Regularized constrained total least squares image restoration

In this paper, the problem of restoring an image distorted by a linear space-invariant (LSI) point-spread function (PSF) that is not exactly known is formulated as the solution of a perturbed set of linear equations. The regularized constrained total least-squares (RCTLS) method is used to solve this set of equations. Using the diagonalization properties of the discrete Fourier transform (DFT) for circulant matrices, the RCTLS estimate is computed in the DFT domain. This significantly reduces the computational cost of this approach and makes its implementation possible even for large images. An error analysis of the RCTLS estimate, based on the mean-squared-error (MSE) criterion, is performed to verify its superiority over the constrained total least-squares (CTLS) estimate. Numerical experiments for different errors in the PSF are performed to test the RCTLS estimator. Objective and visual comparisons are presented with the linear minimum mean-squared-error (LMMSE) and the regularized least-squares (RLS) estimator. Our experiments show that the RCTLS estimator reduces significantly ringing artifacts around edges as compared to the two other approaches     

基于参数估计的降晰函数辨识及图像复原算法

成像系统的点扩展函数(PSF)以及观测噪声,在一般应用过程中是未知信息,因此,点扩展函数的辨识是一个具有挑战性的世界难题.为解决实际工作中遇到的在已知降晰类型情况下的降晰函数辨识和降晰图像复原问题,提出了基于参数估计的降晰函数辨识及降晰图像复原算法.首先,由初始猜测给定降晰函数参数的变化范围和参数的增量步长;然后,最小化降晰图像和由相应点扩展函数及降晰图像得到的实验观测图像的差的Frobenius范数,以确定点扩展函数的参数,进而确定降晰图像的点扩展函数并对降晰图像进行复原.应用基于Wiener滤波的频域循环边界算法对降晰图像进行复原.实验结果表明:在降晰图像信噪比较高的情况下,降晰函数的辨识结果是可靠和准确的,有较好的复原效果.     

Adaptively regularized constrained total least-squares imagerestoration

In this paper, a novel algorithm for image restoration is proposed based on constrained total least-squares (CTLS) estimation, that is, adaptively regularized CTLS (ARCTLS). It is well known that in the regularized CTLS (RCTLS) method, selecting a proper regularization parameter is very difficult. For solving this problem, we take the first-order partial derivative of the classic equation of RCTLS image restoration and do some simplification with it. Then, we deduce an approximate formula, which can be used to adaptively calculate the best regularization parameter along with the degraded image to be restored. We proved that the convergence and the stability of the solution could be well satisfied. The results of our experiments indicate that using this method can make an arbitrary initial parameter be an optimal one, which results in a good restored image of high quality.     

基于神经网络和维纳滤波的半盲离焦图像复原

本文提出了一种基于小波神经网络和维纳(Wiener)滤波的半盲离焦图像复原算法,首先提取训练图像的小波域特点参数向量,将该参数用来训练小波神经网络,利用训练好的网络估计图像离焦模糊参数.由离焦模糊参数获得点扩展函数,然后用Wiener滤波完成图像的复原.实验结果表明:该方法能有效地估计离焦模糊参数和复原模糊图像.     

一种改进的LTE下行系统信道估计算法

基于3GPP长期演进（LTE）下行链路系统,在比较了现有几种不同信道估计算法的基础上,提出了一种适用于LTE下行系统的时频二维联合维纳迭代滤波信道估计算法。具体步骤如下：首先,采用基于奇异值分解（SVD）的线性最小均方误差（LMMSE）算法在频域进行维纳迭代滤波;然后,再利用频域估计出来的值在时域进行一次维纳迭代滤波。仿真结果表明,该算法能够有效地改善信道估计的误比特率（BER）性能,与传统的方法相比,性能更加接近于理想信道估计,同时也没有显著增加算法的运算复杂度。     

Efficient generalized cross-validation with applications toparametric image restoration and resolution enhancement

In many image restoration/resolution enhancement applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or is known only to within a set of parameters. We estimate these PSF parameters for this ill-posed class of inverse problem from raw data, along with the regularization parameters required to stabilize the solution, using the generalized cross-validation method (GCV). We propose efficient approximation techniques based on the Lanczos algorithm and Gauss quadrature theory, reducing the computational complexity of the GCV. Data-driven PSF and regularization parameter estimation experiments with synthetic and real image sequences are presented to demonstrate the effectiveness and robustness of our method.     

水下数字图像盲复原算法研究

图像复原的目的是从观测到的退化图像重建原始图像,它是图像处理、模式识别、机器视觉等的基础。盲复原作为其中一个重要分支,其主要思想是在点扩展函数未知的情况下,力求获得最佳的清晰效果。由于水下图像退化模型中点扩展函数一般为高斯模型,故针对此提出误差一参数估计法,根据图像退化过程,给出频率域的误差形式,并选定参数的变化范围,再利用复原算法做出误差参数曲线,由此估计出点扩展函数的参数值,最后利用经典的复原算法,如维纳滤波对退化图像进行复原。实验证明该方法获得了比较清楚的复原效果。     

A novel approach to the 2-D blind deconvolution problem in medical ultrasound

The finite frequency bandwidth of ultrasound transducers and the nonnegligible width of transmitted acoustic beams are the most significant factors that limit the resolution of medical ultrasound imaging. Consequently, in order to recover diagnostically important image details, obscured due to the resolution limitations, an image restoration procedure should be applied. The present study addresses the problem of ultrasound image restoration by means of the blind-deconvolution techniques. Given an acquired ultrasound image, algorithms of this kind perform either concurrent or successive estimation of the point-spread function (PSF) of the imaging system and the original image. In this paper, a blind-deconvolution algorithm is proposed, in which the PSF is recovered as a preliminary stage of the restoration problem. As the accuracy of this estimation affects all the following stages of the image restoration, it is considered as the most fundamental and important problem. The contribution of the present study is twofold. First, it introduces a novel approach to the problem of estimating the PSF, which is based on a generalization of several fundamental concepts of the homomorphic deconvolution. It is shown that a useful estimate of the spectrum of the PSF can be obtained by applying a proper smoothing operator to both log-magnitude and phase of the spectra of acquired radio-frequency (RF) images. It is demonstrated that the proposed approach performs considerably better than the existing homomorphic (cepstrum-based) deconvolution methods. Second, the study shows that given a reliable estimate of the PSF, it is possible to deconvolve it out of the RF-image and obtain an estimate of the true tissue reflectivity function, which is relatively independent of the properties of the imaging system. The deconvolution was performed using the maximum a-posteriori (MAP) estimation framework for a number of statistical priors assumed for the reflectivity function. It is shown in a series of in vivo experiments that reconstructions based on the priors, which tend to emphasize the "sparseness" of the tissue structure, result in solutions of higher resolution and contrast.     

An EM Algorithm for Nonlinear State Estimation With Model Uncertainties

In most solutions to state estimation problems, e.g., target tracking, it is generally assumed that the state transition and measurement models are known a priori. However, there are situations where the model parameters or the model structure itself are not known a priori or are known only partially. In these scenarios, standard estimation algorithms like the Kalman filter and the extended Kalman Filter (EKF), which assume perfect knowledge of the model parameters, are not accurate. In this paper, the nonlinear state estimation problem with possibly non-Gaussian process noise in the presence of a certain class of measurement model uncertainty is considered. It is shown that the problem can be considered as a special case of maximum-likelihood estimation with incomplete data. Thus, in this paper, we propose an EM-type algorithm that casts the problem in a joint state estimation and model parameter identification framework. The expectation (E) step is implemented by a particle filter that is initialized by a Monte Carlo Markov chain algorithm. Within this step, the posterior distribution of the states given the measurements, as well as the state vector itself, are estimated. Consequently, in the maximization (M) step, we approximate the nonlinear observation equation as a mixture of Gaussians (MoG) model. During the M-step, the MoG model is fit to the observed data by estimating a set of MoG parameters. The proposed procedure, called EM-PF (expectation-maximization particle filter) algorithm, is used to solve a highly nonlinear bearing-only tracking problem, where the model structure is assumed unknown a priori. It is shown that the algorithm is capable of modeling the observations and accurately tracking the state vector. In addition, the algorithm is also applied to the sensor registration problem in a multi-sensor fusion scenario. It is again shown that the algorithm is successful in accommodating an unknown nonlinear model for a target tracking scenario.     

Robust Distributed Estimation Using the Embedded Subgraphs Algorithm

We propose a new iterative, distributed approach for linear minimum mean-square-error (LMMSE) estimation in graphical models with cycles. The embedded subgraphs algorithm (ESA) decomposes a loopy graphical model into a number of linked embedded subgraphs and applies the classical parallel block Jacobi iteration comprising local LMMSE estimation in each subgraph (involving inversion of a small matrix) followed by an information exchange between neighboring nodes and subgraphs. Our primary application is sensor networks, where the model encodes the correlation structure of the sensor measurements, which are assumed to be Gaussian. The resulting LMMSE estimation problem involves a large matrix inverse, which must be solved in-network with distributed computation and minimal intersensor communication. By invoking the theory of asynchronous iterations, we prove that ESA is robust to temporary communication faults such as failing links and sleeping nodes, and enjoys guaranteed convergence under relatively mild conditions. Simulation studies demonstrate that ESA compares favorably with other recently proposed algorithms for distributed estimation. Simulations also indicate that energy consumption for iterative estimation increases substantially as more links fail or nodes sleep. Thus, somewhat surprisingly, sensor network energy conservation strategies such as low-powered transmission and aggressive sleep schedules could actually prove counterproductive. Our results can be replicated using MATLAB code from www.dsp.rice.edu/software.     

An iterative L1-based image restoration algorithm with an adaptive parameter estimation

Regularization methods for the solution of ill-posed inverse problems can be successfully applied if a right estimation of the regularization parameter is known. In this paper, we consider the L(1)-regularized image deblurring problem and evaluate its solution using the iterative forward-backward splitting method. Based on this approach, we propose a new adaptive rule for the estimation of the regularization parameter that, at each iteration, dynamically updates the parameter value, following the evolution of the objective functional. The iterative algorithm automatically stops, without requiring any assumption about the perturbation process, when the parameter has reached a seemingly near optimal value. In spite of the fact that the optimality of this value has not yet been theoretically proved, a large number of numerical experiments confirm that the proposed rule yields restoration results competitive with those of the best state-of-the-art algorithms.     

A cross-validation framework for solving image restoration problems

The restoration problem deals with images in which information has been destroyed or obscured. In this paper, we present a framework for addressing image restoration problems in which the goal is to recover information about the image. Restoration algorithms often use tentative assumptions to compensate for the information lost in the degradation process. We propose cross-validation as a method for testing such assumptions. Viewed in this way, cross-validation is capable of addressing a number of key image restoration problems. We discuss the various options available for defining and evaluating the cross-validation criterion. Furthermore, we survey recent developments concerning cross-validation in image restoration and demonstrate the power of cross-validation in addressing several image restoration problems—regularization parameter estimation, blur identification, constraint assessment, and an optimal stopping rule for iterative restoration.     

Joint iterative interference cancellation and parameter estimation for cdma systems

This letter proposes a unified approach to joint iterative parameter estimation and interference cancellation (IC) for uplink CDMA systems in multipath channels. A unified framework is presented in which the IC problem is formulated as an optimization problem of an IC parameter vector for each stage and user. We also propose detectors based on a least-squares (LS) joint optimization method for estimating the linear receiver filter front-end, the IC, and the channel parameters. Simulations for the uplink of a synchronous DS-CDMA system show that the proposed methods significantly outperform the best known IC schemes.     

一种基于LMMSE改进的FBMC信道估计算法

针对滤波器组多载波(Filter Bank Multicarrier,FBMC)系统的信道估计问题,对系统进行了简要介绍并提出一种基于线性最小均方误差(Liner Minimum Mean-Square Error,LMMSE)算法改进的信道估计算法。在原有的LMMSE算法基础上结合离散傅里叶变换(Discrete Fourier Transform,DFT)算法,并进行迭代估计,同时利用奇异值分解(Singular Value Decomposition,SVD)算法降低了计算的复杂度。仿真结果表明,改进的LMMSE算法明显提高了系统的性能。     

Phase unwrapping for 2-D blind deconvolution of ultrasound images

In most approaches to the problem of two-dimensional homomorphic deconvolution of ultrasound images, the estimation of a corresponding point-spread function (PSF) is necessarily the first stage in the process of image restoration. This estimation is usually performed in the Fourier domain by either successive or simultaneous estimation of the amplitude and phase of the Fourier transform (FT) of the PSE This paper addresses the problem of recovering the FT-phase of the PSF, which is an important reconstruction problem by itself. The purpose of this paper is twofold. First, it provides a theoretical framework, establishing that the FT-phase of the PSF can be effectively estimated by a proper smoothing of the FT-phase of the appropriate radio-frequency (RF) image. Second, it presents a novel approach to the estimation of the FT-phase of the PSF, by solving a continuous Poisson equation over a predefined smooth subspace, in contrast to the discrete Poisson equation solver used for the classical least mean squares phase unwrapping algorithms, followed by a smoothing procedure. The proposed approach is possible due to the distinct properties of the FT-phases, among which the most important property is the availability of precise values of their partial derivatives. This property overcomes the main disadvantage of the discrete schemes, which routinely use wrapped (principal) values of the phase in order to approximate its partial derivatives. Since such an approximation is feasible subject to the restriction that the partial phase differences do not exceed pi in absolute value, the discrete schemes perform satisfactory only for few practical situations. The proposed approach is shown to be independent of this restriction and, thus, it performs for a wider class of the phases with significantly lower errors. The main advantages of the novel method over the algorithms based on discrete schemes are demonstrated in a series of computer simulations and for in vivo measurements.     

Finite dimensional smoothers for MAP state estimation of bilinearsystems

In this paper, we present two finite-dimensional iterative algorithms for maximum a posteriori (MAP) state sequence estimation of bilinear systems. Bilinear models are appealing in their ability to represent or approximate a broad class of nonlinear systems. Our iterative algorithms for state estimation are based on the expectation-maximization (EM) algorithm and outperform the widely used extended Kalman smoother (EKS). Unlike the EKS, these EM algorithms are optimal (in the MAP sense) finite-dimensional solutions to the state sequence estimation problem for bilinear models. We also present recursive (on-line) versions of the two algorithms and show that they outperform the extended Kalman filter (EKF). Our main conclusion is that the EM-based algorithms presented in this paper are novel nonlinear filtering methods that perform better than traditional methods such as the EKF     

A Divergence Minimization Approach to Joint Multiuser Decoding for Coded CDMA

In this paper, a theoretical framework of divergence minimization (DM) is applied to derive iterative receiver algorithms for coded CDMA systems. The DM receiver obtained performs joint channel estimation, multiuser decoding, and noise- covariance estimation. While its structure is similar to that of many ad-hoc receivers in the literature, the DM receiver is the result of applying a formal framework for optimization without further simplifications, namely the DM approach with a factorizable auxiliary model distribution. The well-known expectation- maximization (EM) algorithm and space-alternating generalized expectation-maximization (SAGE) algorithm are special cases of degenerate model distributions within the DM framework. Furthermore, many ad-hoc receiver structures from literature are shown to represent approximations of the proposed DM receiver. The DM receiver has four interesting properties that all result directly from applying the formal framework: (i) The covariances of all estimates involved are taken into account, (ii) The residual interference after interference cancellation is handled by the noise-covariance estimation as opposed to by LMMSE filters in other receivers, (iii) Posterior probabilities of the code symbols are employed rather than extrinsic probabilities, (iv) The iterative receiver is guaranteed to converge in divergence. The theoretical insights are illustrated by simulation results.     

On parameter estimation in long-code DS/CDMA systems: Cramer-Rao bounds and least-squares algorithms

The problem of parameter estimation in direct-sequence code division multiple access (DS/CDMA) systems employing long (aperiodic) spreading codes is considered. In particular, for an asynchronous network, the problem of estimating the amplitudes, phase offsets, propagation delays, and directions of arrival (DoAs) for the CDMA signals transmitted by the active users is examined. First, formulas are provided for the Cramer-Rao bound (CRB) on the error variance of any joint multiuser parameter estimation procedure exploiting a known training sequence. Further, least-squares adaptive algorithms are derived, which, based on the transmission of known pilot symbols, enable adaptive estimation of the parameters with a computational complexity that is only quadratic in the processing gain. In particular, the cases where either the parameters from all of the active users are to be estimated, or the relevant parameters of only one user are to be acquired (based on the knowledge of its spreading code and training sequence only), are considered. This study is completed by an analysis of the convergence properties of the proposed adaptive algorithms and by extensive computer simulation results illustrating the performance of the estimation procedures, also in comparison with the CRB, and the impact of the estimation errors on the performance of the linear minimum mean square error (LMMSE) multiuser detector.     

Estimation of fuzzy Gaussian mixture and unsupervised statisticalimage segmentation

This paper addresses the estimation of fuzzy Gaussian distribution mixture with applications to unsupervised statistical fuzzy image segmentation. In a general way, the fuzzy approach enriches the current statistical models by adding a fuzzy class, which has several interpretations in signal processing. One such interpretation in image segmentation is the simultaneous appearance of several thematic classes on the same site. We introduce a new procedure for estimating of fuzzy mixtures, which is an adaptation of the iterative conditional estimation (ICE) algorithm to the fuzzy framework, We first describe the blind estimation, i.e., without taking into account any spatial information, valid in any context of independent noisy observations. Then we introduce, in a manner analogous to classical hard segmentation, the spatial information by two different approaches: contextual segmentation and adaptive blind segmentation. In the first case, the spatial information is taken into account at the segmentation step level, and in the second case it is taken into account at the parameter estimation step level. The results obtained with the iterative conditional estimation algorithm are compared to those obtained with expectation-maximization (EM) and the stochastic EM algorithms, on both parameter estimation and unsupervised segmentation levels, via simulations. The methods proposed appear as complementary to the fuzzy C-means algorithms.     

基于正则化约束总体最小二乘的单站DOA-TDOA无源定位算法

针对利用单站外辐射源的目标无源定位问题,该文提出一种联合到达角度和时差信息的正则化约束总体最小二乘(RCTLS)定位算法。首先,将非线性的到达角度和时差的观测方程进行线性化处理,分析了方程系数矩阵可能出现的病态问题,将定位问题建立为RCTLS模型,并采用牛顿迭代方法对模型求解,从而得到目标位置估计。最后,推导了算法的理论误差,并按照均方误差最小的原则推导了正则化参数的最优值。仿真结果表明,算法的定位精度和鲁棒性均优于约束总体最小二乘(CTLS)算法。此外,对系统几何精度因子图的分析表明,目标及外辐射源的位置对定位精度也有影响。