Journal: IEEE Transactions on Signal Processing

Abbreviation

IEEE trans. signal process.

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IEEE

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ISSN

1053-587X
1941-0476

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Publications1 - 10 of 55
  • Orthogonal Fourier Analysis on Directed Acyclic Graphs via Mobius Total Variation
    Item type: Journal Article
    Mihal, Vedran; Püschel, Markus (2025)
    IEEE Transactions on Signal Processing
    Signal processing on directed acyclic graphs (DAGs) presents unique challenges. Unlike for undirected graphs, the Laplacian matrix of a DAG lacks a complete eigenbasis in general, and the corresponding adjacency matrix never has one, which prevents the use of conventional graph Fourier analysis. To address these challenges, in this work we propose the first orthogonal Fourier basis that is specifically designed for DAGs, referred to as the Mobius basis. This basis is derived from our novel concept of Mobius total variation (Mobius TV) for DAGs, a generalization of the classical definition of TV in discrete time, which also constitutes a DAG. We then develop two variants of the Mobius basis, which have desirable properties with respect to constant signals. We validate the effectiveness of our Fourier basis against a comprehensive set of prior proposed bases for directed graphs through three types of experiments, considering both synthetic and real-world DAGs and DAG signals.
  • Quantization of filter bank frame expansions through moving horizon optimization
    Item type: Journal Article
    Quevedo, Daniel E.; Bölcskei, Helmut; Goodwin, Graham C. (2009)
    IEEE Transactions on Signal Processing
  • Compressive Sensing Using Iterative Hard Thresholding With Low Precision Data Representation: Theory and Applications
    Item type: Journal Article
    Gürel, Nezihe M.; Kara, Kaan; Stojanov, Alen; et al. (2020)
    IEEE Transactions on Signal Processing
    Modern scientific instruments produce vast amounts of data, which can overwhelm the processing ability of computer systems. Lossy compression of data is an intriguing solution, but comes with its own drawbacks, such as potential signal loss, and the need for careful optimization of the compression ratio. In this work, we focus on a setting where this problem is especially acute: compressive sensing frameworks for interferometry and medical imaging. We ask the following question: can the precision of the data representation be lowered for all inputs, with recovery guarantees and practical performance? Our first contribution is a theoretical analysis of the normalized Iterative Hard Thresholding (IHT) algorithm when all input data, meaning both the measurement matrix and the observation vector are quantized aggressively. We present a variant of low precision normalized IHT that, under mild conditions, can still provide recovery guarantees. The second contribution is the application of our quantization framework to radio astronomy and magnetic resonance imaging. We show that lowering the precision of the data can significantly accelerate image recovery. We evaluate our approach on telescope data and samples of brain images using CPU and FPGA implementations achieving up to a 9x speed-up with negligible loss of recovery quality.
  • Bayesian KalmanNet: Quantifying Uncertainty in Deep Learning Augmented Kalman Filter
    Item type: Journal Article
    Dahan, Yehonatan; Revach, Guy; Dunik, Jindrich; et al. (2025)
    IEEE Transactions on Signal Processing
    Recent years have witnessed a growing interest in tracking algorithms that augment Kalman filters (KFs) with deep neural networks (DNNs). By transforming KFs into trainable deep learning models, one can learn from data to reliably track a latent state in complex and partially known dynamics. However, unlike classic KFs, conventional DNN-based systems do not naturally provide an uncertainty measure, such as error covariance, alongside their estimates, which is crucial in various applications that rely on KF-type tracking. This work bridges this gap by studying error covariance extraction in DNN-aided KFs. We begin by characterizing how uncertainty can be extracted from existing DNN-aided algorithms and distinguishing between approaches by their ability to associate internal features with meaningful KF quantities, such as the Kalman gain and prior covariance. We then identify that uncertainty extraction from existing architectures necessitates additional domain knowledge not required for state estimation. Based on this insight, we propose Bayesian KalmanNet, a novel DNN-aided KF that integrates Bayesian deep learning techniques with the recently proposed KalmanNet and transforms the KF into a stochastic machine learning architecture. This architecture employs sampling techniques to predict error covariance reliably without requiring additional domain knowledge, while retaining KalmanNet's ability to accurately track in partially known dynamics. Our numerical study demonstrates that Bayesian KalmanNet provides accurate and reliable tracking in various scenarios representing partially known dynamic systems.
  • Special Issue on MIMO Wireless Communications
    Item type: Other Journal Item
    Blum, Rick S.; Bölcskei, Helmut; Fitz, Michael P.; et al. (2003)
    IEEE Transactions on Signal Processing
  • Distributed Basis Pursuit
    Item type: Journal Article
    Mota, Joao F.C.; Xavier, Joao M.F.; Aguiar, Pedro M.Q.; et al. (2012)
    IEEE Transactions on Signal Processing
  • KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics
    Item type: Journal Article
    Revach, Guy; Shlezinger, Nir; Ni, Xiaoyong; et al. (2022)
    IEEE Transactions on Signal Processing
    State estimation of dynamical systems in real-time is a fundamental task in signal processing. For systems that are well-represented by a fully known linear Gaussian state space (SS) model, the celebrated Kalman filter (KF) is a low complexity optimal solution. However, both linearity of the underlying SS model and accurate knowledge of it are often not encountered in practice. Here, we present KalmanNet, a real-time state estimator that learns from data to carry out Kalman filtering under non-linear dynamics with partial information. By incorporating the structural SS model with a dedicated recurrent neural network module in the flow of the KF, we retain data efficiency and interpretability of the classic algorithm while implicitly learning complex dynamics from data. We demonstrate numerically that KalmanNet overcomes non-linearities and model mismatch, outperforming classic filtering methods operating with both mismatched and accurate domain knowledge.
  • Jammer-Resilient Time Synchronization in the MIMO Uplink
    Item type: Journal Article
    Marti, Gian; Arquint, Flurin; Studer, Christoph (2025)
    IEEE Transactions on Signal Processing
    Spatial filtering based on multiple-input multiple-output (MIMO) processing is a promising approach to jammer mitigation. Effective MIMO data detectors that mitigate smart jammers have recently been proposed, but they all assume perfect time synchronization between transmitter(s) and receiver. However, to the best of our knowledge, there are no methods for resilient time synchronization in the presence of smart jammers. To remedy this situation, we propose JASS, the first method that enables reliable time synchronization for the single-user MIMO uplink while mitigating smart jamming attacks. JASS detects a randomized synchronization sequence based on a novel optimization problem that fits a spatial filter to the time-windowed receive signal in order to mitigate the jammer. We underscore the efficacy of the proposed optimization problem by proving that it ensures successful time synchronization under certain intuitive conditions. We then derive an efficient algorithm for approximately solving our optimization problem. Finally, we use simulations to demonstrate the effectiveness of JASS against a wide range of different jammer types.
  • Calibration Using Matrix Completion With Application to Ultrasound Tomography
    Item type: Journal Article
    Parhizkar, Reza; Karbasi, Amin; Oh, Sewoong; et al. (2013)
    IEEE Transactions on Signal Processing
  • Discrete Signal Processing on Meet/Join Lattices
    Item type: Journal Article
    Püschel, Markus; Seifert, Bastian; Wendler, Chris (2021)
    IEEE Transactions on Signal Processing
    A lattice is a partially ordered set supporting a meet (join) operation that returns the largest lower bound (smallest upper bound) of two elements. Just like graphs, lattices are a fundamental structure that occurs across domains including social data analysis, natural language processing, computational chemistry and biology, and database theory. In this paper we introduce discrete-lattice signal processing (DLSP), an SP framework for data, or signals, indexed by such lattices. We use the meet (or join) to define a shift operation and derive associated notions of filtering, Fourier basis and transform, and frequency response. We show that the spectrum of a lattice signal inherits the lattice structure of the signal domain and derive a sampling theorem. Finally, we show two prototypical applications: spectral analysis of formal concept lattices in social science and sampling and Wiener filtering on multiset lattices in combinatorial auctions. Formal concept lattices are a representation of relations between objects and attributes. Since relations are equivalent to bipartite graphs and hypergraphs, DLSP offers a form of Fourier analysis for these structures.
Publications1 - 10 of 55