Petre Stoica

Uppsala University, Uppsala, Uppsala, Sweden

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Publications (672)1137.73 Total impact

  • 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.
    IEEE Transactions on Signal Processing 05/2015; 63(13):1-1. DOI:10.1109/TSP.2015.2421472 · 3.20 Impact Factor
  • 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].
    IEEE Signal Processing Magazine 02/2015; 32(2). DOI:10.1109/MSP.2014.2365593 · 4.48 Impact Factor
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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.
    Magnetic Resonance in Medicine 01/2015; DOI:10.1002/mrm.25583 · 3.40 Impact Factor
  • 01/2015; 5. DOI:10.14355/ijrsa.2015.05.002
  • Marcus Björk, Petre Stoica
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    ABSTRACT: Two methods for temporal phase correction are presented and analysed.•Show superior performance in simulation compared to the previous method.•Versatile, computationally efficient, and easy to implement and use.•Phase correction can significantly reduce the bias in multi-component relaxometry.
  • 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.
    IEEE Transactions on Signal Processing 10/2014; 62(20):5458-5470. DOI:10.1109/TSP.2014.2349881 · 3.20 Impact Factor
  • 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.
    Digital Signal Processing 10/2014; 33. DOI:10.1016/j.dsp.2014.06.010 · 1.50 Impact Factor
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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.
    Magnetic Resonance in Medicine 09/2014; 72(3). DOI:10.1002/mrm.24986 · 3.40 Impact Factor
  • 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.
    Signal Processing 09/2014; 102:132–138. DOI:10.1016/j.sigpro.2014.03.013 · 2.24 Impact Factor
  • William Rowe, Petre Stoica, Jian Li
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    ABSTRACT: In active sensing, transmitters emit probing waveforms into the environment. The probing waveforms interact with scatters that reflect distorted copies of the waveforms. Receivers then measure the distorted copies to infer information about the environment. The choice of the probing waveform is important because it affects slant range resolution, Doppler tolerance, clutter, and electronic countermeasures. A traditional performance metric for the probing waveform is the ambiguity function, which describes the correlation between the waveform and a delayed and (narrowband) Doppler shifted copy of the same waveform [1]. The direct synthesis of a waveform given a desired ambiguity function is exceedingly difficult [2]. Often designers focus on optimizing only the waveform?s autocorrelation function (which is the zero Doppler cut of the ambiguity function). Any method that optimizes the autocorrelation function is implicitly performing spectral shaping by trying to flatten the passband of the waveform?s spectrum [1], [2].
    IEEE Signal Processing Magazine 05/2014; 31(3):157-162. DOI:10.1109/MSP.2014.2301792 · 4.48 Impact Factor
  • ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); 05/2014
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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.
    ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); 05/2014
  • 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.
    ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); 05/2014
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    ABSTRACT: In this paper, we deal with cognitive design of the transmit signal and receive filter optimizing the radar detection performance without affecting spectral compatibility with some licensed overlaid electromagnetic radiators. We assume that the radar is embedded in a highly reverberating environment and exploit cognition provided by Radio Environmental Map (REM), to induce spectral constraints on the radar waveform, by a dynamic environmental database, to predict the actual scattering scenario, and by an Electronic Support Measurement (ESM) system, to acquire information about hostile active jammers. At the design stage, we develop an optimization procedure which sequentially improves the Signal to Interference plus Noise Ratio (SINR). Moreover, we enforce a spectral energy constraint and a similarity constraint between the transmitted signal and a known radar waveform. At the analysis stage, we assess the effectiveness of the proposed technique to optimizing SINR while providing spectral coexistence.
    2014 IEEE Radar Conference (RadarCon); 05/2014
  • Marcus Bjork, Petre Stoica
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    ABSTRACT: In this paper we present an algorithm for sequence design with magnitude constraints. We formulate the design problem in a general setting, but also illustrate its relevance to parallel excitation MRI. The formulated non-convex design optimization criterion is minimized locally by means of a cyclic algorithm, consisting of two simple algebraic sub-steps. Since the algorithm truly minimizes the criterion, the obtained sequence designs are guaranteed to improve upon the estimates provided by a previous method, which is based on the heuristic principle of the Iterative Quadratic Maximum Likelihood algorithm. The performance of the proposed algorithm is illustrated in two numerical examples.
    ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); 05/2014
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    ABSTRACT: In this paper, we study the problem of approaching peak periodic or aperiodic correlation bounds for complex-valued sets of sequences. In particular, novel algorithms based on alternating projections are devised to approach a given peak periodic or aperiodic correlation bound. Several numerical examples are presented to assess the tightness of the known correlation bounds as well as to illustrate the effectiveness of the proposed methods for meeting these bounds.
    ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP); 05/2014
  • Source
    Mojtaba Soltanalian, Petre Stoica
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    ABSTRACT: In this paper, we propose a recursive method for finding Costas arrays that relies on a particular formation of Costas arrays from similar patterns of smaller size. By using such an idea, the proposed algorithm is able to dramatically reduce the computational burden (when compared to the exhaustive search), and at the same time, still can find all possible Costas arrays of given size. Similar to exhaustive search, the proposed method can be conveniently implemented in parallel computing. The efficiency of the method is discussed based on theoretical and numerical results.
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    ABSTRACT: In this paper, we study the problem of meeting peak periodic or aperiodic correlation bounds for complex-valued sets of sequences. To this end, the Welch, Levenstein, and Exponential bounds on the peak inner-product of sequence sets are considered and used to provide compound peak correlation bounds in both periodic and aperiodic cases. The peak aperiodic correlation bound is further improved by using the intrinsic dimension deficiencies associated with its formulation. In comparison to the compound bound, the new aperiodic bound contributes an improvement of more than 35% for some specific values of the sequence length $n$ and set cardinality $m$ . We study the tightness of the provided bounds by using both analytical and computational tools. In particular, novel algorithms based on alternating projections are devised to approach a given peak periodic or aperiodic correlation bound. Several numerical examples are presented to assess the tightness of the provided correlation bounds as well as to illustrate the effectiveness of the proposed methods for meeting these bounds.
    IEEE Transactions on Signal Processing 03/2014; 62(5):1210-1220. DOI:10.1109/TSP.2014.2300064 · 3.20 Impact Factor
  • Prabhu Babu, Petre Stoica
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    ABSTRACT: In this note we show that the sparse estimation technique named Square-Root LASSO (SR-LASSO) is connected to a previously introduced method named SPICE. More concretely we prove that the SR-LASSO with a unit weighting factor is identical to SPICE. Furthermore we show via numerical simulations that the performance of the SR-LASSO changes insignificantly when the weighting factor is varied. SPICE stands for sparse iterative covariance-based estimation and LASSO for least absolute shrinkage and selection operator.
    Signal Processing 02/2014; 95:10-14. DOI:10.1016/j.sigpro.2013.08.011 · 2.24 Impact Factor
  • Source
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    ABSTRACT: In this paper, we study the joint design of Doppler robust transmit sequence and receive filter to improve the performance of an active sensing system dealing with signal-dependent interference. The signal-to-noise-plus-interference (SINR) of the filter output is considered as the performance measure of the system. The design problem is cast as a max-min optimization problem to robustify the system SINR with respect to the unknown Doppler shifts of the targets. To tackle the design problem, which belongs to a class of NP-hard problems, we devise a novel method (which we call DESIDE) to obtain optimized pairs of transmit sequence and receive filter sharing the desired robustness property. The proposed method is based on a cyclic maximization of SINR expressions with relaxed rank-one constraints, and is followed by a novel synthesis stage. We devise synthesis algorithms to obtain high quality pairs of transmit sequence and receive filter that well approximate the behavior of the optimal SINR (of the relaxed problem) with respect to target Doppler shift. Several numerical examples are provided to analyze the performance obtained by DESIDE.
    IEEE Transactions on Signal Processing 02/2014; 62(4):772-785. DOI:10.1109/TSP.2013.2288082 · 3.20 Impact Factor

Publication Stats

22k Citations
1,137.73 Total Impact Points

Institutions

  • 1970–2015
    • Uppsala University
      • • Department of Information Technology
      • • Division of Systems and Control
      Uppsala, Uppsala, Sweden
  • 2010–2011
    • KTH Royal Institute of Technology
      • Automatic Control Lab (AC)
      Tukholma, Stockholm, Sweden
  • 1995–2011
    • University of Florida
      • Department of Electrical and Computer Engineering
      Gainesville, Florida, United States
    • Ecole Nationale Supérieure d’Electrotechnique, d’Electronique, d’Informatique, d’Hydraulique et des Télécommunications
      Tolosa de Llenguadoc, Midi-Pyrénées, France
  • 2006
    • Embry-Riddle Aeronautical University
      PRC, Arizona, United States
    • California Institute of Technology
      • Department of Electrical Engineering
      Pasadena, CA, United States
  • 2005
    • George Washington University
      • Department of Electrical & Computer Engineering
      Washington, D. C., DC, United States
  • 2004
    • University of California, Los Angeles
      Los Angeles, California, United States
    • Karlstads universitet
      Karlstad, Värmland, Sweden
  • 2002
    • Queensland University of Technology
      Brisbane, Queensland, Australia
  • 2000–2002
    • McMaster University
      • Department of Electrical and Computer Engineering
      Hamilton, Ontario, Canada
    • University of Western Sydney
      Penrith, New South Wales, Australia
  • 1999–2002
    • Stevens Institute of Technology
      • Department of Electrical & Computer Engineering
      Hoboken, NJ, United States
    • Ruhr-Universität Bochum
      Bochum, North Rhine-Westphalia, Germany
  • 1992–2002
    • Stanford University
      • Information Systems Laboratory
      Stanford, CA, United States
  • 2001
    • The University of Hong Kong
      • Department of Electrical and Electronic Engineering
      Hong Kong, Hong Kong
    • Tampere University of Technology
      • Signaalinkäsittelyn laitos
      Tampere, Western Finland, Finland
  • 1997–2001
    • Brigham Young University - Provo Main Campus
      • Department of Electrical and Computer Engineering
      Provo, UT, United States
  • 1994–1998
    • Chalmers University of Technology
      • Department of Signals and Systems
      Göteborg, Vaestra Goetaland, Sweden
    • University of Minnesota Duluth
      • Department of Electrical Engineering
      Duluth, Minnesota, United States
  • 1993–1995
    • Tel Aviv University
      • School of Electrical Engineering
      Tel Aviv, Tel Aviv, Israel
  • 1977–1994
    • Polytechnic University of Bucharest
      Bucureşti, Bucureşti, Romania
  • 1987–1991
    • Yale University
      • Department of Electrical Engineering
      New Haven, Connecticut, United States
  • 1988
    • National Polytechnic Institute
      Ciudad de México, Mexico City, Mexico
    • Technische Universiteit Eindhoven
      • Department of Electrical Engineering
      Eindhoven, North Brabant, Netherlands