm and the number of superpixels of the transformation, resulting in a truly blind (from the parameters setting perspective) unmixing method. Experimental results attest the superior performance of the proposed method when comparing with other, state-of-the-art, related strategies.

Endmember (EM) spectral variability can greatly impact the performance of standard hyperspectral image analysis algorithms. Extended parametric models have been successfully applied to account for the EM spectral variability. However, these models still lack the compromise between flexibility and low-dimensional representation that is necessary to properly explore the fact that spectral variability is often confined to a low-dimensional manifold in real scenes. In this paper we propose to learn a spectral variability model directly form the observed data, instead of imposing it \emph{a priori}. This is achieved through a deep generative EM model, which is estimated using a variational autoencoder (VAE). The encoder and decoder that compose the generative model are trained using pure pixel information extracted directly from the observed image, what allows for an unsupervised formulation. The proposed EM model is applied to the solution of a spectral unmixing problem, which we cast as an alternating nonlinear least-squares problem that is solved iteratively with respect to the abundances and to the low-dimensional representations of the EMs in the latent space of the deep generative model. Simulations using both synthetic and real data indicate that the proposed strategy can outperform the competing state-of-the-art algorithms.

Endmember (EM) variability has an important impact on the performance of hyperspectral image (HI) analysis algorithms. Recently, extended linear mixing models have been proposed to account for EM variability in the spectral unmixing (SU) problem. The direct use of these models has led to severely ill-posed optimization problems. Different regularization strategies have been considered to deal with this issue, but none so far has consistently exploited the information provided by the existence of multiple pure pixels often present in HIs. In this work, we propose to break the SU problem into a sequence of two problems. First, we use pure pixel information to estimate an interpolated tensor of scaling factors representing spectral variability. This is done by considering the spectral variability to be a smooth function over the HI and confining the energy of the scaling tensor to a low-rank structure. Afterwards, we solve a matrix-factorization problem to estimate the fractional abundances using the variability scaling factors estimated in the previous step, what leads to a significantly more well-posed problem. Simulation swith synthetic and real data attest the effectiveness of the proposed strategy.

Traditional hyperspectral unmixing methods neglect the underlying variability of spectral signatures often observed in typical hyperspectral images (HI), propagating these missmodeling errors throughout the whole unmixing process. Attempts to model material spectra as members of sets or as random variables tend to lead to severely ill-posed unmixing problems. Although parametric models have been proposed to overcome this drawback by handling endmember variability through generalizations of the mixing model, the success of these techniques depend on employing appropriate regularization strategies. Moreover, the existing approaches fail to adequately explore the natural multidimensinal representation of HIs. Recently, tensor-based strategies considered low-rank decompositions of hyperspectral images as an alternative to impose low-dimensional structures on the solutions of standard and multitemporal unmixing problems. These strategies, however, present two main drawbacks: 1) they confine the solutions to low-rank tensors, which often cannot represent the complexity of real-world scenarios; and 2) they lack guarantees that endmembers and abundances will be correctly factorized in their respective tensors. In this work, we propose a more flexible approach, called ULTRA-V, that imposes low-rank structures through regularizations whose strictness is controlled by scalar parameters. Simulations attest the superior accuracy of the method when compared with state-of-the-art unmixing algorithms that account for spectral variability., Comment: arXiv admin note: substantial text overlap with arXiv:1803.06355

Image fusion combines data from different heterogeneous sources to obtain more precise information about an underlying scene. Hyperspectral-multispectral (HS-MS) image fusion is currently attracting great interest in remote sensing since it allows the generation of high spatial resolution HS images, circumventing the main limitation of this imaging modality. Existing HS-MS fusion algorithms, however, neglect the spectral variability often existing between images acquired at different time instants. This time difference causes variations in spectral signatures of the underlying constituent materials due to different acquisition and seasonal conditions. This paper introduces a novel HS-MS image fusion strategy that combines an unmixing-based formulation with an explicit parametric model for typical spectral variability between the two images. Simulations with synthetic and real data show that the proposed strategy leads to a significant performance improvement under spectral variability and state-of-the-art performance otherwise.

Spectral variability in hyperspectral images can result from factors including environmental, illumination, atmospheric and temporal changes. Its occurrence may lead to the propagation of significant estimation errors in the unmixing process. To address this issue, extended linear mixing models have been proposed which lead to large scale nonsmooth ill-posed inverse problems. Furthermore, the regularization strategies used to obtain meaningful results have introduced interdependencies among abundance solutions that further increase the complexity of the resulting optimization problem. In this paper we present a novel data dependent multiscale model for hyperspectral unmixing accounting for spectral variability. The new method incorporates spatial contextual information to the abundances in extended linear mixing models by using a multiscale transform based on superpixels. The proposed method results in a fast algorithm that solves the abundance estimation problem only once in each scale during each iteration. Simulation results using synthetic and real images compare the performances, both in accuracy and execution time, of the proposed algorithm and other state-of-the-art solutions.

Tensor-based methods have recently emerged as a more natural and effective formulation to address many problems in hyperspectral imaging. In hyperspectral unmixing (HU), low-rank constraints on the abundance maps have been shown to act as a regularization which adequately accounts for the multidimensional structure of the underlying signal. However, imposing a strict low-rank constraint for the abundance maps does not seem to be adequate, as important information that may be required to represent fine scale abundance behavior may be discarded. This paper introduces a new low-rank tensor regularization that adequately captures the low-rank structure underlying the abundance maps without hindering the flexibility of the solution. Simulation results with synthetic and real data show that the the extra flexibility introduced by the proposed regularization significantly improves the unmixing results.

A control logic has a central role in many echo cancellation systems for optimizing the performance of adaptive filters while estimating the echo path. For reliable control, accurate double-talk (DT) and channel change (CC) detectors are usually incorporated to the echo canceler. This work expands the usual detection strategy to define a classification problem characterizing four possible states of the echo canceler operation. The new formulation allow the use of decision theory to continuously control the transitions among the different modes of operation. The classification rule reduces to a low cost statistics for which it is possible to determine the probability of error under all hypotheses, allowing the classification performance to be accessed analytically. Monte Carlo simulations using synthetic and real data illustrate the reliability of the proposed method.

Endmember variability is an important factor for accurately unveiling vital information relating the pure materials and their distribution in hyperspectral images. Recently, the extended linear mixing model (ELMM) has been proposed as a modification of the linear mixing model (LMM) to consider endmember variability effects resulting mainly from illumination changes. In this paper, we further generalize the ELMM leading to a new model (GLMM) to account for more complex spectral distortions where different wavelength intervals can be affected unevenly. We also extend the existing methodology to jointly estimate the variability and the abundances for the GLMM. Simulations with real and synthetic data show that the unmixing process can benefit from the extra flexibility introduced by the GLMM.

Kernel-based nonlinear mixing models have been applied to unmix spectral information of hyperspectral images when the type of mixing occurring in the scene is too complex or unknown. Such methods, however, usually require the inversion of matrices of sizes equal to the number of spectral bands. Reducing the computational load of these methods remains a challenge in large scale applications. This paper proposes a centralized method for band selection (BS) in the reproducing kernel Hilbert space (RKHS). It is based upon the coherence criterion, which sets the largest value allowed for correlations between the basis kernel functions characterizing the unmixing model. We show that the proposed BS approach is equivalent to solving a maximum clique problem (MCP), that is, searching for the biggest complete subgraph in a graph. Furthermore, we devise a strategy for selecting the coherence threshold and the Gaussian kernel bandwidth using coherence bounds for linearly independent bases. Simulation results illustrate the efficiency of the proposed method.

Mixing phenomena in hyperspectral images depend on a variety of factors such as the resolution of observation devices, the properties of materials, and how these materials interact with incident light in the scene. Different parametric and nonparametric models have been considered to address hyperspectral unmixing problems. The simplest one is the linear mixing model. Nevertheless, it has been recognized that mixing phenomena can also be nonlinear. The corresponding nonlinear analysis techniques are necessarily more challenging and complex than those employed for linear unmixing. Within this context, it makes sense to detect the nonlinearly mixed pixels in an image prior to its analysis, and then employ the simplest possible unmixing technique to analyze each pixel. In this paper, we propose a technique for detecting nonlinearly mixed pixels. The detection approach is based on the comparison of the reconstruction errors using both a Gaussian process regression model and a linear regression model. The two errors are combined into a detection statistics for which a probability density function can be reasonably approximated. We also propose an iterative endmember extraction algorithm to be employed in combination with the detection algorithm. The proposed Detect-then-Unmix strategy, which consists of extracting endmembers, detecting nonlinearly mixed pixels and unmixing, is tested with synthetic and real images.