Publications (45)48.57 Total impact

 [Show abstract] [Hide abstract] ABSTRACT: The conventional necessary and sufficient condition defined in the frequency domain for maximally decimated Mchannel mirrored paraunitary linear phase FIR filter banks consists of a finite number of quadratic functional equations. As a functional equation consists of an infinite number of discrete equations, the conventional condition consists of an infinite number of discrete quadratic equations. This results in a very difficult situation for the design of these filter banks. To address this difficulty, this paper derives a finite number of necessary and sufficient discrete quadratic equations defined in the frequency domain for maximally decimated Mchannel mirrored paraunitary linear phase FIR filter banks. These conditions facilitate the design.
 [Show abstract] [Hide abstract] ABSTRACT: In this paper, a perfect reconstruction condition for nonuniform transmultiplexers with block samplers is derived. The distortions due to the transmultiplexers are illuminated. Hence, the proposed transmultiplexers can be improved the signal to noise ratio of the transmission.
 [Show abstract] [Hide abstract] ABSTRACT: This paper proposes a reconfiguration design of variable bandwidth symmetric/antisymmetric finite impulse response (FIR) single band peak constrained least squares (PCLS) filters for wireless communication systems. When the bandwidth of the filter changes, a new set of filter coefficients based on the old set of filter coefficients is derived via the method of bisection. Since the algorithm is very efficient, the new set of filter coefficients can be obtained in real time. Also, the new set of filter coefficients can be arbitrarily close to the globally optimal solution of the new PCLS optimization problem.
 [Show abstract] [Hide abstract] ABSTRACT: This paper proposes an optimal blind decoding scheme for linear transceivers based on orthonormal real valued short time block codes. The decoding scheme is to minimize the total decoding error within the blocks subject to the orthonormal property among the encoded vectors. The decoding problem is actually an optimization problem with a quadratic objective function subject to a quadratic matrix equality constraint. The solution of the optimization problem is solved analytically via a singular value decomposition approach. As no computer aided design tool is required for solving the problem, the computational power for solving the problem is very low and the solution can be obtained in realtime. Computer numerical simulation results show that our proposed method achieves a lower total decoding error compared to those of existing decoding schemes.
 [Show abstract] [Hide abstract] ABSTRACT: This paper proposes to extend the conventional discrete Fourier transform (DFT) descriptor to discrete fractional Fourier transform (DFrFT) descriptors for representing edges in images. The DFrFT descriptors of training images are employed for constructing a dictionary. However, it is required to determine the optimal rotational angles. This problem is formulated as an optimization problem such that the Fisher discriminant is minimized. Nevertheless, this optimization problem is nonconvex. Also, both the intraclass and interclass separations of the DFrFT descriptors are independent of the rotational angles if these separations are defined using the 2norm operator. To tackle these difficulties, the 1norm operator is employed instead. However, this reformulated optimization problem is nonsmooth. To solve this problem, the nondifferentiable points of the objective function are found. Then, the stationary points between any two consecutive nondifferentiable points are identified. After that, the objective functional values are evaluated at these nondifferentiable points and stationary points. The smallest L objective functional values are picked up and the corresponding rotational angles are chosen for constructing the dictionary. Here, L is the total number of the rotational angles for constructing the dictionary. Finally, a 1NN classification rule is applied for performing the image retrieval. Computer numerical simulation results show that our proposed method outperforms the conventional DFT descriptor approach.
 [Show abstract] [Hide abstract] ABSTRACT: This paper extends the existing L1 norm separable surrogate functional (SSF) iterative shrinkage algorithm to approximate the objective function of a weighted Lp norm and L2 norm optimization problem by N one dimensional independent objective functions. However, as the weighted Lp norm and L2 norm optimization problem is nonconvex, there may be more than one locally optimal solution. Hence, it is difficult to find the globally optimal solution. To address this difficulty, this paper further characterizes the regions that the signs of the convexity of the objective function within the regions remain unchanged. Then, the optimal solution within each region and eventually the globally optimal solution of the original optimization problem are found.

 [Show abstract] [Hide abstract] ABSTRACT: A new compressive sensing (CS) scheme using the structured random matrix and the discrete periodic Radon transform (DPRT) is proposed. The new scheme first prerandomises the sensing image and the DPRT is applied to the randomised samples to generate the socalled DPRT projections. They are then randomly selected to obtain the final sensing measurements. As the DPRT is friendly to hardware/optics implementation, it improves the operability and lowers the cost for realtime CS applications. Compared with other similar transforms such as the WalshHadamard transform, the proposed DPRT scheme gives much better reconstructed images as shown in the simulation results.

 [Show abstract] [Hide abstract] ABSTRACT: This paper presents a novel methodology for extracting the underlying trends of signals via a joint empirical mode decomposition (EMD) and sparse binary programming approach. The EMD is applied to the signals and the corresponding intrinsic mode functions (IMFs) are obtained. The underlying trends of the signals are obtained by the sums of the IMFs where these IMFs are either selected or discarded. The total number of the selected IMFs is minimized subject to a specification on the maximum absolute differences between the denoised signals (signals obtained by discarding the first IMFs) and the underlying trends. Since the total number of the selected IMFs is minimized, the obtained solutions are sparse and only few IMFs are selected. The selected IMFs correspond to the components of the underlying trend of the signals. On the other hand, the L∞ norm specification guarantees that the maximum absolute differences between the underlying trends and the denoised signals are bounded by an acceptable level. This forces the underlying trends to follow the global changes of the signals. As the IMFs are either selected or discarded, the coefficients are either zero or one. This problem is actually a sparse binary programming problem with an L0 norm objective function subject to an L∞ norm constraint. Nevertheless, the problem is nonconvex, nonsmooth, and NP hard. It requires an exhaustive search for solving the problem. However, the required computational effort is too heavy to be implemented practically. To address these difficulties, we approximate the L0 norm objective function by the L1 norm objective function, and the solution of the sparse binary programming problem is obtained by applying the zero and one quantization to the solution of the corresponding continuousvalued L1 norm optimization problem. Since the isometry condition is satisfied and the number of the IMFs is small for most  f practical signals, this approximation is valid and verified via our experiments conducted on practical data. As the L1 norm optimization problem can be reformulated as a linear programming problem and many efficient algorithms such as simplex or interior point methods can be applied for solving the linear programming problem, our proposed method can be implemented in real time. Also, unlike previously reported techniques that require precursor models or parameter specifications, our proposed adaptive method does not make any assumption on the characteristics of the original signals. Hence, it can be applied to extract the underlying trends of more general signals. The results show that our proposed method outperforms existing EMD, classical lowpass filtering and the wavelet methods in terms of the efficacy.
 [Show abstract] [Hide abstract] ABSTRACT: In this chapter, a twochannel linear phase finite impulse response (FIR) quadrature mirror filter (QMF) bank minimax design problem is formulated as a nonconvex optimization problem so that a weighted sum of the maximum amplitude distortion of the filter bank, the maximum passband ripple magnitude, and the maximum stopband ripple magnitude of the prototype filter is minimized subject to specifications on these performances. A joint norm relaxed sequential quadratic programming and filled function method is proposed for finding the global minimum of the nonconvex optimization problem. Computer numerical simulations show that our proposed design method is efficient and effective. © 2013 SpringerVerlag Berlin Heidelberg. All rights are reserved.

Conference Paper: Extracting underlying trend and predicting power usage via joint SSA and sparse binary programming
[Show abstract] [Hide abstract] ABSTRACT: This paper proposes a novel methodology for extracting the underlying trend and predicting the power usage through a joint singular spectrum analysis (SSA) and sparse binary programming approach. The underlying trend is approximated by the sum of a part of SSA components, in which the total number of the SSA components in the sum is minimized subject to a specification on the maximum absolute difference between the original signal and the approximated underlying trend. As the selection of the SSA components is binary, this selection problem is to minimize the L0 norm of the selection vector subject to the L∞ norm constraint on the difference between the original signal and the approximated underlying trend as well as the binary valued constraint on the elements of the selection vector. This problem is actually a sparse binary programming problem. To solve this problem, first the corresponding continuous valued sparse optimization problem is solved. That is, to solve the same problem without the consideration of the binary valued constraint. This problem can be approximated by a linear programming problem when the isometry condition is satisfied, and the solution of the linear programming problem can be obtained via existing simplex methods or interior point methods. By applying the binary quantization to the obtained solution of the linear programming problem, the approximated solution of the original sparse binary programming problem is obtained. Unlike previously reported techniques that require a precursor model or parameter specifications, the proposed method is completely adaptive. Experiment results show that our proposed method is very effective and efficient for extracting the underlying trend and predicting the power usage. 
 [Show abstract] [Hide abstract] ABSTRACT: This paper develops a combined optimal pulse width modulation (PWM) and pulse frequency modulation (PFM) strategy for controlling switched mode DCDC converters. The peak ripple magnitudes of both the outputvoltages and currents during all operating modes over a wide range of loads are minimised subject to specifications on the minimum efficiency bounds of the converters. This problem is posed as a multiobjective functional inequality constrained optimal control problem. By expressing the initial state of each operating mode at the steady state as a function of the switched time instants, as well as applying the time scaling transform method and the constraint transcription method, the multiobjective functional inequality constrained optimal control problem is converted to a conventional optimal control problem. Finally, a control parameterisation technique is applied to solve the problem. Computer numerical simulations show that the combined control strategy could achieve low peak ripple magnitudes of both the outputvoltages and currents for all operating modes over a wide range of loads and guarantees the satisfaction of the specifications on the minimum efficiency bounds of the converter over a wide range of loads.


Conference Paper: Trend extraction based on HilbertHuang transform
[Show abstract] [Hide abstract] ABSTRACT: Trend extraction is an important tool for the analysis of data sequences. This paper presents a new methodology for trend extraction based on HilbertHuang transform. Signals are initially decomposed through use of EMD into a finite number of intrinsic mode functions (IMFs). The Hilbert marginal spectrum of each IMF is then calculated and a new criterion, termed the cross energy ratio of the Hilbert marginal spectrum of consecutive IMFs, is defined. Finally, through use of the new criterion, the underlying trend is obtained by adaptively selecting appropriate IMFs obtained by EMD. Results from experimental trials are included to demonstrate the benefits of the proposed method for extracting trends in data streams. 
Conference Paper: Optimal overcomplete kernel design for sparse representations via discrete fractional Fourier transforms
[Show abstract] [Hide abstract] ABSTRACT: This paper proposes to use a set of discrete fractional Fourier transform (DFrFT) matrices with different rotational angles to construct an overcomplete kernel for sparse representations of signals. The design of the rotational angles is formulated as an optimization problem. To solve the problem, it is shown that this design problem is equivalent to an optimal sampling problem. Furthermore, the optimal sampling frequencies are the roots of a set of harmonic functions. As the frequency responses of the filters are required to be computed only at frequencies in a discrete set, the globally optimal rotational angles can be found very efficiently and effectively.  [Show abstract] [Hide abstract] ABSTRACT: This paper proposes a novel methodology for the optimal and simultaneous designs of both Hermitian transforms and masks for reducing the intraclass separations of feature vectors for anomaly detection of diabetic retinopathy images. Each class of training images associates with a Hermitian transform, a mask and a known represented feature vector. The optimal and simultaneous designs of both the Hermitian transforms and the masks are formulated as least squares optimization problems subject to the Hermitian constraints. Since the optimal mask of each class of training images is dependent on the corresponding optimal Hermitian transform, only the Hermitian transforms are required to be designed. Nevertheless, the Hermitian transform design problems are optimization problems with highly nonlinear objective functions subject to the complex valued quadratic Hermitian constraints. This kind of optimization problems is very difficult to solve. To address the difficulty, this paper proposes a singular value decomposition approach for deriving a condition on the solutions of the optimization problems as well as an iterative approach for solving the optimization problems. Since the matrices characterizing the discrete Fourier transform, discrete cosine transform and discrete fractional Fourier transform are Hermitian, the Hermitian transforms designed by our proposed approach are more general than existing transforms. After both the Hermitian transforms and the masks for all classes of training images are designed, they are applied to test images. The test images will assign to the classes where the Euclidean 2norms of the differences between the processed feature vectors of the test images and the corresponding represented feature vectors are minimum. Computer numerical simulation results show that the proposed methodology for the optimal and simultaneous designs of both the Hermitian transforms and the masks is very efficient and effective. The proposed technique is also  ery efficient and effective for reducing the intraclass separations of feature vectors for anomaly detection of diabetic retinopathy images.

Article: Global Optimal Design of IIR Filters via Constraint Transcription and Filled Function Methods
[Show abstract] [Hide abstract] ABSTRACT: In this paper, we consider a globally optimal design of IIR filters. We formulate the design problem as a nonconvex optimization problem with a continuous inequality constraint and a nonconvex constraint. To solve this problem, the constraint transcription method is applied to tackle the continuous inequality constraint. In order to avoid the obtained solution being on the boundary of the feasible set, more than one initial points are used. Moreover, since the objective and the constraints are nonconvex functions, there may be many local minima. To address this problem, the filled function method is applied to escape from the local minima. Some numerical computer simulation results are presented to illustrate the effectiveness and efficiency of the proposed method.
Publication Stats
161  Citations  
48.57  Total Impact Points  
Top Journals
Institutions

20122014

GuangDong University of Technology
Shengcheng, Guangdong, China 
University of Lincoln
 School of Engineering
Lincoln, England, United Kingdom


20072011

King's College London
 Department of Electronic Engineering
Londinium, England, United Kingdom


20052011

The Hong Kong Polytechnic University
 • Department of Electronic and Information Engineering
 • Department of Applied Mathematics
Hong Kong, Hong Kong
