Generalized maximum a posteriori processing of multichannel images and applications

This paper considers several aspects of robust estimation in the restoration of mutichannel images. Robust functionals emerging from a generalized maximum a posteriori (MAP) approach are employed for the representation of both the noise and the signal statistics. Several linear multichannel techniques can be derived as special cases of the approach presented. In addition, the robust approach derives nonlinear algorithms that simultaneously account for the suppression of nominal noise and outliers, and for the efficient reconstruction of sharp detailed structure in the estimate. The robust multichannel approach is presented as a general approach for the regularization of the ill-posed restoration problem. From this perspective, we develop a method for the selection of the regularization parameter, which can be used in a wide variety of applications that may or may not involve noise outliers. We consider several issues associated with the application of robust algorithms to multichannel images, we discuss computational inefficiencies of such algorithms, and we propose approximations that are appropriate for their cost-efficient multichannel implementation. We demonstrate the robust approach in two examples from the rapidly developing fields of color image processing and multiresolution image processing in the wavelet domain.The research presented in this paper was partially supported by the Graduate School of the University of Minnesota under Summer Research Fellowship no. 15556 and Grant-in-Aid Award no. 15987.     

Design of a new restoration algorithm based on the constrained mean-square-error criterion

In this paper the joint optimization of different criteria is addressed, as a powerful means of incorporatinga priori information in linear image-restoration algorithms. Theconstrained mean-square-error (CMSE) approach is introduced, which enables the incorporation of both spatial and spectral information regarding the peculiarities of the problem. Depending on the nature of the spatial information, this approach can be interpreted as either a regularized or an adaptive scheme. As a regularized scheme, it offers an alternative to conventional approaches, in which the ringing artifacts are efficiently suppressed by means of the regularizing operator. As an adaptive scheme, the CMSE approach offers the flexibility of applying either linear Wiener filtering or inverse filtering, depending on the local signal activity. Optimal techniques for the selection of the regularization parameter in both nonadaptive and adaptive cases are introduced. The capabilities of the CMSE approach as a regularized scheme and an adaptive scheme, are demonstrated through restoration examples.     

Efficient Huber-Markov edge-preserving image restoration.

The regularization of the least-squares criterion is an effective approach in image restoration to reduce noise amplification. To avoid the smoothing of edges, edge-preserving regularization using a Gaussian Markov random field (GMRF) model is often used to allow realistic edge modeling and provide stable maximum a posteriori (MAP) solutions. However, this approach is computationally demanding because the introduction of a non-Gaussian image prior makes the restoration problem shift-variant. In this case, a direct solution using fast Fourier transforms (FFTs) is not possible, even when the blurring is shift-invariant. We consider a class of edge-preserving GMRF functions that are convex and have nonquadratic regions that impose less smoothing on edges. We propose a decomposition-enabled edge-preserving image restoration algorithm for maximizing the likelihood function. By decomposing the problem into two subproblems, with one shift-invariant and the other shift-variant, our algorithm exploits the sparsity of edges to define an FFT-based iteration that requires few iterations and is guaranteed to converge to the MAP estimate.     

偏差补偿比例互相关熵算法

为了解决输入信号含有噪声和非高斯输出噪声的稀疏系统辨识问题,本文提出一种偏差补偿比例更新互相关熵算法。基于互相关熵的自适应滤波算法可以消除非高斯噪声的影响, 进一步应用无偏准则来解决含噪输入信号带来的估计偏差问题。另外,将比例更新机制引入算法,通过自适应调节步长参数以增强算法的跟踪性能。仿真结果表明所提算法对于输入信号受噪声干扰和非高斯输出噪声环境下的稀疏系统辨识问题具有强的鲁棒性和稳态性能。      

Signal separation by symmetric adaptive decorrelation: stability,convergence, and uniqueness

The performance of signal enhancement systems based on adaptive filtering is highly dependent on the quality of the noise reference. In the LMS algorithm, signal leakage into the noise reference leads to signal distortion and poor noise cancellation. The origin of the problem lies in the fact that LMS decorrelates the signal estimate with the noise reference, which, in the case of signal leakage, makes little sense. An algorithm is proposed that decorrelates the signal estimate with a “signal-free” noise estimate, obtained by adding a symmetric filter to the classical structure. The symmetric adaptive decorrelation (SAD) algorithm no longer makes a distinction between signal and noise and is therefore a signal separator rather than a noise canceler. Stability and convergence are of the utmost importance in adaptive algorithms and hence are carefully studied. Apart from limitations on the adaptation constants, stability around the desired solution can only be guaranteed for a subclass of signal mixtures. Furthermore, the decorrelation criterion does not yield a unique solution, and expressions for the “phantom” solutions are derived. Simulations with short FIR filters confirm the predicted behavior     

Multichannel blind deconvolution of spatially misaligned images.

Existing multichannel blind restoration techniques assume perfect spatial alignment of channels, correct estimation of blur size, and are prone to noise. We developed an alternating minimization scheme based on a maximum a posteriori estimation with a priori distribution of blurs derived from the multichannel framework and a priori distribution of original images defined by the variational integral. This stochastic approach enables us to recover the blurs and the original image from channels severely corrupted by noise. We observe that the exact knowledge of the blur size is not necessary, and we prove that translation misregistration up to a certain extent can be automatically removed in the restoration process.     

基于Matlab平台的含噪图像恢复

根据噪声的先验特点，建立了基于Markov随机场的退化图像恢复模型，从而将图像的恢复问题转化为求解最大后验概率(MAP)的问题。本文以模拟退火算法的思想为基础，通过引入随机判据的方法代替退火过程来进行MAP的估计，实验结果证明了这种方法的有效性。     

A class of robust entropic functionals for image restoration

This paper considers the concept of robust estimation in regularized image restoration. Robust functionals are employed for the representation of both the noise and the signal statistics. Such functionals allow the efficient suppression of a wide variety of noise processes and permit the reconstruction of sharper edges than their quadratic counterparts. A new class of robust entropic functionals is introduced, which operates only on the high-frequency content of the signal and reflects sharp deviations in the signal distribution. This class of functionals can also incorporate prior structural information regarding the original image, in a way similar to the maximum information principle. The convergence properties of robust iterative algorithms are studied for continuously and noncontinuously differentiable functionals. The definition of the robust approach is completed by introducing a method for the optimal selection of the regularization parameter. This method utilizes the structure of robust estimators that lack analytic specification. The properties of robust algorithms are demonstrated through restoration examples in different noise environments.     

星载SAR斜视模式运动目标方位多通道信号重建方法

在星载方位多通道SAR斜视模式下,方位斜视角度和运动目标的速度分别导致回波多普勒频谱发生2次混叠和通道失衡,影响运动目标方位多通道信号重建。针对该问题,该文提出一种适用于多通道斜视模式下的运动目标的重建方法。首先通过方位向去斜预处理消除了斜视导致的2次多普勒混叠,然后通过修正的多通道重建矩阵来解决目标速度导致的通道失衡。此外,该文还研究了通道冗余情况下的杂波抑制能力,分析了估计速度误差带来的残余相位误差,给出了一种星载方位多通道SAR斜视模式下的运动目标速度快速估计搜索方法。最后,通过点目标仿真验证了方法的有效性。     

Adaptive multichannel filters for colour image processing

This paper addresses the problem of noise suppression for multichannel data, such as colour images. The proposed filters utilize adaptive data dependent nonparametric techniques. Simulation results indicate that the new filters suppress impulsive as well as Gaussian noise and preserve edges and details.     

Multichannel Linear Prediction and Maximum-Entropy Spectral Analysis Using Least Squares Modeling

Autoregressive data modeling using the least squares linearprediction method is generalized for multichannel time series. A recursive algorithm is obtained for the formation of the system of multichannel normal equations which determine the least squares solution of the multichannel linear-prediction problem. Solution of these multichannel normal equations is accomplished by the Cholesky factorization method. The corresponding multichannel maximum-entropy spectrum derived from these least squares estimates of the autoregressive-model parameters is compared to that obtained using parameters estimated by a multichannel generalization of Burg's algorithm. Numerical experiments have shown that the multichannel spectrum obtained by the least squares method provides for more accurate frequency determination for truncated sinusoids in the presence of additive white noise.     

A unified feature and instance selection framework using optimum experimental design

The goal of feature selection is to identify the most informative features for compact representation, whereas the goal of active learning is to select the most informative instances for prediction. Previous studies separately address these two problems, despite of the fact that selecting features and instances are dual operations over a data matrix. In this paper, we consider the novel problem of simultaneously selecting the most informative features and instances and develop a solution from the perspective of optimum experimental design. That is, by using the selected features as the new representation and the selected instances as training data, the variance of the parameter estimate of a learning function can be minimized. Specifically, we propose a novel approach, which is called Unified criterion for Feature and Instance selection (UFI), to simultaneously identify the most informative features and instances that minimize the trace of the parameter covariance matrix. A greedy algorithm is introduced to efficiently solve the optimization problem. Experimental results on two benchmark data sets demonstrate the effectiveness of our proposed method.     

Adaptive Volterra filters for active control of nonlinear noiseprocesses

This paper presents a Volterra filtered-X least mean square (LMS) algorithm for feedforward active noise control. The research has demonstrated that linear active noise control (ANC) systems can be successfully applied to reduce the broadband noise and narrowband noise, specifically, such linear ANC systems are very efficient in reduction of low-frequency noise. However, in some situations, the noise that comes from a dynamic system may he a nonlinear and deterministic noise process rather than a stochastic, white, or tonal noise process, and the primary noise at the canceling point may exhibit nonlinear distortion. Furthermore, the secondary path estimate in the ANC system, which denotes the transfer function between the secondary source (secondary speaker) and the error microphone, may have nonminimum phase, and hence, the causality constraint is violated. If such situations exist, the linear ANC system will suffer performance degradation. An implementation of a Volterra filtered-X LMS (VFXLMS) algorithm based on a multichannel structure is described for feedforward active noise control. Numerical simulation results show that the developed algorithm achieves performance improvement over the standard filtered-X LMS algorithm for the following two situations: (1) the reference noise is a nonlinear noise process, and at the same time, the secondary path estimate is of nonminimum phase; (2) the primary path exhibits the nonlinear behavior. In addition, the developed VFXLMS algorithm can also be employed as an alternative in the case where the standard filtered-X LMS algorithm does not perform well     

Pseudo-maximum-likelihood data estimation algorithm and itsapplication over band-limited channels

A pseudo-maximum-likelihood data estimation (PML) algorithm for discrete channels with finite memory in additive white Gaussian noise environment is developed. Unlike the traditional methods that utilize the Viterbi algorithm (VA) for data sequence estimation, the PML algorithm offers an alternative solution to the problem. The simplified PML algorithm is introduced to reduce the computational complexity of the PML algorithm for channels with long impulse response. The adaptive version of the PML algorithm suitable for time-varying channels such as frequency-selective Rayleigh fading channels is also introduced. Computer simulation results demonstrate the performance of these algorithms and compare them to the VA-based techniques for different types of channels. The performance design criterion for the PML algorithm is derived in the Appendix     

Fusion of magnetometer and gradiometer sensors of MEG in the presence of multiplicative error

Novel neuroimaging techniques have provided unprecedented information on the structure and function of the living human brain. Multimodal fusion of data from different sensors promises to radically improve this understanding, yet optimal methods have not been developed. Here, we demonstrate a novel method for combining multichannel signals. We show how this method can be used to fuse signals from the magnetometer and gradiometer sensors used in magnetoencephalography (MEG), and through extensive experiments using simulation, head phantom and real MEG data, show that it is both robust and accurate. This new approach works by assuming that the lead fields have multiplicative error. The criterion to estimate the error is given within a spatial filter framework such that the estimated power is minimized in the worst case scenario. The method is compared to, and found better than, existing approaches. The closed-form solution and the conditions under which the multiplicative error can be optimally estimated are provided. This novel approach can also be employed for multimodal fusion of other multichannel signals such as MEG and EEG. Although the multiplicative error is estimated based on beamforming, other methods for source analysis can equally be used after the lead-field modification.     

A regularized iterative image restoration algorithm

The development of the algorithm is based on a set theoretic approach to regularization. Deterministic and/or statistical information about the undistorted image and statistical information about the noise are directly incorporated into the iterative procedure. The restored image is the center of an ellipsoid bounding the intersection of two ellipsoids. The proposed algorithm, which has the constrained least squares algorithm as a special case, is extended into an adaptive iterative restoration algorithm. The spatial adaptivity is introduced to incorporate properties of the human visual system. Convergence of the proposed iterative algorithms is established. For the experimental results which are shown, the adaptively restored images have better quality than the nonadaptively restored ones based on visual observations and on an objective criterion of merit which accounts for the noise masking property of the visual system     

A rapid hybrid algorithm for image restoration combining parametric Wiener filtering and wave atom transform

Image restoration refers to removal or minimization of known degradations in an image. This includes de-blurring images degraded by the limitations of sensors or source of captures in addition to noise filtering and correction of geometric distortion due to sensors. There are several classical image restoration methods such as Wiener filtering. To find an estimate of the original image, Wiener filter requires the prior knowledge of the degradation phenomenon, the blurred image and the statistical properties of the noise process. In this work, we propose a new rapid and blind algorithm for image restoration that does not require a priori knowledge of the noise distribution. The degraded image is first de-convoluted in Fourier space by parametric Wiener filtering, and then, it is smoothed by the wave atom transform after setting the threshold to its coefficients. Experiment results are significant and show the efficiency of our algorithm compared with other techniques in use.     

Bayesian multichannel image restoration using compound Gauss-Markov random fields

We develop a multichannel image restoration algorithm using compound Gauss-Markov random fields (CGMRF) models. The line process in the CGMRF allows the channels to share important information regarding the objects present in the scene. In order to estimate the underlying multichannel image, two new iterative algorithms are presented and their convergence is established. They can be considered as extensions of the classical simulated annealing and iterative conditional methods. Experimental results with color images demonstrate the effectiveness of the proposed approaches.     

适应于图像复原的无参考图像质量评价方法

由于图像降质过程的复杂性、成像获取条件限制,以及图像本身的复杂性和图像复原过程的病态性,图像复原解大多都是近似的或畸变的,一种适应于图像复原质量评价的计算方法将大大提升图像复原的应用范围。针对图像复原过程的病态性,提出了一种针对图像复原图像质量评价的计算方法,该算法通过在图像质量算子中引入图像相似矩阵和图像复原趋势矩阵,使其能适应复原对于图像结构或噪声结构的变化。该图像质量评价算子计算无需参考图像,可以很好地反映图像的模糊程度和噪声程度,并且计算简单。实验证明了该图像质量评价算子的有效性。     

Color image noise removal algorithm utilizing hybrid vector filtering

This paper proposes a robust approach to color image noise removal that efficiently eliminates noisy pixels by exploiting several vector-class characteristics of multichannel pixels. This algorithm treats multichannel images as a vector class and takes both magnitude and phase angles of the pixel vectors into consideration. It consists of two steps: an efficient noise detector based on pixel vector angle statistics and impulse noise filtering with a hybrid of vector magnitude and vector angle function. Extensive experimental results demonstrate that the proposed approach significantly outperforms several other well-known techniques for color image noise removal.