Global Optimum Design of Uniform FIR Filter Bank With Magnitude Constraints

The optimum design of a uniform finite impulse response filter bank can be formulated as a nonlinear semi-infinite optimization problem. However, this optimization problem is nonconvex with infinitely many inequality constraints. In this paper, we propose a new hybrid approach for solving this highly challenging nonlinear, nonconvex semi-infinite optimization problem. In this approach, a gradient-based method is used in conjunction with a filled function method to determine a global minimum of the problem. This new hybrid approach finds an optimal result independent of the initial guess of the solution. The method is applied to some existing examples. The results obtained are superior to those obtained by other existing methods.      

二阶锥规划方法对于低群延时复系数有限冲激响应数字滤波器优化设计

针对低群延时复系数有限冲激响应数字滤波器优化设计问题,提出了一种幅度和相位独立约束的等纹波设计新方法.该方法在相位误差一定的条件下对幅度的上界和下界分别采取复数圆约束和线性不等式约束,不仅提高了幅度约束的精度,而且将非凸的滤波器设计问题转化为二阶锥规划问题;同时,为抑制通带边缘附近较大的群延时震荡效应,引入了相位误差一...     

Joint Source and Relay Precoder Design in Amplify-and-Forward MIMO Relay Systems with Direct Link

This paper investigates the precoder design problem in a two-hop amplify-and-forward multiple-input-multiple-output relay system. Many previous works on this problem are based on the minimum mean-square error criterion and the presence of a direct link between the source and the destination is ignored. In this paper, we propose a new method for joint source and relay precoder design based on maximizing the mutual information between the source and the destination, taking both the relay link and the direct link into account. In contrast to previous works, which consider the transmit power constraints of the source and the relay independently, we assume a total power constraint on the sum transmit power of the source and the relay instead to study also the optimal power distribution over the two nodes. A constrained optimization problem with respect to the unknown source precoder matrix and relay precoder matrix is then formulated, which is nonconvex and very difficult to solve directly. We propose a structural constraint on the precoders by analyzing the structure of the problem and referring to related works. With the proposed precoders’ structure and by applying the Hadamard’s inequality, the original problem is simplified from a matrix-valued problem to a scalar-valued one. However, the new scalar-valued problem is still nonconvex and we manage to convert it into two subproblems and solve it in an iterative fashion. By using the Karash–Kuhn–Tucker (KKT) conditions, we give out the closed-form solutions to the subprobelms. Simulation results demonstrate that the proposed design method converges rapidly and significantly outperforms the existing methods.     

Efficient design of orthonormal wavelet bases for signal representation

The efficient representation of a signal as a linear combination of elementary "atoms" or building blocks is central to much signal processing theory and many applications. Wavelets provide a powerful, flexible, and efficiently implementable class of such atoms. In this paper, we develop an efficient method for selecting an orthonormal wavelet that is matched to a given signal in the sense that the squared error between the signal and some finite resolution wavelet representation of it is minimized. Since the squared error is not an explicit function of the design parameters, some form of approximation of this objective is required if conventional optimization techniques are to be used. Previous approximations have resulted in nonconvex optimization problems, which require delicate management of local minima. In this paper, we employ an approximation that results in a design problem that can be transformed into a convex optimization problem and efficiently solved. Constraints on the smoothness of the wavelet can be efficiently incorporated into the design. We show that the error incurred in our approximation is bounded by a function that decays to zero as the number of vanishing moments of the wavelet grows. In our examples, we demonstrate that our method provides wavelet bases that yield substantially better performance than members of standard wavelet families and are competitive with those designed by more intricate nonconvex optimization methods.     

Multiuser MIMO Transceiver Design for Uplink and Downlink with Imperfect CSI

This paper considers a joint linear transmitter and receiver design for multi-user multiple-input multiple-output (MU-MIMO) systems using total mean square error (TMSE) criterion, subject to a total transmit power constraint assuming imperfect channel state information. Both the uplink and downlink MU-MIMO systems, which is employed with improper constellations such as binary phase shift-keying and $M$ -ary amplitude shift-keying are considered. A minimum TMSE design is formulated as a nonconvex optimization problem under a total transmit power constraint and the closed-form optimum linear precoder and decoder for both the downlink and uplink MU-MIMO systems with improper modulation are determined by solving this nonconvex optimization problem. A novel contribution in this paper is to derive a closed-form optimum linear precoder and decoder for both the downlink and uplink MU-MIMO systems with improper modulation by solving the nonconvex optimization problem under total power constraint. The simulation results show that the performance of the proposed design is improved over the previous design.     

Cellular radio channel assignment using a modified Hopfield network

The channel-assignment problem is important in mobile telephone communication. Since the usable range of the frequency spectrum is limited, the optimal channel-assignment problem has become increasingly important. A new channel-assignment algorithm using a modified Hopfield (1985, 1986) neural network is proposed. The channel-assignment problem is formulated as an energy-minimization problem that is implemented by a modified discrete Hopfield network. Also, a new technique to escape the local minima is introduced. In this algorithm, an energy function is derived, and the appropriate interconnection weights between the neurons are specified. The interconnection weights between the neurons are designed in such a way that each neuron receives inhibitory support if the constraint conditions are violated and receives excitatory support if the constraint conditions are satisfied. To escape the local minima, if the number of assigned channels are less than the required channel numbers (RCNs), one or more channels are assigned in addition to already assigned channels such that the total number of assigned channels is the same as the required number of channels in the cell even though the energy is increased. Various initialization techniques, which use the specific characteristics of frequency-assignment problems in cellular radio networks, such as cosite constraint (CSC), adjacent channel constraint (ACC), and cochannel constraint (CCC), and updating methods are investigated. In the previously proposed neural-network approach, some frequencies are fixed to accelerate the convergence time. In our algorithms, no frequency is fixed before the frequency-assignment procedure. This new algorithm, together with the proposed initialization and updating techniques and without fixing frequencies in any cells, has better performance results than the results reported previously utilizing fixed frequencies in certain cells     

Local hull-based surface construction of volumetric data from silhouettes

The marching cubes (MC) is a general method which can construct a surface of an object from its volumetric data generated using a shape from silhouette method. Although MC is efficient and straightforward to implement, a MC surface may have discontinuity even though the volumetric data is continuous. This is because surface construction is more sensitive to image noise than the construction of volumetric data. To address this problem, we propose a surface construction algorithm which aggregates local surfaces constructed by the 3-D convex hull algorithm. Thus, the proposed method initially classifies local convexities from imperfect MC vertices based on sliced volumetric data. Experimental results show that continuous surfaces are obtained from imperfect silhouette images of both convex and nonconvex objects.     

Optimal filtering for multirate systems

For a multirate system where the output sampling is slower than the input updating, this brief aims at designing filters for fast state estimation in the H/sub 2/ and H/sub /spl infin// settings. Because of the multirate nature, linear matrix inequality solutions to the design problems involve a nonconvex constraint, which is numerically tackled by the product reduction algorithm. Finally, a design example is given and the effectiveness of the approach is illustrated.     

Multiminima heuristic methods for antenna optimization

Two general approaches to multiminima optimization are considered. The first approach is based on repetition of a single minima method (e.g., the Nelder-Mead simplex applied to the best solution in a set of random trials). The second approach is based on a coarse estimation of local minima using initial set of points and local optimization starting from these local minima (e.g., random search as a generator of the initial set of points and Nelder-Mead simplex as a local optimizer). A comparison of various optimization algorithms has been done on one analytical problem and two well-known examples of antenna design. It is found that: a) the multiminima method based on coarse estimation enables finding more minima with smaller number of iterations than that based on repetition, b) the best multiminima methods are comparable with the best single minima methods in a number of iterations needed for finding the global minima, and c) the multiminima method based on coarse estimation restarted with different weighting coefficients of multiobjective cost function enables efficient Pareto optimization.     

无源时差定位方程的半定松弛解法

针对基于到达时差量测的多站无源定位系统,提出了一种基于半定松弛的时差定位方程求解方法.该方法首先将关于目标位置估计的非凸二次优化问题转换成等价的非凸半定规划问题,然后通过秩1松弛得到一个凸优化问题,最后对松弛半定规划问题的最优解进行秩1近似,从而提取出最终的目标位置估计.计算机仿真结果表明这种松弛解法可以有效求解目标位置.     

DCTT统计最优化的进一步策略和方法＊

本文基于半无穷不可微最优化方法的框架和模型,提出了求解电路成品率极大的中心值设计,容差设计,调整设计及电路制造费用极小化为一体的统计最优化(DCTT)的求解方法及其策略。该方法不需要电路函数的凸性要求和构成可按受域的电路性能函数的半光滑假设。在引入抑制约束膨胀的策略后,该方法在确定性优化框架下可解决较大规模的统计最优化问题。为统计最优化的进一步发展开辟了一条新径。     

基于波形优化和天线位置选择的MIMO雷达波束扫描算法研究

为实现集中式多输入多输出(MIMO)雷达波束扫描,本文在峰值平均功率比(PAPR)、能量以及布尔(天线位置选择)约束下,基于min-max波束图匹配准则,首次提出MIMO雷达天线位置和多组探测波形(一组波形对应一个独立的波束图)的联合优方法。由于非凸PAPR约束、布尔约束以及min-max目标函数的非凸非光滑性导致了优化问题成为典型的大规模NP-难问题。为求解该NP-难优化问题,该文首先利用Lawson算法将min-max问题转化为迭代加权最小二乘(ILS)问题,然后根据上界函数最小化(MM)准则简化ILS优化问题,最后用交替方向乘子法(ADMM)求解简化后的上界优化问题。数值仿真结果检验了所提算法的有效性。      

Multispectral image segmentation using the rough-set-initialized EM algorithm

The problem of segmentation of multispectral satellite images is addressed. An integration of rough-set-theoretic knowledge extraction, the Expectation Maximization (EM) algorithm, and minimal spanning tree (MST) clustering is described. EM provides the statistical model of the data and handles the associated measurement and representation uncertainties. Rough-set theory helps in faster convergence and in avoiding the local minima problem, thereby enhancing the performance of EM. For rough-set-theoretic rule generation, each band is discretized using fuzzy-correlation-based gray-level thresholding. MST enables determination of nonconvex clusters. Since this is applied on Gaussians, determined by granules, rather than on the original data points, time required is very low. These features are demonstrated on two IRS-1A four-band images. Comparison with related methods is made in terms of computation time and a cluster quality measure.     

分布式MIMO雷达的目标定位

针对多输入多输出雷达系统，研究了目标定位问题，并提出基于双基测距的分布式多输入多输出(Multiple-Input Multiple-Output, MIMO)雷达的目标定位算法。首先，通过引入多余参数和这些参数与未知目标定位的关系，将目标定位问题转化为约束二次规划(Quadratically Constrained Quadratic Programming, QCQP)问题，然后，考虑到QCQP问题是非凸和NP-Hard，再将每个非凸约束近似为线性约束，最终QCQP问题就转化为线性约束二次规划(Linearly Constrained Quadratic Programming, LCQP)问题。最后，利用迭代约束权重最小二乘(Iterative Constrained Weighted Least Square, ICWLS)算法求解LCQP问题。实验数据表明，提出的ICWLS算法能够收敛于一个最优值。     

Globally convergent edge-preserving regularized reconstruction: anapplication to limited-angle tomography

We introduce a generalization of a deterministic relaxation algorithm for edge-preserving regularization in linear inverse problems. This algorithm transforms the original (possibly nonconvex) optimization problem into a sequence of quadratic optimization problems, and has been shown to converge under certain conditions when the original cost functional being minimized is strictly convex. We prove that our more general algorithm is globally convergent (i.e., converges to a local minimum from any initialization) under less restrictive conditions, even when the original cost functional is nonconvex. We apply this algorithm to tomographic reconstruction from limited-angle data by formulating the problem as one of regularized least-squares optimization. The results demonstrate that the constraint of piecewise smoothness, applied through the use of edge-preserving regularization, can provide excellent limited-angle tomographic reconstructions. Two edge-preserving regularizers-one convex, the other nonconvex-are used in numerous simulations to demonstrate the effectiveness of the algorithm under various limited-angle scenarios, and to explore how factors, such as the choice of error norm, angular sampling rate and amount of noise, affect the reconstruction quality and algorithm performance. These simulation results show that for this application, the nonconvex regularizer produces consistently superior results.     

Analytical form of globally optimal solution of weighted sum of intraclass separation and interclass separation

The Fisher linear discriminant analysis (FLDA)-based method is a common method for jointly optimizing the intraclass separation and the interclass separation of the projected feature vectors by defining the objective function as the ratio of the intraclass separation over the interclass separation. To address the eigenproblem of the FLDA, a quadratic equality constraint is imposed on the square of the \(l_{2}\) norm of the decision vector. However, the constrained optimization problem is highly nonconvex. This paper proposes to reformulate the objective function as a weighted sum of the intraclass separation and the interclass separation subject to the same quadratic equality constraint on the square of the \(l_{2}\) norm of the decision vector. Although both the objective function and the feasible set of the optimization problem are still nonconvex, this paper shows that the global minimum of the objective functional value is equal to the minimum singular value of the Hessian matrix of the objective function. Also, the globally optimal solution of the optimization problem is in the null space of the Hessian matrix minus this singular value multiplied by the identity matrix. As it is only required to find the singular value of the Hessian matrix, no numerical optimization-based computer aided design tool is required to find the globally optimal solution. Therefore, the globally optimal solution can be found in real time. Experimental results demonstrate the effectiveness of our proposed method.     

FIR数字滤波器幅频响应约束最大加权相位误差最小化设计

多数信号滤波应用,对滤波器幅频响应的要求高于相频响应.本文研究了满足幅频响应约束的有限脉冲响应（Infinite Impulse Response,FIR）数字滤波器设计,提出了最大加权相位误差最小化方法.用凸的椭圆误差约束代替非凸的幅值误差约束,将设计问题转化为凸问题;通过与二分技术结合,提出了给定权函数的幅值误差约束最大加权相位误差最小化设计的求解算法.以此算法为核心,构建了迭代重加权最大加权相位误差最小化算法,其中的权函数不再固定,而是基于修改的群延迟误差包络线在迭代中不断更新.权函数收敛后,所得滤波器具有近似等纹波的群延迟误差,最大群延迟误差得到了有效减小.仿真实验表明,与现有相位误差约束最大幅值误差最小化方法相比,得到的FIR滤波器具有更小的最大相位误差和最大群延迟误差.     

Markovian reconstruction using a GNC approach

This paper is concerned with the reconstruction of images (or signals) from incomplete, noisy data, obtained at the output of an observation system. The solution is defined in maximum a posteriori (MAP) sense and it appears as the global minimum of an energy function joining a convex data-fidelity term and a Markovian prior energy. The sought images are composed of nearly homogeneous zones separated by edges and the prior term accounts for this knowledge. This term combines general nonconvex potential functions (PFs) which are applied to the differences between neighboring pixels. The resultant MAP energy generally exhibits numerous local minima. Calculating its local minimum, placed in the vicinity of the maximum likelihood estimate, is inexpensive but the resultant estimate is usually disappointing. Optimization using simulated annealing is practical only in restricted situations. Several deterministic suboptimal techniques approach the global minimum of special MAP energies, employed in the field of image denoising, at a reasonable numerical cost. The latter techniques are not directly applicable to general observation systems, nor to general Markovian prior energies. This work is devoted to the generalization of one of them, the graduated nonconvexity (GNC) algorithm, in order to calculate nearly-optimal MAP solutions in a wide range of situations. In fact, GNC provides a solution by tracking a set of minima along a sequence of approximate energies, starting from a convex energy and progressing toward the original energy. In this paper, we develop a common method to derive efficient GNC-algorithms for the minimization of MAP energies which arise in the context of any observation system giving rise to a convex data-fidelity term and of Markov random field (MRF) energies involving any nonconvex and/or nonsmooth PFs. As a side-result, we propose how to construct pertinent initializations which allow us to obtain meaningful solutions using local minimization of these MAP energies. Two numerical experiments-an image deblurring and an emission tomography reconstruction-illustrate the performance of the proposed technique.     

Medial-based deformable models in nonconvex shape-spaces for medical image segmentation

We explore the application of genetic algorithms (GA) to deformable models through the proposition of a novel method for medical image segmentation that combines GA with nonconvex, localized, medial-based shape statistics. We replace the more typical gradient descent optimizer used in deformable models with GA, and the convex, implicit, global shape statistics with nonconvex, explicit, localized ones. Specifically, we propose GA to reduce typical deformable model weaknesses pertaining to model initialization, pose estimation and local minima, through the simultaneous evolution of a large number of models. Furthermore, we constrain the evolution, and thus reduce the size of the search-space, by using statistically-based deformable models whose deformations are intuitive (stretch, bulge, bend) and are driven in terms of localized principal modes of variation, instead of modes of variation across the entire shape that often fail to capture localized shape changes. Although GA are not guaranteed to achieve the global optima, our method compares favorably to the prevalent optimization techniques, convex/nonconvex gradient-based optimizers and to globally optimal graph-theoretic combinatorial optimization techniques, when applied to the task of corpus callosum segmentation in 50 mid-sagittal brain magnetic resonance images.