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  • 1.
    Li, Kezhi
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Cong, S.
    A robust compressive quantum state tomography algorithm using ADMM2014In: IFAC Proceedings Volumes (IFAC-PapersOnline), 2014, p. 6878-6883Conference paper (Refereed)
    Abstract [en]

    The possible state space dimension increases exponentially with respect to the number of qubits. This feature makes the quantum state tomography expensive and impractical for identifying the state of merely several qubits. The recent developed approach, compressed sensing, gives us an alternative to estimate the quantum state with fewer measurements. It is proved that the estimation then can be converted to a convex optimization problem with quantum mechanics constraints. In this paper we present an alternating augmented Lagrangian method for quantum convex optimization problem aiming to recover pure or near pure quantum states corrupted by sparse noise given observables and the expectation values of the measurements. The proposed algorithm is much faster, robust to outlier noises (even very large for some entries) and can solve the reconstruction problem distributively. The simulations verify the superiority of the proposed algorithm and compare it to the conventional least square and compressive quantum tomography using the Dantzig method.

  • 2.
    Li, Kezhi
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Cong, Shuang
    State of the art and prospects of structured sensing matrices in compressed sensing2015In: Frontiers of Computer Science, ISSN 2095-2228, E-ISSN 2095-2236, Vol. 9, no 5, p. 665-677Article, review/survey (Refereed)
    Abstract [en]

    Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate. However, the pure random sensing matrices usually require huge memory for storage and high computational cost for signal reconstruction. Many structured sensing matrices have been proposed recently to simplify the sensing scheme and the hardware implementation in practice. Based on the restricted isometry property and coherence, couples of existing structured sensing matrices are reviewed in this paper, which have special structures, high recovery performance, and many advantages such as the simple construction, fast calculation and easy hardware implementation. The number of measurements and the universality of different structure matrices are compared.

  • 3.
    Li, Kezhi
    et al.
    Imperial College London, United Kingdom.
    Rojas, Cristian R.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Yang, Tao
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Cong, S.
    Piecewise sparse signal recovery via piecewise orthogonal matching pursuit2016In: 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 4608-4612Conference paper (Refereed)
    Abstract [en]

    In this paper, we consider the recovery of piecewise sparse signals from incomplete noisy measurements via a greedy algorithm. Here piecewise sparse means that the signal can be approximated in certain domain with known number of nonzero entries in each piece/segment. This paper makes a two-fold contribution to this problem: 1) formulating a piecewise sparse model in the framework of compressed sensing and providing the theoretical analysis of corresponding sensing matrices; 2) developing a greedy algorithm called piecewise orthogonal matching pursuit (POMP) for the recovery of piecewise sparse signals. Experimental simulations verify the effectiveness of the proposed algorithms.

  • 4.
    Li, Kezhi
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Medical Research Council, Imperial College London, White City, United Kingdom.
    Sundin, Martin
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rojas, Cristian
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Alternating strategies with internal ADMM for low-rank matrix reconstruction2016In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 121, p. 153-159Article in journal (Refereed)
    Abstract [en]

    This paper focuses on the problem of reconstructing low-rank matrices from underdetermined measurements using alternating optimization strategies. We endeavour to combine an alternating least-squares based estimation strategy with ideas from the alternating direction method of multipliers (ADMM) to recover low-rank matrices with linear parameterized structures, such as Hankel matrices. The use of ADMM helps to improve the estimate in each iteration due to its capability of incorporating information about the direction of estimates achieved in previous iterations. We show that merging these two alternating strategies leads to a better performance and less consumed time than the existing alternating least squares (ALS) strategy. The improved performance is verified via numerical simulations with varying sampling rates and real applications.

  • 5.
    Yang, Tao
    et al.
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Yuan, Ye
    Li, Kezhi
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Goncalves, J.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Finite-time road grade computation for a vehicle platoon2014In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2014, no February, p. 6105-6110Conference paper (Refereed)
    Abstract [en]

    Given a platoon of vehicles traveling uphill, this paper considers the finite-time road grade computation problem. We propose a decentralized algorithm for an arbitrarily chosen vehicle to compute the road grade in a finite number of time-steps by using only its own successive velocity measurements. Simulations then illustrate the theoretical results. These new results can be applied to real-world vehicle platooning problems to reduce fuel consumption and carbon dioxide emissions.

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