Li Chai

Wuhan University of Science and Technology, Wu-han-shih, Hubei, China

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Publications (34)51.53 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: The problem of state dimension reduction and quantizer design under communication constraints is discussed for state estimation in quantized linear systems. Subject to the limited signal power, number and bandwidth of the parallel channels, a differential pulse code modulation (DPCM)-like structure is adopted to generate the quantized innovations as the transmitted signals, and the multi-level quantized Kalman filter (MLQ-KF) is used to serve as the pre- and post-filters. The dimension reduction matrix and quantizer are designed jointly under the MMSE criterion of estimation at the channel receiver. To demonstrate the validity of state estimation under the adopted framework, the state estimability based on quantized innovations is analyzed by using information theoretic method. This leads to a sufficient and necessary condition of a certain estimability Gramian matrix having full rank. The quantized Gramian is proved to converge to that of the original unquantized system when the quantization intervals turn to zero. Our work also provides an auxiliary analytic support for the estimation under 1-bit quantization. Simulations show that under communication constraints, the estimation performance is satisfactory when the designed dimension reduction method and quantizer are applied. The analytic conclusion of estimability is also verified by illustrative simulations.
    Signal Processing. 01/2014; 105:363–375.
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    ABSTRACT: Time domain oversampled lapped transforms (TDOLTs) with lattice structure can guarantee linear phase and perfect reconstruction and have the advantage of improving coding efficiency and reducing blocking effects which usually exist in DCT transforms. The post-filter is not unique in TDOLTs for a fixed pre-filter. In this paper, we propose a method to design the optimal post-filter for TDOLTs and partial TDOLTs with known noises. We also study the worst-case design of post-filters when the spectrum of noises are unknown. The obtained optimal post-filter is applied to JPEG codec. The performance in reducing the blocking artifacts and effectiveness of the proposed methods are demonstrated by various examples.
    Signal Processing. 09/2013; 93(9):2516–2524.
  • Yu Pan, Li Chai, Yuxia Sheng
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    ABSTRACT: The Laplacian pyramid (LP) plays an important role in multiresolution processing. It can be viewed as a special oversampled filter bank (OFB) frame that provides a redundant signal representation. This paper studies the computation and optimization of frame bounds for the LP frame. For any given N-level LP, an algorithm is developed to compute its polyphase matrix, based on which the linear matrix inequality (LMI) conditions are provided to compute the frame bounds. We show that the frame bound ratio can be decreased by adjusting the gain of each sub-channel without changing frequency selective property. The minimal ratio as well as the corresponding optimal gain factors has been obtained by solving some LMIs, which can be easily solved by existing handy software. Various numerical examples are given to show the effectiveness of the proposed methods.
    Control and Decision Conference (CCDC), 2013 25th Chinese; 01/2013
  • Yu Pan, Li Chai, Yuxia Sheng
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    ABSTRACT: The upper (lower) bound of a frame is an important index in the analysis and design of filter bank frames. There is lack of effectively numerical methods to compute the frame bounds for two-dimensional (2-D) filter banks (FBs). This paper investigates the computation problem of frame bounds and provides a frequency-independent solution. Firstly, the state space realization of 2-D FIR discrete FBs is given in the form of Roesser model. Then an LMI based optimization method is presented by using the generalized Kalman-Yakubovich-Popov (KYP) lemma. Finally, various examples are given on wavelet and Laplacian pyramid frames to demonstrate the effectiveness of the proposed method for 2-D frames.
    Control and Automation (ICCA), 2013 10th IEEE International Conference on; 01/2013
  • Li Chai, Minyue Fu
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    ABSTRACT: This paper considers the quantized infinite-horizon LQG control system, of which the measurement signal is quantized by a fixed-rate quantizer before going into the controller. It turns out that only weak separation principle holds for the LQG control system with communication channels. We study the problem of quantized LQG for a single-input-single-output (SISO) system. An adaptive fixed-rate quantizer is designed to achieve the mean-square stability and the optimal distortion performance. For a quantizer with a fixed bit rate of R (per sample), we show that the quantization distortion order is R2-2R for a large R. Simulation examples are given to demonstrate the effectiveness of the proposed methods.
    Control Conference (CCC), 2012 31st Chinese; 01/2012
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    ABSTRACT: Shift variance bounds of critically sampled multirate filter banks are usually defined by using eigensystem analysis of the commutator operator. Computational methods are provided for two-channel FIR filter banks by Aach and Fuhr (2009). This paper investigates shift variance bounds in oversampled multi-channel filter banks and derives some general results which include some of Aach and Fuhr (2009) as special cases. Using polyphase representation, numerical methods are provided to compute the shift variance bounds for arbitrary filter banks. Examples are given to demonstrate the effectiveness of the obtained results.
    Circuits and Systems (ISCAS), 2012 IEEE International Symposium on; 01/2012
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    ABSTRACT: This paper investigates Zero Forcing (ZF) precoding in MIMO FB channels subject to individual channel power constraints. It shows that the optimal ZF precoder is non-causal in general and presents a general formulation for the design of optimal noncausal ZF precoder subject to individual channel power constraints. A convex optimization based method is derived from the formulation to design optimal noncausal precoder. Numerical example demonstrates the effectiveness of the design method and the advantage of the designed optimal noncausal ZF precoder.
    Signal Processing Conference (EUSIPCO), 2012 Proceedings of the 20th European; 01/2012
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    ABSTRACT: Oversampled filter banks (FBs) with lattice structure allow fast implementation and guarantee the linear phase and perfect reconstruction property. For such FBs, the synthesis FB is not unique. This nonuniqueness provides extra design freedom for optimal reduction of subband noise required in many applications. However, the existing design methods of synthesis FB for optimal reduction of subband noise cannot guarantee the linear phase and lattice structure property. This paper studies the design of oversampled synthesis FBs with guaranteed lattice structure for optimal reduction of subband noise. Based on a state space parameterization of all synthesis FBs with lattice structure, the explicit formulae are derived to find the optimal solution for noise reduction. Numerical examples are presented to demonstrate the effectiveness of the new design methods obtained.
    IEEE Transactions on Signal Processing 09/2011; · 2.81 Impact Factor
  • Source
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    ABSTRACT: In one-dimensional signal processing, the perfect reconstruction (PR) synthesis FB is not unique for a given analysis LP oversampled filter bank (FB). Optimal Design methods have been developed to choose the optimal noise reduction linear phase (LP) synthesis FB. This paper deals with the optimal design of LP synthesis FBs for separable 2D image processing. With the same analysis LP oversampled FB for row and column processing separately, we show that the optimal synthesis FBs for row and column processing are generally not the same. A design method is developed when the spectrum of the subband noises is known. Numerical examples are given to demonstrate the effectiveness of our results.
    Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011, May 22-27, 2011, Prague Congress Center, Prague, Czech Republic; 01/2011
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    ABSTRACT: Two-sided diagonal scaling for transfer matrices is formulated. An efficient algorithm is proposed to compute globally optimal solutions using the iterated bi-section and linear matrix inequality (LMI) solver. It is shown that the two-sided scaling of filter bank (FB) frames can be implemented by the adjustment of channel gains and the periodic precoding of source signal, and that the frame-bound-ratio of FB frames can be effectively im- proved by such scaling. Explicit formulas are established for both uniform and nonuniform FB frames, including detail formulas for discrete Weyl-Heisenberg frames and tree-structured FBs (discrete wavelets). Different examples show the effectiveness of the obtained results.
    IEEE Transactions on Signal Processing 01/2011; 59:5830-5841. · 2.81 Impact Factor
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    Li Chai, Jingxin Zhang
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    ABSTRACT: Frame (upper and lower) bound ratio is a key factor of numerical stability of frame systems. While tight frames, of which the minimal ratio 1 is achieved, are much preferred in many practical situations, they may not be easily (even impossible) designed due to other criteria (for example, good subband frequency shape). In these situations, we may find alternative methods for improving the frame-bound-ratio. This paper studies the minimization of frame-bound-ratio for filter bank frames by using periodic precoding. A convex optimization based algorithm is proposed. Examples show the effectiveness of our results.
    Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011, May 22-27, 2011, Prague Congress Center, Prague, Czech Republic; 01/2011
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    Li Chai, Minyue Fu
    [Show abstract] [Hide abstract]
    ABSTRACT: We study the infinite-horizon LQG control systems with the constraint that the measurement signal is quantized by a fixed-rate quantizer before going into the controller. It has been shown recently that only weak separation principle holds for the LQG control system with communication channels. In this paper, we study the problem of quantized LQG for a scalar system. An adaptive fixed-rate quantizer is designed to achieve the mean-square stability and the good long term average performance. The long term average cost is divided into two parts. The first part depends on the classical LQG cost, and the second part depends on the distortion of the quantizer. For a quantizer with a fixed bit rate of R (per sample), we show that the quantization distortion order is R2<sup>-2R</sup> for a large R.
    Intelligent Control and Automation (WCICA), 2010 8th World Congress on; 08/2010
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    ABSTRACT: This paper investigates and solves the problem of frame bound ratio minimization for oversampled perfect reconstruction (PR) filter banks (FBs). For a given analysis PRFB, a finite dimensional convex optimization algorithm is derived to redesign the subband gain of each channel. The redesign minimizes the frame bound ratio of the FB while maintaining its original properties and performance. The obtained solution is precise without involving frequency domain approximation and can be applied to many practical problems in signal processing. The optimal solution is applied to subband noise suppression and tree structured FB gain optimization, resulting in deeper insights and novel solutions to these two general classes of problems and considerable performance improvement. Effectiveness of the optimal solution is demonstrated by extensive numerical examples.
    IEEE Transactions on Signal Processing 02/2010; · 2.81 Impact Factor
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    ABSTRACT: This paper investigates optimal signal predictive quantization in the presence of source model uncertainties. It uses polytopic system model to represent the uncertainties in source signal and uses the recent results on robust filtering to obtain a robust H<sub>∞</sub> optimal design of signal predictor. Results of computational study is presented to demonstrate the advantages of the obtained design.
    Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on; 01/2010
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    ABSTRACT: This paper presents a frame analysis of Zero Forcing (ZF) precoding problem. It shows that from a frame point of view, the filter bank (FB) channel is a synthesis frame and its canonical dual analysis frame is the optimal ZF precoder under total power constraint. Based on this analysis, a new precoder design is presented. The new design removes the minimum phase assumption of polyphase FB channel in the existing methods and gives rise to optimal noncausal (stable) precoder. It provides a general framework for optimal zero-forcing precoding under total power constraint. The numerical results show that the new design outperforms existing causal stable design.
    Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2010, 14-19 March 2010, Sheraton Dallas Hotel, Dallas, Texas, USA; 01/2010
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    ABSTRACT: This paper studies the optimal noise reduction problem for oversampled filter banks (FBs) with perfect reconstruction (PR) constraint. Both the optimal design and worst case design are considered, where the former caters for the noise with known power spectral density (PSD) and the latter for the noise with unknown PSD. State-space based explicit formulae involving only algebraic Riccati equation and matrix manipulations are provided for the general (IIR or FIR) oversampled PR FBs, and the relations between different cases are analyzed and revealed. Extensive numerical examples are provided to illustrate the proposed design methods and to show their effectiveness.
    IEEE Transactions on Signal Processing 11/2009; · 2.81 Impact Factor
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    ABSTRACT: For an oversampled linear phase (LP) perfect reconstruction filter banks with lattice structure, the synthesis FB is not unique. However, existing methods to choose a synthesis FB for ldquooptimalrdquo noise reduction may destroy the linear phase and lattice structure property. This paper studies the noise reduction design problem for oversampled filter banks (FBs) preserving lattice structure. Both the optimal design and worst case design are considered, where the former caters for the noise with known power spectral density (PSD), and the latter for the noise with unknown PSD. Explicit formula for the former and LMI-based algorithms for the latter are provided.
    Asian Control Conference, 2009. ASCC 2009. 7th; 09/2009
  • Conference Paper: Robust H
    Proceedings of the 48th IEEE Conference on Decision and Control, CDC 2009, combined withe the 28th Chinese Control Conference, December 16-18, 2009, Shanghai, China; 01/2009
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    ABSTRACT: This correspondence presents a simple and effective method for computing the optimal frame bounds of oversampled perfect reconstruction (PR) filter banks (FBs). It first shows that computation of the optimal frame bounds for complex-valued oversampled PR FBs can be formulated as a convex optimization subject to complex-valued linear matrix inequality (LMI) constraints and solved by effective interior-point algorithms. It then deals with discrete-time Weyl-Heisenberg (WH) frames to compute bounds on the WH frames by real-valued LMI optimization. The WH frames are closely related to modulated FBs and have complex coefficients. Four examples are given to illustrate the generality and effectiveness of the proposed method.
    IEEE Transactions on Signal Processing 08/2008; · 2.81 Impact Factor
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    ABSTRACT: This paper is concerned with signal predictive subband quantization in oversampled filter banks. It uses the analysis tools of robust filtering and control to obtain a worst case power spectral analysis of the prediction error system. The analysis removes the unrealistic assumptions on the quantization noises in the present literature and leads to the definition of H<sub>infin</sub> optimal signal predictor. Based on this analysis, an LMI optimization based method is obtained to design the H<sub>infin</sub> optimal signal predictor with guaranteed inverse stability. Simulation results are presented to show the advantages of the H<sub>infin</sub> optimal signal predictor over the conventional signal predictor.
    Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on; 05/2008

Publication Stats

111 Citations
51.53 Total Impact Points

Institutions

  • 2008–2014
    • Wuhan University of Science and Technology
      Wu-han-shih, Hubei, China
  • 2010
    • Wuhan University of Technology
      Wu-han-shih, Hubei, China
  • 2005–2010
    • Monash University (Australia)
      • Department of Electrical and Computer Systems Engineering, Clayton
      Melbourne, Victoria, Australia
  • 2006
    • Hangzhou Dianzi University
      Hang-hsien, Zhejiang Sheng, China