一种频域卷积反演的新方法

本文提出了一种卷积反演的新方法。这种方法也是通过离散傅里叶变换(DFT)在频域实现的,但是避免了通常所用的离散傅里叶变换方法当位于分母位置的信号频谱有零点存在时计算失效的问题。本文讨论了新方法与普通离散傅里叶变换方法之间的关系,并且给出了计算示例。     

GENERALIZED INVERSE GROUP OF SIGNAL AND ITS IMPLEMENTATION WITH NEURAL NETWORKS

A new concept, the generalized inverse group (GIG) of signal, is firstly proposed and its properties, leaking coefficients and implementation with neural networks are presented. Theoretical analysis and computational simulation have shown that (1) there is a group of finite length of generalized inverse signals for any given finite signal, which forms the GIG; (2) each inverse group has different leaking coefficients, thus different abnormal states; (3) each GIG can be implemented by a grouped and improved single-layer perceptron which appears with fast convergence. When used in deconvolution, the proposed GIG can form a new parallel finite length of filtering deconvolution method. On off-line processing, the computational time is reduced to O(N) from O(N2). And the less the leaking coefficient is, the more reliable the deconvolution will be.     

A NEW IMEMENTATION FOR DFT BASED ON DELTA MODULATION

This paper proposes a new implementation for DFT based on delta modulation which isdifferent from the conventional PCM implementation.The hardware structure of the method is multiplier-free,simple and low in cost.Theoretical analyses show that its SNR can approach conventional one's,forinstance,FFT.Computer simulations demonstrate that for deterministic signals,the results agree withtheoretical analyses.For handlimited Gaussian signals,we can still get results similar to the conventionalDFT's if selecting the step size suitably.A hardware structure which simply consists of ROM,an adder andother auxiliary circuits is also given.     

On the computational model of a kind of deconvolution problem

It is known that discretization of a continuous deconvolution problem can alleviate the ill-posedness of the problem. The currently used circulant matrix model, however, does not play such a role. Moreover, the approximation of deconvolution problems by circulant matrix model is rational only if the size of the kernel function is very small. We propose an aperiodic model of deconvolution. For discrete and finite deconvolution problems the new model is an exact one. In the general case, the new model can lead to a nonsingular system of equations that has a lower condition number than the circulant one, and the related computations in the deconvolution can be done efficiently by means of the DFT technique, as in the ease for circulant matrices. The rationality of the new model holds without regard to the size of the kernel and the image. The use of the aperiodic model is illustrated by gradient-based algorithms.     

A new implementation for DFT based on delta modulation

This paper proposes a new implementation for DFT based on delta modulation which is different from the conventional PCM implementation. The hardware structure of the method is multiplier-free, simple and low in cost. Theoretical analyses show that its SNR can approach conventional one's, for instance, FFT. Computer simulations demonstrate that for deterministic signals, the results agree with theoretical analyses. For bandlimited Gaussian signals, we can still get results similar to the conventional DFT's if selecting the step size suitably. A hardware structure which simply consists of ROM, an adder and other auxiliary circuits is also given. This Project is supported by the National Natural Science Fundation of China.     

A NEW ITERATIVE SIGNAL RESTORATION METHOD

A new iterative method for signal, restoration has been presented. An estimateoperator W_κ which is related to error operator B_κ in the restoration process is introduced todecrease the estimate error and increase the convergence rate. The effect of noise on the estimateprocess has also been described. Finally, the method has been applied to the deconvolution of ablurred signal, and the results validate the method. A comparison between the presented methodand the general method has also been given.     

有限域上任意长度的DFT

有限域上的ＤＦＴ在数字信号处理，纠错码等领域都有重要应用。通常的有限域上ＤＦＴ仅限于长度与有限域特征互素的情形，它远远不能满足处理任意长度数据的需要。本文提出了有限域上任意长度的ＤＦＴ，研究了新变换的有关性质，并讨论了它在密码、编码中的应用。     

Minimax deconvolution design of multirate systems with channelnoises: a unified approach

The conventional signal reconstruction problem of multirate systems with channel noises can be cast as a robust multirate deconvolution design problem. We investigate a unified minimax approach for the robust deconvolution design of multirate systems. We discuss two typical multirate systems: the multirate filter bank system and the transmultiplexer system. We consider transmission noises resulting from quantization coding errors or external noises. The deconvolution filters for these systems that we derive are all IIR filters. The keypoint is converting the original robust deconvolution design problem to an equivalent minimax matching problem via polyphase decomposition and noble identities. Then, in spite of the presence of input signals and channel noises, we can solve this minimax matching problem by an optimization technique. The proposed method can be interpreted as designing an optimal multirate deconvolution filter such that the worst-case multirate system reconstruction error is minimized over all possible inputs and noises from the energy perspective. Therefore, our proposed design method is more robust than the conventional design method for multirate systems in the presence of uncertain input signals and channel noises. We present several numerical examples that show the good performance of our design method     

信号的广义逆群及其神经网络实现

本文首次提出了信号的广义逆群这一新概念,并讨论了它的性质、泄漏系数和神经网络实现技术。研究表明,有限长信号存在多组有限长广义逆信号,它们构成原信号的广义逆群;各广义逆群的泄漏系数一般不相同,因而其病态程度不同;广义逆群可以用一个特殊的神经网络并行实现且收敛快.最后指出,广义逆群用于反卷积时可形成一种新的并行有限长滤波反卷积方法,对于离线处理,计算时间可从N2阶次降到N阶次;最低泄漏系数广义逆群对应的反卷积最可信。     

再论X（K）有零点的卷积反演的DFT算法

本文提出X[k]有零点而Y[k]无这些零点的卷积反演的DFT方法。     

A new method for optimal deconvolution

Using an innovation analysis method in the time domain, the problem of optimal input estimation is considered, Two algorithms for calculating optimal deconvolution estimators are presented. A new tool for obtaining the estimators is described. It is based on the projection method and innovation theory. The approach covers input prediction, filtering, and smoothing problems. The solution is also applied to unstable linear systems, disturbances, or input models     

用窗口卷积实现反卷积的算法研究

本文提出了一种用窗口卷积实现反卷积的新算法,这种算法解决了用圆周卷积计算反卷积时出现的病态问题.对用圆周卷积、线性卷积和窗口卷积实现反卷积三种方法进行误差、计算量与存储空间的分析和对比.结果表明,用窗口卷积实现反卷积运算的误差、计算量和存储空间都是最小的.     

A unified computational framework for deconvolution to reconstruct multiple fibers from diffusion weighted MRI

Diffusion magnetic resonance imaging (MRI) is a relatively new imaging modality which is capable of measuring the diffusion of water molecules in biological systems noninvasively. The measurements from diffusion MRI provide unique clues for extracting orientation information of brain white matter fibers and can be potentially used to infer the brain connectivity in vivo using tractography techniques. Diffusion tensor imaging (DTI), currently the most widely used technique, fails to extract multiple fiber orientations in regions with complex microstructure. In order to overcome this limitation of DTI, a variety of reconstruction algorithms have been introduced in the recent past. One of the key ingredients in several model-based approaches is deconvolution operation which is presented in a unified deconvolution framework in this paper. Additionally, some important computational issues in solving the deconvolution problem that are not addressed adequately in previous studies are described in detail here. Further, we investigate several deconvolution schemes towards achieving stable, sparse, and accurate solutions. Experimental results on both simulations and real data are presented. The comparisons empirically suggest that nonnegative least squares method is the technique of choice for the multifiber reconstruction problem in the presence of intravoxel orientational heterogeneity.     

Adele, a fast suboptimal estimator for real-time deconvolution

It is shown how a Kalman filter approach can solve an orthogonalisation problem that occurs when accelerating the convergence of the Kaczmarz algorithm for real-time deconvolution. A new suboptimal estimator is developed in the case of noise and input stationary statistics. Simulation results in reflection seismology are presented.     

一种不用乘法器的增量调制DFT新结构

本文提出一种基于增量调制(DM)序列的离散傅里叶变换(DFT)结构,它不同于基于脉冲编码调制(PCM)的常规方法。提出这一想法是为了解决在常规的数字信号处理中的乘法运算问题,从而减小系统的复杂性,降低设备成本。我们将看到,本文提出的新的DFT结构取消了A/D变换器和乘法器,可望简化硬件设计、降低造价,而信噪比同样能够达到与常规的处理方法,如FFT相近的结果。计算机模拟表明,对于确定性信号,结果与常规的DFT相一致。对于带限高斯信号,只要适当地选择步长和过采样率系数,同样也能得到与常规DFT相近的结果。我们采用ROM存贮各个系数值,因此,整个运算完全是阅读和求和的过程,因而速度快,硬件结构简单,适用于语音、地震等信号的处理。本文最后给出了硬件实现方案和各个参数的选择方法,同时提供了计算机模拟结果。     

Wiener filter design using polynomial equations

A simplified way of deriving realizable and explicit Wiener filters is presented. Discrete-time problems are discussed in a polynomial equation framework. Optimal filters, predictors, and smoothers are calculated by means of spectral factorizations and linear polynomial equations. A tool for obtaining these equations, for a given problem structure, is described. It is based on the evaluation of orthogonality in the frequency domain, by means of canceling stable poles with zeros. Comparisons are made to previously known derivation methodologies such as completing the squares for the polynomial systems approach and the classical Wiener solution. The simplicity of the proposed derivation method is particularly evident in multistage filtering problems. To illustrate, two examples are discussed: a filtering and a generalized deconvolution problem. A new solvability condition for linear polynomial equation appearing in scalar problems is also presented     

Genetic algorithm approach to fixed-order mixed H/sub 2//H/sub /spl infin// optimal deconvolution filter designs

The mixed H/sub 2//H/sub /spl infin// optimal deconvolution filter is proposed to achieve the H/sub 2/ optimal reconstruction and a desired robustness against the effect of uncertainties in signal processing from the H/sub /spl infin// norm perspective. However, the conventional mixed H/sub 2//H/sub /spl infin// optimal design filters are very complicated and are not practical for industrial applications. For simplicity of implementation and conservation of operation time, the fixed-order mixed H/sub 2//H/sub /spl infin// optimal deconvolution filter design is interesting for engineers in signal processing from the practical design perspective. In this study, to avoid the trap of local minima, a design method based on the genetic algorithm is introduced to treat the nonlinear optimization design problem of the fixed-order mixed H/sub 2//H/sub /spl infin// deconvolution filter. The convergence property of our design algorithm is also discussed. Finally, an example is presented to illustrate the design procedure and confirm the robustness performance of the proposed method.     

多输入多输出盲解卷问题的最大熵解法

本文研究的问题是从观察信号中分离出两个(或者更多个)输入信号,其中每一组信号分别通过不同的未知多输入多输出线性系统.本文证明了当输入信号是两两相互独立的独立同分布信号时可以分离出输入信号,并导出了基于最大熵的多输入多输出盲解卷新算法.这个算法不需要任何关于输入信号和混合滤波器的先验知识.     

基于聚谱分析的多通道盲信号自适应分离算法

该文提出一种在多传感器中多种信号混叠的分离方法。该方法通过分析传感器数据的聚谱来提取未知信号,并利用线性方程基本算法估计有限脉冲响应的耦合系统,该方法对于多通道谱重叠的有色输入信号盲解卷积十分有效。作为该算法的扩展,可以应用于包括准周期信号等非平稳信号的分离。并将该算法应用于电磁辐射的测试,仿真结果证明了其有效性和快速性。