A stochastic continuation approach to piecewise constant reconstruction.

We address the problem of reconstructing a piecewise constant 3-D object from a few noisy 2-D line-integral projections. More generally, the theory developed here readily applies to the recovery of an ideal n-D signal (n > or =1) from indirect measurements corrupted by noise. Stabilization of this ill-conditioned inverse problem is achieved with the Potts prior model, which leads to a challenging optimization task. To overcome this difficulty, we introduce a new class of hybrid algorithms that combines simulated annealing with deterministic continuation. We call this class of algorithms stochastic continuation (SC). We first prove that, under mild assumptions, SC inherits the finite-time convergence properties of generalized simulated annealing. Then, we show that SC can be successfully applied to our reconstruction problem. In addition, we look into the concave distortion acceleration method introduced for standard simulated annealing and we derive an explicit formula for choosing the free parameter of the cost function. Numerical experiments using both synthetic data and real radiographic testing data show that SC outperforms standard simulated annealing.     

Solving inverse problems with piecewise linear estimators: from Gaussian mixture models to structured sparsity

A general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper. The approach is based on Gaussian mixture models, which are estimated via a maximum a posteriori expectation-maximization algorithm. A dual mathematical interpretation of the proposed framework with a structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques. We demonstrate that, in a number of image inverse problems, including interpolation, zooming, and deblurring of narrow kernels, the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art.     

Non white Gaussian multiple access channels with feedback

Although feedback does not increase the capacity of an additive white noise Gaussian channel, it enables prediction of the noise for non-white additive Gaussian noise channels and results in an improvement of capacity, but at most by a factor of 2 (Pinsker, Ebert, Pombra, and Cover). Although the capacity of white noise channels cannot be increased by feedback, multiple access white noise channels have a capacity increase due to the cooperation induced by feedback. Thomas has shown that the total capacity (sum of the rates of all the senders) of an m-user Gaussian white noise multiple access channel with feedback is less than twice the total capacity without feedback. The present authors show that this factor of 2 bound holds even when cooperation and prediction are combined, by proving that feedback increases the total capacity of an m-user multiple access channel with non-white additive Gaussian noise by at most a factor of 2     

Accelerating evolutionary algorithms with Gaussian process fitness function models

We present an overview of evolutionary algorithms that use empirical models of the fitness function to accelerate convergence, distinguishing between evolution control and the surrogate approach. We describe the Gaussian process model and propose using it as an inexpensive fitness function surrogate. Implementation issues such as efficient and numerically stable computation, exploration versus exploitation, local modeling, multiple objectives and constraints, and failed evaluations are addressed. Our resulting Gaussian process optimization procedure clearly outperforms other evolutionary strategies on standard test functions as well as on a real-world problem: the optimization of stationary gas turbine compressor profiles.     

基于“数据重用”的常模盲均衡算法分析

基于"数据重用"的常模均衡算法可以用于解决短时突发信号的盲均衡问题,但是对于这类算法应用中重要特性的研究还需要进一步深入.首先对数据重复导致的误收敛特性进行了分析并给出了产生这种误收敛的约束条件;然后对短数据重用常模算法能够达到和无重复使用的长数据常模均衡相同稳态误差的条件进行了详细分析并给出了相应的结论.这些分析和结论对于该类盲均衡方法的应用非常重要,计算机仿真验证了这些分析和结论的有效性.     

Two iterative image restoration algorithms with applications to nuclear medicine

Two methods for recovering an image that has been degraded while being processed are presented. The restoration problem is formulated as a constrained optimization problem in which a measure of smoothness based on the second derivatives of the restored image is maximized subject to the constraint that noise energy is equal to the energy in the difference between the distorted and blurred images. The approach is based on the Lagrange multiplier method. The first algorithm reduces the problem to the computation of few discrete Fourier transforms and allows control of the degree of sharpness and smoothness of the restored image. The second algorithm with weight matrices included allows the handling of edges and flat regions in the image in a pleasing manner for the human visual system. In this case the iterative conjugate gradient method is used in conjunction with the discrete Fourier transform to minimize the Lagrangian function. The application of these algorithms to nuclear medicine images is presented.     

Optimal coding in two-user white Gaussian channels with feedback

The optimal coding problem in two-user white Gaussian channels with feedback is discussed. The messages are taken as Gauss-Markov processes. The optimal decoder pair and the optimal linear encoder pair are developed. A nonlinear class (additive feedback type) of encoder pairs in which the optimal linear encooer pair is optimal is presented.     

3-D electrical impedance tomography for piecewise constant domains with known internal boundaries

Electrical impedance tomography (EIT) is a badly posed inverse problem, but can be stabilized if one assumes that the conductivity is piecewise constant, with a relatively small number of distinct regions, and that the region boundaries are known, for example from prior anatomical imaging. With this assumption, we introduce a three-dimensional (3-D) boundary element method (BEM) model for the forward EIT map from injected currents to measured voltages, and 3-D inverse solutions for both BEM and the finite element method (FEM) which explicitly take into account the parameterization implied by the known boundary locations. We develop expressions for the Jacobians for both methods, since they are nonlinear, to more rapidly solve the inverse problem. We show simulation results in a torso geometry with the heart and lungs as inhomogeneities. In a simulation study, we could reconstruct the conductive values of some internal organs of a human torso with more than 92% accuracy even with inaccurate internal boundary locations, a randomized rather than constant conductivity profile (with the standard deviation of the Gaussian-distributed conductivities set to 20% of their mean values), signal to measurement noise of 50 dB, and with different meshes used for the forward and inverse problems. BEM and FEM perform similarly, leading to the conclusion that the choice between them should be based on secondary considerations such as computational efficiency or the need to model conductivity anisotropies     

常数阵实现开环系统对角优势的寻优算法

在详细分析文用常数补偿矩阵在单点处实现对角优势的充分必要条件和用常数补偿矩阵在某频段内实现对角优势的充分条件的基础上,对上述两个条件做了工程应用方面的实用化扩展。针对所分析算法的计算结果较差的缺点,给出了两种优化算法。实例仿真结果表明:本文是计算在某频段上实现对角优势的常数补偿矩阵更为有效的工程实用化算法。     

Synthesis of the frequency response of a resistive strip with a piecewise constant profile

A new approach is proposed here to synthesize a desired frequency response of a resistive strip with a piecewise constant resistive profile. The strip can be attached at both ends to resistive (with constant resistance) or perfect electric conducting half-planes. The main feature of this method is the use ofutd solutions for the scattered field in a cost function which depends on the desired frequency response. The cost function is minimized by an iterative numerical scheme to determine the piecewise constant resistive profile. The scattered field in the frequency or spatial domains is then calculated usingutd or method of moments techniques. Several examples are shown for a Chebyshev frequency response.     

The capacity of the white Gaussian multiple access channel with feedback

Since the appearance of [10] by Gaarder and Wolf, it has been well known that feedback can enlarge the capacity region of the multiple access channel. In this paper a deterministic feedback code is presented for the two-user Gaussian multiple access channel, which is shown to allow reliable communication at all points inside a region larger than any previously obtained. An outer bound is given which is shown to coincide with the achievable region, thus yielding the capacity region of this channel exactly.     

Mutual information of the white Gaussian channel with and without feedback

The following model for the white Gaussian channel with or without feedback is considered: begin{equation} Y(t) = int_o ^{t} phi (s, Y_o ^{s} ,m) ds + W(t) end{equation} wheremdenotes the message,Y(t)denotes the channel output at timet,Y_o ^ {t}denotes the sample pathY(theta), 0 leq theta leq t. W(t)is the Brownian motion representing noise, andphi(s, y_o ^ {s} ,m)is the channel input (modulator output). It is shown that, under some general assumptions, the amount of mutual informationI(Y_o ^{T} ,m)between the messagemand the output pathY_o ^ {T}is directly related to the mean-square causal filtering error of estimatingphi (t, Y_o ^{t} ,m)from the received dataY_o ^{T} , 0 leq t leq T. It follows, as a corollary to the result forI(Y_o ^ {T} ,m), that feedback can not increase the capacity of the nonband-limited additive white Gaussian noise channel.     

Adaptive algorithms with nonlinear data and error functions

The tools of nonlinear system theory are used to examine several common nonlinear variants of the LMS algorithm and derive a persistence of excitation criterion for local exponential stability. The condition is tight when the inputs are periodic, and a generic counterexample is demonstrated which gives (local) instability for a large class of such nonlinear versions of LMS, specifically, those which utilize a nonlinear data function. The presence of a nonlinear error function is found to be relatively benign in that it does not affect the stability of the error system. Rather, it defines the cost function the algorithm tends to minimize. Specific examples include the dead zone modification, the cubed data nonlinearity, the cubed error nonlinearity, the signed regressor algorithm, and a single-layer version of the backpropagation algorithm     

Statistics of the binary quantizer error in single-loop sigma-deltamodulation with white Gaussian input

Representations and statistical properties of the process e¯ defined by e¯_n+1=λ(e¯_n+ξ_n ), are given. Here λ(u):=u-b·sign(u)+m and {ξ_n}_n=0^+∞ is Gaussian white noise. The process e¯ represents the binary quantizer error in a model for single-loop sigma-delta modulation. The innovations variables are found and the existence and uniqueness of an invariant probability measure, ergodicity properties, as well as the existence of the exponential moment with respect to the invariant probability are proved using Markov process theory. We consider also e¯ as a random perturbation, for small values of the variance of ξ_n, Of the orbits of s_n+1=λ(s_n). Here s_n has the uniform invariant distribution on the interval [m-h, m+b]. Analytical approximations to the structure of the power spectrum of e¯ are obtained using a linear prediction in terms of the innovations variables and the perturbation approach     

高斯白噪声下L阵二维波达方向快速估计

针对L型阵列,提出一种在高斯白噪声环境下的二维波达方向( DOA)快速估计方法。首先利用阵列结构特点构建两个互协方差矩阵,同时实现了噪声分量的有效抑制,再依据协方差矩阵的性质构造了波达方向矩阵。对该矩阵进行一次特征分解即可分别得到包含方位角和俯仰角信息的方向矢量和方向元素,实现二维DOA估计。该算法避免了传统算法的谱峰搜索或大矩阵构造及其特征分解过程,计算量小,且参数自动配对。仿真结果表明,该算法在低性噪比和少快拍下的估计精度与2 D ESPRIT算法近似,但计算复杂度大幅降低,适用于实时性高的工程应用背景。     

Two EM-type channel estimation algorithms for OFDM with transmitter diversity

We study channel estimation for orthogonal frequency-division multiplexing (OFDM) systems utilizing transmitter diversity and operating over multipath fading channels. Two expectation-maximization (EM)-type algorithms are introduced and compared with each other in terms of convergence rate. At each iteration and for every OFDM link, the EM-type algorithms partition the problem of estimating a multi-input channel into independent channel estimations for each transmit-receive antenna pair, therefore avoiding the matrix inversion encountered in the joint least-square estimation. The EM-type algorithms can also be used to efficiently implement a recently proposed algorithm, termed the significant-tap-catching estimator, so that the system performance is more robust to different multipath channel delay profiles.     

Object dependency of resolution in reconstruction algorithms with interiteration filtering applied to PET data

In this paper, we study the resolution properties of those algorithms where a filtering step is applied after every iteration. As concrete examples we take filtered preconditioned gradient descent algorithms for the Poisson log likelihood for PET emission data. For nonlinear estimators, resolution can be characterized in terms of the linearized local impulse response (LLIR). We provide analytic approximations for the LLIR for the class of algorithms mentioned above. Our expressions clearly show that when interiteration filtering (with linear filters) is used, the resolution properties are, in most cases, spatially varying, object dependent and asymmetric. These nonuniformities are solely due to the interaction between the filtering step and the Poisson noise model. This situation is similar to penalized likelihood reconstructions as studied previously in the literature. In contrast, nonregularized and postfiltered maximum-likelihood expectation maximization (MLEM) produce images with nearly "perfect" uniform resolution when convergence is reached. We use the analytic expressions for the LLIR to propose three different approaches to obtain nearly object independent and uniform resolution. Two of them are based on calculating filter coefficients on a pixel basis, whereas the third one chooses an appropriate preconditioner. These three approaches are tested on simulated data for the filtered MLEM algorithm or the filtered separable paraboloidal surrogates algorithm. The evaluation confirms that images obtained using our proposed regularization methods have nearly object independent and uniform resolution.     

Application of the finite-element method for solving a spectral problem in a waveguide with piecewise constant bi-isotropic filling

A spectral problem in a bi-isotropic waveguide filled nonuniformly in the cross section is considered. A generalized formulation of the problem is considered, making possible, while using Lagrange finite elements, a substantial reduction in the number of spurious modes in the spectral region of interest and shifting them to the higher frequency region. An algorithm for calculating the propagation constants and fields in the given waveguide is implemented. A series of calculations of dispersion curves and fields in a waveguide with different cross-section structures are performed.     

Two algorithms for soft-decision decoding of reed-solomon codes, with application to multilevel coded modulations

In this paper two symbol-level soft-decision decoding algorithms for Reed-Solomon codes, derived form the ordered statistics (OS) and from the generalized minimum-distance (GMD) decoding methods, are presented and analyzed. Both the OS and the GMD algorithms are based on the idea of producing a list of candidate code words, among which the one having the larger likelihood is selected as output. We propose variants of the mentioned algorithms that allow to finely tune the size of the list in order to obtain the desired decoding complexity. The method proposed by Agrawal and Vardy for computing the error probability of the GMD algorithm is extended to our decoding methods. Examples are presented where these algorithms are applied to singly-extended Reed-Solomon codes over GF(16) used as outer codes in a 128-dimensional coded modulation scheme that attains good performance, with manageable decoding complexity.     

Two fast algorithms to compute the discrete receding horizon control gains

Two fast algorithms are proposed to calculate the feedback gains of the receding horizon method to suboptimally control linear time-invariant multi-input, multi-output discrete systems.