Super-Resolution and Reconstruction of Sparse Sub-Wavelength Images (2009)
Gazit, Snir, Szameit, Alexander, Eldar, Yonina C., Segev, Mordechai
We use compressed sensing to demonstrate theoretically the reconstruction of sub-wavelength features from measured far-field, and provide experimental proof-of-concept. The methods can be applied to...
Xampling--Part I: Practice (2009)
Mishali, Moshe, Eldar, Yonina C., Elron, Asaf
We introduce Xampling, a design methodology for sub-Nyquist sampling of continuous-time analog signals. The main principles underlying this framework are the ability to capture a broad signal model,...
Expected RIP: Conditioning of The Modulated Wideband Converter (2009)
Mishali, Moshe, Eldar, Yonina C.
The sensing matrix of a compressive system impacts the stability of the associated sparse recovery problem. In this paper, we study the sensing matrix of the modulated wideband converter, a recently...
Shrinkage Algorithms for MMSE Covariance Estimation (2009)
Chen, Yilun, Wiesel, Ami, Eldar, Yonina C., Hero III, Alfred O.
We address covariance estimation in the sense of minimum mean-squared error (MMSE) for Gaussian samples. Specifically, we consider shrinkage methods which are suitable for high dimensional problems...
Recovering Signals from Lowpass Data (2009)
Eldar, Yonina C., Pohl, Volker
The problem of recovering a signal from its low frequency components occurs often in practical applications due to the lowpass behavior of many physical systems. Here we study in detail conditions...
Non-Invertible Gabor Transforms (2009)
Matusiak, Ewa, Michaeli, Tomer, Eldar, Yonina C.
Time-frequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the...
Compressed Sensing of Block-Sparse Signals: Uncertainty Relations and Efficient Recovery (2009)
Eldar, Yonina C., Kuppinger, Patrick, Bölcskei, Helmut
We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An uncertainty relation for block-sparse signals is derived, based...
The Cramer-Rao Bound for Sparse Estimation (2009)
Ben-Haim, Zvika, Eldar, Yonina C.
The goal of this paper is to characterize the best achievable performance for the problem of estimating an unknown parameter having a sparse representation. Specifically, we consider the setting in...
Low Rate Sampling Schemes for Time Delay Estimation (2009)
Gedalyahu, Kfir, Eldar, Yonina C.
Time delay estimation arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel. Various approaches have been proposed in the literature...
Average Case Analysis of Multichannel Sparse Recovery Using Convex Relaxation (2009)
Eldar, Yonina C., Rauhut, Holger
In this paper, we consider recovery of jointly sparse multichannel signals from incomplete measurements. Several approaches have been developed to recover the unknown sparse vectors from the given...
Near-Oracle Performance of Basis Pursuit under Random Noise (2009)
Ben-Haim, Zvika, Eldar, Yonina C., Elad, Michael
We consider the problem of estimating a deterministic sparse vector x0 from underdetermined noisy measurements, in which the noise is a Gaussian random vector. Two techniques which are commonly used...
Covariance estimation in decomposable Gaussian graphical models (2009)
Wiesel, Ami, Eldar, Yonina C., Hero III, Alfred O.
Graphical models are a framework for representing and exploiting prior conditional independence structures within distributions using graphs. In the Gaussian case, these models are directly related...
From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals (2009)
Mishali, Moshe, Eldar, Yonina C.
Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of spectrum-blind sub-Nyquist...
Efficient Sampling of Sparse Wideband Analog Signals (2009)
Mishali, Moshe, Eldar, Yonina C., Tropp, Joel A.
Periodic nonuniform sampling is a known method to sample spectrally sparse signals below the Nyquist rate. This strategy relies on the implicit assumption that the individual samplers are exposed to...
Block-Sparsity: Coherence and Efficient Recovery (2008)
Eldar, Yonina C., Bolcskei, Helmut
We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occuring in clusters. Based on an uncertainty relation for block-sparse signals, we define...
Uncertainty Relations for Analog Signals (2008)
In the past several years there has been a surge of research investigating various aspects of sparse representations and compressed sensing. Most of this work has focused on the finite-dimensional...
Robust Recovery of Signals From a Structured Union of Subspaces (2008)
Eldar, Yonina C., Mishali, Moshe
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements...
Compressed Sensing of Analog Signals in Shift-Invariant Spaces (2008)
A traditional assumption underlying most data converters is that the signal should be sampled at a rate exceeding twice the highest frequency. This statement is based on a worst-case scenario in...
A Lower Bound on the Bayesian MSE Based on the Optimal Bias Function (2008)
Ben-Haim, Zvika, Eldar, Yonina C.
A lower bound on the minimum mean-squared error (MSE) in a Bayesian estimation problem is proposed in this paper. The bound is based on the approach of Young and Westerberg, in which a connection to...
Generalized SURE for Exponential Families: Applications to Regularization (2008)
Stein's unbiased risk estimate (SURE) was proposed by Stein for the independent, identically distributed (iid) Gaussian model in order to derive estimates that dominate least-squares (LS). In recent...
Enhancement of Color Images By Efficient (2008)
Liron D. Grossmann, Yonina C. Eldar
We propose an efficient method for reconstructing a full-color image from its partially sampled ver-sion. The suggested algorithm is non-iterative and is based on the properties of the human visual...
Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors (2008)
Mishali, Moshe, Eldar, Yonina C.
The rapid developing area of compressed sensing suggests that a sparse vector lying in an arbitrary high dimensional space can be accurately recovered from only a small set of non-adaptive linear...
A neural network implementing optimal state estimation based on dynamic spike train decoding (2008)
Omer Bobrowski, Ron Meir, Shy Shoham, Yonina C. Eldar
It is becoming increasingly evident that organisms acting in uncertain dynamical environments often employ exact or approximate Bayesian statistical calculations in order to continuously estimate the...
Omer Bobrowski, Ron Meir, Yonina C. Eldar
Neural Computation, In Press A key requirement facing organisms acting in uncertain dynamic environments is the real-time estimation and prediction of environmental states, based upon which effective...
LINEAR MIMO PRECODERS FOR FIXED RECEIVERS (2007)
Ami Wiesel, Yonina C. Eldar, Shlomo Shamai (shitz
We consider the problem of designing linear multiple input multiple output (MIMO) precoders for fixed receivers. We first derive a precoder that minimizes the average power subject to Signal to...
Blind Minimax Estimation (2007)
Ben-Haim, Zvika, Eldar, Yonina C.
We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax...
Blind Multi-Band Signal Reconstruction: Compressed Sensing for Analog Signals (2007)
Mishali, Moshe, Eldar, Yonina C.
We address the problem of reconstructing a multi-band signal from its sub-Nyquist point-wise samples. To date, all reconstruction methods proposed for this class of signals assumed knowledge of the...
A neural network implementing optimal state estimation based on dynamic spike train decoding (2007)
Omer Bobrowski, Ron Meir, Shy Shoham, Yonina C. Eldar
It is becoming increasingly evident that organisms acting in uncertain dynamical environments often employ exact or approximate Bayesian statistical calculations in order to continuously estimate the...
Optimal Encoding of Classical Information in a Quantum Medium (2006)
We investigate optimal encoding and retrieval of digital data, when the storage/communication medium is described by quantum mechanics. We assume an m-ary alphabet with arbitrary prior distribution,...
Non-ideal sampling and interpolation from noisy observations in shift-invariant spaces (2006)
Yonina C. Eldar, Michael Unser
Abstract—Digital analysis and processing of signals inherently relies on the existence of methods for reconstructing a continuoustime signal from a sequence of corrupted discrete-time samples. In...
Characterization of Oblique Dual Frame Pairs (2006)
Yonina C. Eldar, Ole Christensen
Given a frame for a subspace 𝒲 of a Hilbert space ℋ, we consider all possible families of oblique dual frame vectors on an appropriately chosen subspace 𝒱. In place of the standard...
A constructive inversion framework for twisted convolution (2005)
Eldar, Yonina C., Matusiak, Ewa, Werther, Tobias
In this paper we develop constructive invertibility conditions for the twisted convolution. Our approach is based on splitting the twisted convolution with rational parameters into a finite number of...
Quantum Detection with Unknown States (2005)
We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a...
Linear precoding via conic optimization for fixed MIMO receivers (2004)
Ami Wiesel, Yonina C. Eldar, Shlomo Shamai (Shitz)
We consider the problem of designing linear precoders for fixed multiple input multiple output (MIMO) receivers. Two di#erent design criteria are considered. In the first, we minimize the transmitted...
Multiuser Precoders for Fixed Receivers (2004)
Ami Wiesel Yonina, Yonina C. Eldar, Shlomo Shamai (shitz
We consider the problem of designing precoders for multiuser systems using fixed receivers. We first derive a precoder that minimizes the transmitted power subject to signal to interference plus...
Optimal quantum detectors for unambiguous detection of mixed states (2003)
Eldar, Yonina C., Stojnic, Mihailo, Hassibi, Babak
We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space...
Von Neumann Measurement is Optimal for Detecting Linearly Independent Mixed Quantum States (2003)
We consider the problem of designing a measurement to minimize the probability of a detection error when distinguishing between a collection of possibly non-orthogonal mixed quantum states. We show...
A Competitive Minimax Approach to Robust Estimation in Linear Models (2003)
We consider the problem of estimating, in the presence of model uncertainties, a random vector x that is observed through a linear transformation H and corrupted by additive noise. We first assume...
Optimal Detection of Symmetric Mixed Quantum States (2002)
Eldar, Yonina C., Megretski, Alexandre, Verghese, George C.
We develop a sufficient condition for the least-squares measurement (LSM), or the square-root measurement, to minimize the probability of a detection error when distinguishing between a collection of...
Mixed quantum state detection with inconclusive results (2002)
We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a...
A Semidefinite Programming Approach to Optimal Unambiguous Discrimination of Quantum States (2002)
In this paper we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the...
Designing Optimal Quantum Detectors Via Semidefinite Programming (2002)
Eldar, Yonina C., Megretski, Alexandre, Verghese, George C.
We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of...
www.elsevier.com/locate/laa Least-squares orthogonalization using semidefinite programming
Geometrically Uniform Frames (2001)
Eldar, Yonina C., Bolcskei, H.
We introduce a new class of frames with strong symmetry properties called geometrically uniform frames (GU), that are defined over an abelian group of unitary matrices and are generated by a single...
On quantum detection and the square-root measurement (2001)
Yonina C. Eldar, Student Member, G. David Forney
Abstract—In this paper, we consider the problem of constructing measurements optimized to distinguish between a collection of possibly nonorthogonal quantum states. We consider a collection of pure...
Fast communication Orthogonal multiuser detection (2001)
In this paper we propose a new linear multiuser detector for synchronous CDMA systems. Speci cally, the received signal is demodulated using an orthogonal multiuser (OMU) receiver that is matched to...
MMSE whitening and subspace whitening (2001)
This paper develops a linear whitening transformation that minimizes the mean squared error (MSE) between the original and whitened data, i.e., that results in a white output that is as close as...
On Quantum Detection and the Square-Root Measurement (2000)
Eldar, Yonina C., Forney Jr, G. David
In this paper we consider the problem of constructing measurements optimized to distinguish between a collection of possibly non-orthogonal quantum states. We consider a collection of pure states and...
Competitive Mean-Squared Error Beamforming (1998)
Eldar, Yonina C., Nehorai, Arye
We consider the problem of designing a linear beamformer to estimate a source signal s(t) from array observations. Conventional beamforming methods typically aim at maximizing the...