基于加权最小二乘正则化方法的混合滤波器组最优化设计

模拟分析滤波器的实现误差以及数字综合滤波器有效阶数实现的设计误差造成的病态问题都将影响混合滤波器组(HFB)的重构效果.提出一种新的满足近似完美重构的基于加权最小二乘(WLS)正则化算法的IIR形式综合滤波器设计方法.该算法根据误差量二阶统计特性采用WLS算法抑制滤波器实现误差以及随机噪声等扰动因素影响,使得到的综合滤波器组频域响应解的加权误差平方和最小化,并通过Tikhonov正则化方法优化解的稳定性.提出一种IIR类型综合滤波器设计算法,并利用正则化方法优化滤波器系数,减小设计误差.该方法可应用于过采样HFB的设计.仿真结果表明该算法的有效提高系统鲁棒性和改善重构性能.     

频域和时域最小二乘法在声场重建中的性能比较

最小二乘法在声场重建中应用广泛,主要分为频域和时域两种实现形式.频域最小二乘法是对各频点上的声场重建误差进行最小化控制,通常需要在各频点进行独立的正则化处理,导致重建滤波器的非因果性,在实际应用中需要引入时延因子.时域最小二乘法是对控制点上的时域重建误差进行最小化控制,对重建滤波器系数进行整体求解,不存在非因果问题.本文利用两种算法仿真了自由场假设下的单目标区域和多目标区域的声场重建问题,仿真结果表明,在滤波器阶数相同的情况下,两种算法在单目标区域声场重建问题中表现相近,在多目标区域的声场重建问题中,时域算法明显优于频域算法.     

CGLS 算法在综合孔径微波辐射计中的应用

高效的反演成像算法是综合孔径微波辐射计的关键技术之一。由于综合孔径微波辐射计反演成像在数学上是病态的反问题,所以需要进行正则化处理以克服其病态特性而获得稳定的解。与直接正则化方法相比,共轭梯度最小二乘(Conjugate Gradients Least Squares, CGLS)迭代法具有无须明确正则化参数、无须对传递矩阵求逆等优点。提出将共轭梯度最小二乘法应用于综合孔径辐射计成像中,并基于全极化干涉式微波辐射计(Full Polarization Interferometric Radiometer, FPIR)系统,比较了其与经典的最小范数正则化的性能。仿真结果表明:与最小范数正则化相比,CGLS 正则化算法能有效降低FPIR 系统图像反演误差,以获取高精确度的观测场景的亮温分布满足FPIR 系统探测海面风场、海表面盐度和土壤湿度等应用需求。     

基于拉普拉斯算子的综合孔径辐射计成像算法

成像反演是综合孔径辐射计的一项关键内容.然而,综合孔径辐射计成像反演是病态的反问题.虽然传统的正则化方法能有效克服其病态性,但依然存在较大的重构误差.为了进一步降低重构误差,提出一种基于拉普拉斯算子的综合孔径辐射计成像算法.与传统的单参数正则化不同,该算法通过引入拉普拉斯算子项,对差分亮温构造拉普拉斯混合正则化,并利用...     

具有任意幅度频响的二维线性相位FIR数字滤波器的设计

本文提出了设计任意幅度频响的二维线性相位ＦＩＲ数字滤波器的解析最小二乘方法，通过最小化频域平方误差函数得到了滤波器系数的闭式解，运用导出的闭式式，可根据给定的任意幅度频响指标直接计算滤波器的系数，从而简化了滤波器设计程序，并大大降低了运算量。     

基于全变差的加权最小二乘法PET图像重建

传统的加权最小二乘法、惩罚项加权最小二乘法虽然能够重建得到较好质量的图像,但在欠采样的条件下不能很好的拟制噪声.全变差作为正则项已广泛用于图像重建中,利用图像稀疏的先验知识能够在欠采样的条件下很好的重建图像.本文结合加权最小二乘法和全变差的优点,构造了基于全变差正则项的加权最小二乘法目标函数,运用交替求解的方法,将目标函数分解为求解二次优化和全变差正则化的优化问题,并分别用超松弛迭代方法和梯度下降法求解这两个优化问题.采用Zubal模型对该算法与传统算法进行仿真验证比较,并用相关系数、方差、信噪比等参数描述图像重建质量.结果表明在欠采样条件下,该算法能够更好的拟制噪声,重构效果比传统的有明显地提高.     

基于SP-LSQR的综合孔径辐射成像方法

综合孔径微波辐射计是被动微波遥感领域中一种重要的探测器。综合孔径辐射计成像反演过程在数学上是病态的反问题,传统正则化方法虽然能够有效克服其病态性,但重构误差较大、对干扰噪声鲁棒性不强。与传统正则化方法相比,最小二乘Q-R矩阵(Least Square Q-R matrix, LSQR)分解算法具有计算精度高、数值稳定性好等优点,但收敛速度不够快。对此,文中提出利用子空间预处理LSQR(Subspace Preconditioned LSQR, SP-LSQR)算法进行综合孔径辐射计反演成像,提高收敛速度。仿真结果表明：与Tikhonov正则化和带限正则化相比,SP-LSQR方法不仅可以降低重构误差,而且对干扰噪声的鲁棒性更强。此外,与LSQR方法相比,SP-LSQR方法在不降低成像反演精度的情况下,有效提高了计算效率。     

基于IRLS的圆度误差最优化评定

提出了圆度误差评定的迭代重加权最小二乘算法(IRLS)。该算法采用一个迭代过程求解一系列加权最小二乘问题,并在每一步迭代中按照一定的规则对权系数进行调整,使其逐步逼近最优拉格朗日乘子,使最小二乘解逐渐逼近最小区域解。该算法保留了最小二乘法快速、惟一的优点,改正了其误差偏大的缺陷,采用Matlab语言编程,算法计算简单且易于实现,有较高的实用价值。     

混沌模拟信息转换——基于多射法的稀疏信号重构

混沌压缩采样是应用混沌系统实现非线性测量的压缩采样理论。该文研究模拟信号的混沌压缩采样-混沌模拟信息转换。该转换通过稀疏信号激励混沌系统,低速采样系统输出实现;信号重构则以混沌系统参数估计理论为基础,通过稀疏正则化的非线性最小二乘问题进行求解。该文将多射法(MS)与迭代再加权非线性最小二乘算法(IRNLS)结合,给出混沌模拟信息转换的MS-IRNLS信号重构算法。文中以Lorenz系统为例,仿真验证了MS-IRNLS算法的重构性能,结果表明方法的有效性。     

近似完全重构IIR余弦调制滤波器组的优化设计

提出一种新的近似完全重构因果稳定的IIR余弦调制滤波器组的设计方法。基于预先给定的极点值,IIR原型滤波器的设计问题可以简化成一个凸极大值极小化的优化问题,从而采用二阶锥规划法求解。所得余弦调制滤波器组具有良好的频率特性和合理的完全重构误差。所设计的原型滤波器是因果稳定的,并且其多相因子分母相同,简化了完全重构条件,可以用来进一步优化得到的完全重构系统。     

Optimal design of two-channel nonuniform-division FIR filter bankswith -1, 0, and +1 coefficients

This paper deals with the optimal design of two-channel nonuniform-division filter (NDF) banks whose linear-phase FIR analysis and synthesis filters have coefficients constrained to -1, 0, and +1 only. Utilizing an approximation scheme and a weighted least squares algorithm, we present a method to design a two-channel NDF bank with continuous coefficients under each of two design criteria, namely, least-squares reconstruction error and stopband response for analysis filters and equiripple reconstruction error and least-squares stopband response for analysis filters. It is shown that the optimal filter coefficients can be obtained by solving only linear equations. In conjunction with the proposed filter structure, a method is then presented to obtain the desired design result with filter coefficients constrained to -1, 0, and +1 only. The effectiveness of the proposed design technique is demonstrated by several simulation examples     

一种基于遗传算法的混合滤波器组设计方法

针对可满足近似完全重构的双通道混合滤波器组,其中高阶数的模拟滤波器一般不容易设计优化。采用遗传算法设计5阶模拟分解滤波器,并基于逆快速傅里叶变换实现数字综合滤波器的设计优化以滤除掉镜像频谱,保证近似完全重构。文中设计了由5阶模拟分解滤波器和32阶数字综合滤波器组成的混合滤波器组,仿真结果表明:可以实现的最大失真误差为4.761 8×10-11dB,平均失真误差为-9.2×10-14dB,最大混叠误差为-154 dB,平均混叠误差为-200 dB,可满足24 bits的模数转换器系统的要求。     

Optimal design of nonuniform multirate filter banks

The design of general nonuniform filter banks is studied. Contrary to uniform filter banks, in nonuniform filter banks, it may not be possible to achieve perfect reconstruction, but in some cases by using optimization techniques, we can design acceptable filter banks. Here, the initial finite impulse response (FIR) analysis filters are designed according to the characteristics of the input. By the design procedure, the FIR synthesis filters are found so that theH-norm of an error system is minimized over all synthesis filters that have a prespecified order. Then, the synthesis filters obtained in the previous step are fixed, and the analysis filters are found similarly. By iteration, theH-norm of the error system decreases until it converges to its final value. At each iteration, the coefficients of the analysis or synthesis filters are obtained by finding the least squares solution of a system of linear equations. If necessary, the frequency characteristics of the filters can be altered by adding penalty terms to the objective function.This research was supported by the Natural Sciences and Engineering Research Council of Canada.     

Least squares approximation of perfect reconstruction filter banks

Designing good causal filters for perfect reconstruction (PR) filter banks is a challenging task due to the unusual nature of the design constraints. We present a new least squares (LS) design methodology for approximating PRFBs that avoids most of these difficult constraints. The designer first selects a set of subband analysis filters from an almost unrestricted class of rational filters. Then, given some desired reconstruction delay, this design procedure produces the causal and rational synthesis filters that result in the best least squares approximation to a PRFB. This technique is built on a multi-input multi-output (MIMO) system model for filter banks derived from the filter bank polyphase representation. Using this model, we frame the LS approximation problem for PRFBs as a causal LS equalization problem for MIMO systems. We derive the causal LS solution to this design problem and present an algorithm for computing this solution. The resulting algorithm includes a MIMO spectral factorization that accounts for most of the complexity and computational cost for this design technique. Finally, we consider some design examples and evaluate their performance     

Time-domain design of FIR multirate filter banks

A new time-domain methodology for designing FIR multirate filter banks is proposed. The conditions for perfect reconstruction systems can only be met by a limited number of systems, and consequently one of the major problems is to design analysis and synthesis filters which reduce the reconstruction error to a minimum. A recursive technique is proposed which uses the synthesis filters from one iteration to update the analysis filters for the next. The Letter shows that this is computationally simpler than previously proposed time-domain methods and produces filter banks in which the reconstruction error is reduced to practically acceptable levels.<>     

A WISE method for designing IIR filters

The problem of designing optimal digital IIR filters with frequency responses approximating arbitrarily chosen complex functions is considered. The real-valued coefficients of the filter's transfer function are obtained by numerical minimization of carefully formulated cost, which is referred here to as the weighted integral of the squared error (WISE) criterion. The WISE criterion linearly combines the WLS criterion that is used in the weighted least squares approach toward filter design and some time-domain components. The WLS part of WISE enforces the quality of the frequency response of the designed filter, while the time-domain part of the WISE criterion restricts the positions of the filter's poles to the interior of an origin-centred circle with arbitrary radius. This allows one not only to achieve stability of the filter but also to maintain some safety margins. A great advantage of the proposed approach is that it does not impose any constraints on the optimization problem and the optimal filter can be sought using off-the-shelf optimization procedures. The power of the proposed approach is illustrated with filter design examples that compare favorably with results published in research literature     

A multiscale relaxation algorithm for SNR maximization innonorthogonal subband coding

Develops a technique for improving the applicability of complete, nonorthogonal, multiresolution transforms to image coding. As is well known, the L(2) norm of the quantization errors is not preserved by nonorthogonal transforms, so the L(2) reconstruction error may be unacceptably large. However, given the quantizers and synthesis filters, the authors show that this artifact can be eliminated by formulating the coding problem as that of minimizing the L(2) reconstruction error over the set of possible encoded images. With this new formulation, the coding problem becomes a high-dimensional, discrete optimization problem and features a coupling between the redundancy-removing and quantization operations. A practical solution to the optimization problem is presented in the form of a multiscale relaxation algorithm, using inter- and intrascale quantization noise feedback filters. Bounds on the coding gain over the standard coding technique are derived. A simple extension of the algorithm allows for the use of a weighted L(2) error criterion and deadband (non-MMSE) quantizers. Experiments using biorthogonal spline filter banks demonstrate appreciable SNR gains over the standard coding technique, and comparable visual improvements.     

Minimax design of two-channel low-delay perfect-reconstruction FIRfilter banks

The authors deal with the design problem of low-delay perfect-reconstruction filter banks for which the FIR analysis and synthesis filters have equiripple magnitude response. Based on the minimax error criterion, the design problem is formulated in such a manner that the coefficients for the FIR analysis filters can be found by minimising the weighted peak error of the designed analysis filters, subject to the perfect-reconstruction constraints. A design technique based on a modified dual-affine scaling variant of Karmarkar's (1989) algorithm, in conjunction with approximation schemes, is then developed for solving the resulting nonlinear optimisation problem. The effectiveness of the proposed design technique is demonstrated by several simulation examples     

基于协方差加权的卡尔曼滤波融合跟踪算法

针对卡尔曼滤波融合跟踪对系统模型准确度和先验信息精度要求较高的问题,提出一种基于协方差加权的卡尔曼滤波融合方法,利用最小二乘准则作为误差加权的标准,使误差小的传感器加权因子大。基于此,再利用卡尔曼滤波融合,充分保留有用信息,抑制噪声干扰。在目标跟踪应用中,即使噪声统计信息未知且噪声互相关,利用该方法仍能够获得最小均方误差准则下的最优目标状态跟踪估计。     

A direct approach to the design of QMF banks via frequency domainoptimization

This paper studies the design of quadrature mirror filter (QMF) banks via frequency domain optimization. A direct approach is adopted that gives the necessary and sufficient condition for perfect reconstruction (PR). While analysis filter banks are designed to achieve frequency domain specifications required for subband coding, synthesis filter banks are designed to minimize the reconstruction error in frequency domain. The criterion used to measure the reconstruction error is H_∞ or Chebyshev norm (sup-norm). State-space solutions are derived for the H_∞ optimization, and numerical algorithms are developed to obtain the optimal synthesis filter bank. Moreover, the asymptotic PR property is established for optimal H_∞ solution of the synthesis filter bank