arXiv subjects

Yonina Eldar

Publications and source records attributed to Yonina Eldar.

9 recordsLinked to original sources

arXiv2026

Holographic Surface Enabled Integrated Sensing and Communications

Integrated sensing and communications (ISAC) is an essential 6G capability for joint data transmission and environmental sensing. To support 6G scenarios with stringent ISAC performance requirements, existing massive-MIMO-based systems are expected to scale toward ultra-massive MIMO. However, this scaling incurs prohibitive cost and power consumption when realized using widely adopted phased arrays with complex phase shifters and feeding networks. Recently, holographic integrated sensing and communications (HISAC) has emerged as a promising paradigm to address this issue. It employs reconfigurable holographic surfaces (RHSs), a type of leaky-wave antenna, as a cost- and energy-efficient implementation of ultra-massive MIMO-based ISAC, and offers enhanced flexibility for ISAC beam synthesis through holographic beamforming. In this paper, we provide a comprehensive tutorial on HISAC, focusing on how RHS-enabled holographic beamforming can be exploited to jointly support communication and sensing under practical hardware constraints. We first introduce the fundamentals of RHSs and discuss the unique leakage power constraint of holographic beamforming. We then present a general optimization framework for HISAC and show how HISAC enhances joint communication and sensing, sensing-assisted communication, and communication-assisted sensing. We further present HISAC system implementations and experimental results. Finally, we outline promising research directions for HISAC, highlighting the potential of HISAC in advancing efficient, flexible, and high-performance ISAC networks.

eess.SP↗

arXiv2023

DeepCut: Unsupervised Segmentation using Graph Neural Networks Clustering

Image segmentation is a fundamental task in computer vision. Data annotation for training supervised methods can be labor-intensive, motivating unsupervised methods. Current approaches often rely on extracting deep features from pre-trained networks to construct a graph, and classical clustering methods like k-means and normalized-cuts are then applied as a post-processing step. However, this approach reduces the high-dimensional information encoded in the features to pair-wise scalar affinities. To address this limitation, this study introduces a lightweight Graph Neural Network (GNN) to replace classical clustering methods while optimizing for the same clustering objective function. Unlike existing methods, our GNN takes both the pair-wise affinities between local image features and the raw features as input. This direct connection between the raw features and the clustering objective enables us to implicitly perform classification of the clusters between different graphs, resulting in part semantic segmentation without the need for additional post-processing steps. We demonstrate how classical clustering objectives can be formulated as self-supervised loss functions for training an image segmentation GNN. Furthermore, we employ the Correlation-Clustering (CC) objective to perform clustering without defining the number of clusters, allowing for k-less clustering. We apply the proposed method for object localization, segmentation, and semantic part segmentation tasks, surpassing state-of-the-art performance on multiple benchmarks.

cs.CV↗

arXiv2020

Phase Retrieval of Low-Rank Matrices by Anchored Regression

We study the low-rank phase retrieval problem, where we try to recover a $d_1\times d_2$ low-rank matrix from a series of phaseless linear measurements. This is a fourth-order inverse problem, as we are trying to recover factors of matrix that have been put through a quadratic nonlinearity after being multiplied together. We propose a solution to this problem using the recently introduced technique of anchored regression. This approach uses two different types of convex relaxations: we replace the quadratic equality constraints for the phaseless measurements by a search over a polytope, and enforce the rank constraint through nuclear norm regularization. The result is a convex program that works in the space of $d_1 \times d_2$ matrices. We analyze two specific scenarios. In the first, the target matrix is rank-$1$, and the observations are structured to correspond to a phaseless blind deconvolution. In the second, the target matrix has general rank, and we observe the magnitudes of the inner products against a series of independent Gaussian random matrices. In each of these problems, we show that the anchored regression returns an accurate estimate from a near-optimal number of measurements given that we have access to an anchor matrix of sufficient quality. We also show how to create such an anchor in the phaseless blind deconvolution problem, again from an optimal number of measurements, and present a partial result in this direction for the general rank problem.

cs.IT↗

arXiv2016

Subspace Learning with Partial Information

The goal of subspace learning is to find a $k$-dimensional subspace of $\mathbb{R}^d$, such that the expected squared distance between instance vectors and the subspace is as small as possible. In this paper we study subspace learning in a partial information setting, in which the learner can only observe $r \le d$ attributes from each instance vector. We propose several efficient algorithms for this task, and analyze their sample complexity

cs.LG↗

arXiv2015

Super-Resolution in Phase Space

This work considers the problem of super-resolution. The goal is to resolve a Dirac distribution from knowledge of its discrete, low-pass, Fourier measurements. Classically, such problems have been dealt with parameter estimation methods. Recently, it has been shown that convex-optimization based formulations facilitate a continuous time solution to the super-resolution problem. Here we treat super-resolution from low-pass measurements in Phase Space. The Phase Space transformation parametrically generalizes a number of well known unitary mappings such as the Fractional Fourier, Fresnel, Laplace and Fourier transforms. Consequently, our work provides a general super- resolution strategy which is backward compatible with the usual Fourier domain result. We consider low-pass measurements of Dirac distributions in Phase Space and show that the super-resolution problem can be cast as Total Variation minimization. Remarkably, even though are setting is quite general, the bounds on the minimum separation distance of Dirac distributions is comparable to existing methods.

cs.IT↗

arXiv2011

Phase Retrieval via Matrix Completion

This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that any complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent literature on matrix completion. More importantly, we also demonstrate that our noise-aware algorithms are stable in the sense that the reconstruction degrades gracefully as the signal-to-noise ratio decreases. Finally, we introduce some theory showing that one can design very simple structured illumination patterns such that three diffracted figures uniquely determine the phase of the object we wish to recover.

cs.IT↗

arXiv2011

C-HiLasso: A Collaborative Hierarchical Sparse Modeling Framework

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this work we combine the sparsity-inducing property of the Lasso model at the individual feature level, with the block-sparsity property of the Group Lasso model, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured. This results in the Hierarchical Lasso (HiLasso), which shows important practical modeling advantages. We then extend this approach to the collaborative case, where a set of simultaneously coded signals share the same sparsity pattern at the higher (group) level, but not necessarily at the lower (inside the group) level, obtaining the collaborative HiLasso model (C-HiLasso). Such signals then share the same active groups, or classes, but not necessarily the same active set. This model is very well suited for applications such as source identification and separation. An efficient optimization procedure, which guarantees convergence to the global optimum, is developed for these new models. The underlying presentation of the new framework and optimization approach is complemented with experimental examples and theoretical results regarding recovery guarantees for the proposed models.

stat.ML↗

arXiv2008

A Fast and Flexible Method for the Segmentation of aCGH Data

Motivation: Array Comparative Genomic Hybridization (aCGH) is used to scan the entire genome for variations in DNA copy number. A central task in the analysis of aCGH data is the segmentation into groups of probes sharing the same DNA copy number. Some well known segmentation methods suffer from very long running times, preventing interactive data analysis. Results: We suggest a new segmentation method based on wavelet decomposition and thresholding, which detects significant breakpoints in the data. Our algorithm is over 1,000 times faster than leading approaches, with similar performance. Another key advantage of the proposed method is its simplicity and flexibility. Due to its intuitive structure it can be easily generalized to incorporate several types of side information. Here we consider two extensions which include side information indicating the reliability of each measurement, and compensating for a changing variability in the measurement noise. The resulting algorithm outperforms existing methods, both in terms of speed and performance, when applied on real high density CGH data. Availability: Implementation is available under software tab at: http://www.ee.technion.ac.il/Sites/People/YoninaEldar/ Contact: yonina@ee.technion.ac.il

q-bio.QM↗

arXiv2004

Quantum State Detector Design: Optimal Worst-Case a posteriori Performance

The problem addressed is to design a detector which is maximally sensitive to specific quantum states. Here we concentrate on quantum state detection using the worst-case a posteriori probability of detection as the design criterion. This objective is equivalent to asking the question: if the detector declares that a specific state is present, what is the probability of that state actually being present? We show that maximizing this worst-case probability (maximizing the smallest possible value of this probability) is a quasiconvex optimization over the matrices of the POVM (positive operator valued measure) which characterize the measurement apparatus. We also show that with a given POVM, the optimization is quasiconvex in the matrix which characterizes the Kraus operator sum representation (OSR) in a fixed basis. We use Lagrange Duality Theory to establish the optimality conditions for both deterministic and randomized detection. We also examine the special case of detecting a single pure state. Numerical aspects of using convex optimization for quantum state detection are also discussed.

quant-ph↗