Petre Stoica

Uppsala University, Uppsala, Uppsala, Sweden

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Publications (687)1108.05 Total impact

  • Source
    Zai Yang · Lihua Xie · Petre Stoica

    Full-text · Dataset · Jan 2016
  • Source
    Zai Yang · Lihua Xie · Petre Stoica

    Full-text · Conference Paper · Jun 2015
  • Source
    Zai Yang · Lihua Xie · Petre Stoica
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    ABSTRACT: The Vandermonde decomposition of Toeplitz matrices, discovered by Carath\'{e}odory and Fej\'{e}r in the 1910s and rediscovered by Pisarenko in the 1970s, forms the basis of modern subspace methods for 1D frequency estimation. Many related numerical tools have also been developed for multidimensional (MD), especially 2D, frequency estimation; however, a fundamental question has remained unresolved as to whether an analog of the Vandermonde decomposition holds for multilevel Toeplitz matrices in the MD case. In this paper, an affirmative answer to this question and a constructive method for finding the decomposition are provided when the matrix rank is lower than the dimension of each Toeplitz block. A numerical method for searching for a decomposition is also proposed when the matrix rank is higher. The new results are applied to studying MD frequency estimation within the recent super-resolution framework. A precise formulation of the atomic $\ell_0$ norm is derived using the Vandermonde decomposition. Practical algorithms for frequency estimation are proposed based on relaxation techniques. Extensive numerical simulations are provided to demonstrate the effectiveness of these algorithms compared to the existing atomic norm method.
    Preview · Article · May 2015
  • Source
    Zai Yang · Lihua Xie · Petre Stoica
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    ABSTRACT: The Vandermonde decomposition of Toeplitz matrices, discovered by Carathéodory and Fejér in the 1910s and rediscovered by Pisarenko in the 1970s, forms the basis of modern subspace methods for 1D frequency estimation. Many related numerical tools have also been developed for multidimensional (MD), especially 2D, frequency estimation; however, a fundamental question has remained unresolved as to whether an analog of the Vandermonde decomposition holds for multilevel Toeplitz matrices in the MD case. In this paper, an affirmative answer to this question and a constructive method for finding the decomposition are provided when the matrix rank is lower than the dimension of each Toeplitz block. A numerical method for searching for a decomposition is also proposed when the matrix rank is higher. The new results are applied to studying MD frequency estimation within the recent super-resolution framework. A precise formulation of the atomic 0 norm is derived using the Vandermonde decomposition. Practical algorithms for frequency estimation are proposed based on relaxation techniques. Extensive numerical simulations are provided to demonstrate the effectiveness of these algorithms compared to the existing atomic norm method.
    Full-text · Article · May 2015
  • Zai Yang · Lihua Xie · Petre Stoica
    [Show abstract] [Hide abstract]
    ABSTRACT: The Vandermonde decomposition of Toeplitz matrices, discovered by Carathéodory and Fejér in the 1910s and rediscovered by Pisarenko in the 1970s, forms the basis of modern subspace methods for 1D frequency estimation. Many related numerical tools have also been developed for multidimensional (MD), especially 2D, frequency estimation; however, a fundamental question has remained unresolved as to whether an analog of the Vandermonde decomposition holds for multilevel Toeplitz matrices in the MD case. In this paper, an affirmative answer to this question and a constructive method for finding the decomposition are provided when the matrix rank is lower than the dimension of each Toeplitz block. A numerical method for searching for a decomposition is also proposed when the matrix rank is higher. The new results are applied to studying MD frequency estimation within the recent super-resolution framework. A precise formulation of the atomic 0 norm is derived using the Vandermonde decomposition. Practical algorithms for frequency estimation are proposed based on relaxation techniques. Extensive numerical simulations are provided to demonstrate the effectiveness of these algorithms compared to the existing atomic norm method.
    No preview · Article · May 2015
  • Source
    Dave Zachariah · Petre Stoica
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    ABSTRACT: In this paper we derive an online estimator for sparse parameter vectors which, unlike the LASSO approach, does not require the tuning of any hyperparameters. The algorithm is based on a covariance matching approach and is equivalent to a weighted version of the square-root LASSO. The computational complexity of the estimator is of the same order as that of the online versions of regularized least-squares (RLS) and LASSO. We provide a numerical comparison with feasible and infeasible implementations of the LASSO and RLS to illustrate the advantage of the proposed online hyperparameter-free estimator.
    Preview · Article · May 2015 · IEEE Transactions on Signal Processing
  • Dave Zachariah · Petre Stoica
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    ABSTRACT: The estimation of multiple parameters is a common task in signal processing. The Cramer-Rao bound (CRB) sets a statistical lower limit on the resulting errors when estimating parameters from a set of random observations. It can be understood as a fundamental measure of parameter uncertainty [1], [2]. As a general example, suppose denotes the vector of sought parameters and that the random observation model can be written as y = xi + w, (1) where xi is a function or signal parameterized by i and w is a zero-mean Gaussian noise vector. Then the CRB for i has the following notable properties: 1) For a fixed i, the CRB for i decreases as the dimension of y increases. 2) For a fixed y, if additional parameters i u are estimated, then the CRB for i increases as the dimension of i u increases. 3) If adding a set of observations yu requires estimating additional parameters, i u then the CRB for i decreases as the dimension of yu increases, provided the dimension of i u does not exceed that of yu [3]. This property implies both 1) and 2) above. 4) Among all possible distributions of w with a fixed covariance matrix, the CRB for i attains its maximum when w is Gaussian, i.e., the Gaussian scenario is the "worst case" for estimating θ [4]-[6].
    No preview · Article · Feb 2015 · IEEE Signal Processing Magazine
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    ABSTRACT: PurposeModels based on a sum of damped exponentials occur in many applications, particularly in multicomponent T2 relaxometry. The problem of estimating the relaxation parameters and the corresponding amplitudes is known to be difficult, especially as the number of components increases. In this article, the commonly used non-negative least squares spectrum approach is compared to a recently published estimation algorithm abbreviated as Exponential Analysis via System Identification using Steiglitz–McBride.Methods The two algorithms are evaluated via simulation, and their performance is compared to a statistical benchmark on precision given by the Cramér–Rao bound. By applying the algorithms to an in vivo brain multi-echo spin-echo dataset, containing 32 images, estimates of the myelin water fraction are computed.ResultsExponential Analysis via System Identification using Steiglitz–McBride is shown to have superior performance when applied to simulated T2 relaxation data. For the in vivo brain, Exponential Analysis via System Identification using Steiglitz–McBride gives an myelin water fraction map with a more concentrated distribution of myelin water and less noise, compared to non-negative least squares.Conclusion The Exponential Analysis via System Identification using Steiglitz–McBride algorithm provides an efficient and user-parameter-free alternative to non-negative least squares for estimating the parameters of multiple relaxation components and gives a new way of estimating the spatial variations of myelin in the brain. Magn Reson Med, 2015. © 2015 Wiley Periodicals, Inc.
    No preview · Article · Jan 2015 · Magnetic Resonance in Medicine
  • Ode Ojowu · Luzhou Xu · Jian Li · John Anderson · Lam Nguyen · Petre Stoica

    No preview · Article · Jan 2015
  • H. Hu · M. Soltanalian · P. Stoica · X. Zhu
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    ABSTRACT: Owing to the inherent sparsity of the target scene, compressed sensing (CS) has been successfully employed in radar applications. It is known that the performance of target scene recovery in CS scenarios depends highly on the coherence of the sensing matrix (CSM), which is determined by the radar transmit waveform. In this paper, we present a cyclic optimization algorithm to effectively reduce the CSM via a judicious design of the radar waveform. The proposed method provides a reduction in the size of the Gram matrix associated with the sensing matrix, and moreover, relies on the fast Fourier transform (FFT) operations to improve the computation speed. As a result, the suggested algorithm can be used for large dimension designs (with 100 variables) even on an ordinary PC. The effectiveness of the proposed algorithm is illustrated through numerical examples.
    No preview · Article · Nov 2014
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    ABSTRACT: In this paper, we devise a computational approach for designing polyphase sequences with two key properties; (i) a phase argument which is piecewise linear, and (ii) an impulse-like autocorrelation. The proposed approach relies on fast Fourier transform (FFT) operations and thus can be used efficiently to design sequences with a large length or alphabet size. Moreover, using the suggested method, one can construct many new such polyphase sequences which were not known and/or could not be constructed by the previous formulations in the literature. Several numerical examples are provided to show the performance of the proposed design framework in different scenarios.
    No preview · Article · Nov 2014
  • M. Soltanalian · P. Stoica · J. Li
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    ABSTRACT: Costas arrays are mainly known as a certain type of optimized time-frequency coding pattern for sonar and radar. In order to fulfill the need for effective computational approaches to find Costas arrays, in this paper, we propose a sparse formulation of the Costas array search problem. The new sparse representation can pave the way for using an extensive number of methods offered by the sparse signal recovery literature. It is further shown that Costas arrays can be obtained using an equivalent quadratic program with linear constraints. A numerical approach is devised and used to illustrate the performance of the proposed formulations.
    No preview · Article · Nov 2014
  • J. Karlsson · J. Li · P. Stoica
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    ABSTRACT: Filter design is a fundamental problem in signal processing and important in many applications. In this paper we consider a communication application with spectral constraints, using filter designs that can be solved globally via convex optimization. Tradeoffs are discussed in order to determine which design is the most appropriate, and for these applications, finite impulse response filters appear to be more suitable than infinite impulse response filters since they allow for more flexible objective functions, shorter transients, and faster filter implementations.
    No preview · Article · Nov 2014
  • Marcus Björk · Petre Stoica
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    ABSTRACT: Estimation of the transverse relaxation time, , from multi-echo spin-echo images is usually performed using the magnitude of the noisy data, and a least squares (LS) approach. The noise in these magnitude images is Rice distributed, which can lead to a considerable bias in the LS-based estimates. One way to avoid this bias problem is to estimate a real-valued and Gaussian distributed dataset from the complex data, rather than using the magnitude. In this paper, we propose two algorithms for phase correction which can be used to generate real-valued data suitable for LS-based parameter estimation approaches. The first is a Weighted Linear Phase Estimation algorithm, abbreviated as WELPE. This method provides an improvement over a previously published algorithm, while simplifying the estimation procedure and extending it to support multi-coil input. The algorithm fits a linearly parameterized function to the multi-echo phase-data in each voxel and, based on this estimated phase, projects the data onto the real axis. The second method is a maximum likelihood estimator of the true decaying signal magnitude, which can be efficiently implemented when the phase variation is linear in time. The performance of the algorithms is demonstrated via Monte Carlo simulations, by comparing the accuracy of the estimates. Furthermore, it is shown that using one of the proposed algorithms enables more accurate estimates; in particular, phase corrected data significantly reduces the estimation bias in multi-component relaxometry example, compared to when using magnitude data. WELPE is also applied to a 32-echo in vivo brain dataset, to show its practical feasibility.
    No preview · Article · Oct 2014 · Journal of Magnetic Resonance
  • Mojtaba Soltanalian · Petre Stoica
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    ABSTRACT: In this paper, perfect root-of-unity sequences (PRUS) with entries in $alpha_p = {x in {BBC} ,vert, x^p =1}$ (where $p$ is a prime) are studied. A lower bound on the number of distinct phases that are used in PRUS over $alpha_p$ is derived. We show that PRUS of length $L geq p(p-1)$ must use all phases in $alpha_p$. Certain conditions on the lengths of PRUS are derived. Showing that the phase values of PRUS must follow a given difference multiset property, we derive a set of equations (which we call the principal equations) that give possible lengths of a PRUS over $alpha_p$ together with their phase distributions. The usefulness of the principal equations is discussed, and guidelines for efficient construction of PRUS are provided. Through numerical results, contributions also are made to the current state-of-knowledge regarding the existence of PRUS. In particular, a combination of the developed ideas allowed us to numerically settle the problem of existence of PRUS with $(L, p)=(28, 7)$ within about two weeks—a problem whose solution (without using the ideas in this paper) would likely take more than three million years on a standard PC.
    No preview · Article · Oct 2014 · IEEE Transactions on Signal Processing
  • Source
    Petre Stoica · Dave Zachariah · Jian Li
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    ABSTRACT: In this paper we present the SPICE approach for sparse parameter estimation in a framework that unifies it with other hyperparameter-free methods, namely LIKES, SLIM and IAA. Specifically, we show how the latter methods can be interpreted as variants of an adaptively reweighted SPICE method. Furthermore, we establish a connection between SPICE and the l1-penalized LAD estimator as well as the square-root LASSO method. We evaluate the four methods mentioned above in a generic sparse regression problem and in an array processing application.
    Preview · Article · Oct 2014 · Digital Signal Processing
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    ABSTRACT: The balanced steady-state free precession (bSSFP) pulse sequence has shown to be of great interest due to its high signal-to-noise ratio efficiency. However, bSSFP images often suffer from banding artifacts due to off-resonance effects, which we aim to minimize in this article. We present a general and fast two-step algorithm for 1) estimating the unknowns in the bSSFP signal model from multiple phase-cycled acquisitions, and 2) reconstructing band-free images. The first step, linearization for off-resonance estimation (LORE), solves the nonlinear problem approximately by a robust linear approach. The second step applies a Gauss-Newton algorithm, initialized by LORE, to minimize the nonlinear least squares criterion. We name the full algorithm LORE-GN. We derive the Cramér-Rao bound, a theoretical lower bound of the variance for any unbiased estimator, and show that LORE-GN is statistically efficient. Furthermore, we show that simultaneous estimation of T1 and T2 from phase-cycled bSSFP is difficult, since the Cramér-Rao bound is high at common signal-to-noise ratio. Using simulated, phantom, and in vivo data, we illustrate the band-reduction capabilities of LORE-GN compared to other techniques, such as sum-of-squares. Using LORE-GN we can successfully minimize banding artifacts in bSSFP. Magn Reson Med, 2013. © 2013 Wiley Periodicals, Inc.
    No preview · Article · Sep 2014 · Magnetic Resonance in Medicine
  • Mojtaba Soltanalian · Heng Hu · Petre Stoica
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    ABSTRACT: MIMO radar beamforming algorithms usually consist of a signal covariance matrix synthesis stage, followed by signal synthesis to fit the obtained covariance matrix. In this paper, we propose a radar beamforming algorithm (called Beam-Shape) that performs a single-stage radar transmit signal design; i.e. no prior covariance matrix synthesis is required. Beam-Shape׳s theoretical as well as computational characteristics, include (i) the possibility of considering signal structures such as low-rank, discrete-phase or low-PAR, and (ii) the significantly reduced computational burden for beampattern matching scenarios with large grid size. The effectiveness of the proposed algorithm is illustrated through numerical examples.
    No preview · Article · Sep 2014 · Signal Processing
  • Mojtaba Soltanalian · Petre Stoica
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    ABSTRACT: The NP-hard problem of optimizing a quadratic form over the unimodular vector set arises in radar code design scenarios as well as other active sensing and communication applications. To tackle this problem, a monotonically error-bound improving technique (MERIT) is proposed to obtain the global optimum or a local optimum of UQP with good sub-optimality guarantees. The provided sub-optimality guarantees are case-dependent and may outperform the π/4 approximation guarantee of semi-definite relaxation.
    No preview · Conference Paper · May 2014
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    ABSTRACT: In this paper, we study the problem of unimodular code design to improve the detection performance of statistical multiple-input multiple-output (MIMO) radar systems. To this end, we consider a system transmitting arbitrary unimodular signals and a discrete-time formulation of the problem. Due to the complicated form of the performance metric of the optimal detector, we resort to the Bhattacharyya distance for code design. We devise a novel method based on the majorization of matrix functions to obtain solutions to the constrained design problem. Simulation results show the effectiveness of the proposed method.
    No preview · Conference Paper · May 2014

Publication Stats

25k Citations
1,108.05 Total Impact Points

Institutions

  • 1970-2015
    • Uppsala University
      • • Division of Systems and Control
      • • Department of Information Technology
      Uppsala, Uppsala, Sweden
  • 1995-2010
    • University of Florida
      • Department of Electrical and Computer Engineering
      Gainesville, FL, United States
    • Ecole Nationale Supérieure d’Electrotechnique, d’Electronique, d’Informatique, d’Hydraulique et des Télécommunications
      Tolosa de Llenguadoc, Midi-Pyrénées, France
  • 2004
    • Karlstads universitet
      • Department of Engineering and Physics
      Karlstad, Värmland, Sweden
  • 1999-2001
    • McMaster University
      • Department of Electrical and Computer Engineering
      Hamilton, Ontario, Canada
    • Stevens Institute of Technology
      • Department of Electrical & Computer Engineering
      Hoboken, New Jersey, United States
    • Ruhr-Universität Bochum
      Bochum, North Rhine-Westphalia, Germany
  • 2000
    • Western Sydney University
      Sydney, New South Wales, Australia
  • 1997-2000
    • Brigham Young University - Provo Main Campus
      • Department of Electrical and Computer Engineering
      Provo, UT, United States
    • KTH Royal Institute of Technology
      • • Division of Optimization and Systems Theory
      • • School of Electrical Engineering (EE)
      Tukholma, Stockholm, Sweden
  • 1994-1998
    • Chalmers University of Technology
      • Department of Signals and Systems
      Göteborg, Vaestra Goetaland, Sweden
  • 1977-1995
    • Polytechnic University of Bucharest
      București, Bucureşti, Romania
  • 1993
    • Tel Aviv University
      • School of Electrical Engineering
      Tel Aviv, Tel Aviv, Israel
  • 1992
    • Stanford University
      • Information Systems Laboratory
      Stanford, CA, United States
  • 1987-1991
    • Yale University
      • Department of Electrical Engineering
      New Haven, Connecticut, United States
  • 1988
    • National Polytechnic Institute
      Ciudad de México, Mexico City, Mexico