Non-local total bounded variation scheme for multiple-coil magnetic resonance image restoration

In this paper, we design a variational model for restoring multiple-coil magnetic resonance images (MRI) corrupted by non-central Chi distributed noise. The energy functional corresponding to the restoration problem is derived using the maximum a posteriori (MAP) estimator. Optimizing this functional yields the solution, which corresponds to the restored version of the image. The non-local total bounded variation prior is being used as the regularization term in the functional derived using the MAP estimation process. Further, the split-Bregman iteration scheme is being followed for fast numerical computation of the model. The results are compared with the state of the art MRI restoration models using visual representations and statistical measures.     

基于噪声分布特性的压缩视频超分辨率重建

该文通过对视频压缩过程进行建模,利用比特流中的量化信息和运动信息,建立了量化噪声和运动估计噪声模型,并考虑成像过程的加性噪声,总的噪声模型对不同的量化器可自适应调整。以Huber-Markov 随机场作为图像的先验模型,用梯度下降法进行MAP超分辨率重建,对其特性进行了分析。仿真实验表明,该算法重建图像的主、客观质量较高。     

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.     

泊松噪声模糊图像的边缘保持变分复原算法

从贝叶斯估计出发,构造了一种新的变分模型,用于复原被泊松噪声污染的模糊图像.首先讨论了模型正则化项中具有边缘保持能力的函数选取以及模型求解的相关问题,然后将变分模型的求解转化为可快速求解的非线性扩散方程,给出了正则化参数选取的初步空间自适应方法,可以区分平滑区域和图像边缘自适应的调节参数.实验结果表明,本文方法的复原效果整体上优于传统的迭代正则化方法,复原图像的边缘得到了有效的保护,泊松噪声的抑制效果明显,复原图像提高的改进信噪比(ISNR)要比迭代正则化方法平均提高1 dB以上.     

A MAP-Based Algorithm for Destriping and Inpainting of Remotely Sensed Images

Remotely sensed images often suffer from the common problems of stripe noise and random dead pixels. The techniques to recover a good image from the contaminated one are called image destriping (for stripes) and image inpainting (for dead pixels). This paper presents a maximum a posteriori (MAP)-based algorithm for both destriping and inpainting problems. The main advantage of this algorithm is that it can constrain the solution space according to a priori knowledge during the destriping and inpainting processes. In the MAP framework, the likelihood probability density function (PDF) is constructed based on a linear image observation model, and a robust Huber-Markov model is used as the prior PDF. The gradient descent optimization method is employed to produce the desired image. The proposed algorithm has been tested using moderate resolution imaging spectrometer images for destriping and China-Brazil Earth Resource Satellite and QuickBird images for simulated inpainting. The experiment results and quantitative analyses verify the efficacy of this algorithm.     

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.     

基于修正最小平方中值定理的鲁棒运动估计

基于修正的最小平方中值定理（ＬＭｅｄＳ），本文提出一种由３Ｄ特征点空间位置估计运动参数的鲁棒方法，首先由ＬＭｅｄＳ给出初始的运动参数估计，然后采用迭代加权估计方法重新计算运动参数，其中一种Ｔｕｋｅｙ权和Ｈｕｂｅｒ权的混合权函数代替原ＬＭｅｄＳ的二分权函数，该算法减轻了当信噪比较低的情况下删除一些出格点的困难，故可得到更好的估计精度，计算机模拟表明其性能令人满意。     

一种新的基于CV模型的图像分割算法

CV模型是一种重要的图像分割模型,本文针对其收敛速度慢、效率低的缺点提出一种求解CV模型的新方法。首先将CV模型的能量泛函改写成与原来有相同稳定解的总变分公式形式,然后使用对偶公式法求总变分公式的极小值,再在其中引入一速度项以加快模型的收敛速度。新方法一方面克服了梯度下降法要求时间步长小、迭代次数多的缺点,经过较少次的迭代就能收敛,减少了迭代计算的次数;另一方面,引入的速度项能够减少每次迭代的时间,从而缩短求解模型的时间。速度项的引入同时减少了对梯度的依赖,增强了抗噪性。另外,可以通过调节速度项得到不同数目的同质区域,以适应相同图像不同分割任务的需求。实验结果表明本文方法是有效的。      

Bi-directional LSTM based channel estimation in 5G massive MIMO OFDM systems over TDL-C model with Rayleigh fading distribution

In this work, a deep learning (DL)-based massive multiple-input multiple-output (mMIMO) orthogonal frequency division multiplexing (OFDM) system is investigated over the tapped delay line type C (TDL-C) model with a Rayleigh fading distribution at frequencies ranging from 0.5 to 100 GHz. The proposed bi-directional long short-term memory (Bi-LSTM) channel state information (CSI) estimator uses online learning during training and offline learning during the practical implementation phase. The design of the estimator takes into account situations in which prior knowledge of channel statistics is limited and targets excellent performance, even with limited pilot symbols (PS). Three separate loss functions (mean square logarithmic error [MSLE], Huber, and Kullback–Leibler Distance [KLD]) are assessed in three classification layers. The symbol error rate (SER) and outage probability performance of the proposed estimator are evaluated using a number of optimization techniques, such as stochastic gradient descent (SGD), momentum, and the adaptive gradient (AdaGrad) algorithm. The Bi-LSTM-based CSI estimator is trained considering a specific number of PS. It can be readily seen that by incorporating a cyclic prefix (CP), the system becomes more resilient to channel impairments, resulting in a lower SER. Simulations show that the SGD optimization approach and Huber loss function-trained Bi-LSTM-based CSI estimator have the lowest SER and very high estimation accuracy. By using deep neural networks (DNNs), the Bi-LSTM method for CSI estimation achieves a superior channel capacity (in bps/Hz) at 10 dB than long short-term memory (LSTM) and other conventional CSI estimators, such as minimum mean square error (MMSE) and least squares (LS). The simulation results validate the analytical results in the study.     

Terra MODIS第5波段红外遥感影像条带噪声的探测与校正

由于Terra MODIS传感器第5波段（1.230~1.250 m）中部分探测元件出现故障,从而导致整幅影像上存在明显的条带噪声。对于地理校正后的MODIS影像数据,其条带噪声的分布并不是完全规则的,还可能存在不连续的现象,加大了对噪声进行处理的难度。提出一种对条带噪声进行检测与去除的方法,首先利用局部梯度对条带噪声的位置进行探测。然后在基于最大后验概率的框架下结合噪声模型与Huber-Markov先验,并通过梯度下降算法进行噪声的去除。使用真实的遥感数据进行了实验,所展示的恢复后数据和对应的频谱图都证明了文中方法的有效性。     

Robust Huber adaptive filter

Classical filtering methods are not optimal when the statistics of the signals violate the underlying assumptions behind the theoretical development. Most of the classical filtering theory like least-squares filtering assumes Gaussianity as its underlying distribution. We present a new adaptive filter that is optimal in the presence of Gaussian noise and robust to outliers. This novel robust adaptive filter minimizes the Huber objective function. An estimator based on the Huber objective function behaves as an L₁ norm estimator for large residual errors and as an L₂ norm estimator for small residual errors. Simulation results show the improved performance of the Huber adaptive filter (configured as a line enhancer) over various nonlinear filters in the presence of impulsive noise and Gaussian noise     

Joint-MAP Bayesian tomographic reconstruction with a gamma-mixture prior

We address the problem of Bayesian image reconstruction with a prior that captures the notion of a clustered intensity histogram. The problem is formulated in the framework of a joint-MAP (maximum a posteriori) estimation with the prior PDF modeled as a mixture-of-gammas density. This prior PDF has appealing properties, including positivity enforcement. The joint MAP optimization is carried out as an iterative alternating descent wherein a regularized likelihood estimate is followed by a mixture decomposition of the histogram of the current tomographic image estimate. The mixture decomposition step estimates the hyperparameters of the prior PDF. The objective functions associated with the joint MAP estimation are complicated and difficult to optimize, but we show how they may be transformed to allow for much easier optimization while preserving the fixed point of the iterations. We demonstrate the method in the context of medical emission and transmission tomography.     

Exact distribution of edge-preserving MAP estimators for linearsignal models with Gaussian measurement noise

We derive the exact statistical distribution of maximum a posteriori (MAP) estimators having edge-preserving nonGaussian priors. Such estimators have been widely advocated for image restoration and reconstruction problems. Previous investigations of these image recovery methods have been primarily empirical; the distribution we derive enables theoretical analysis. The signal model is linear with Gaussian measurement noise. We assume that the energy function of the prior distribution is chosen to ensure a unimodal posterior distribution (for which convexity of the energy function is sufficient), and that the energy function satisfies a uniform Lipschitz regularity condition. The regularity conditions are sufficiently general to encompass popular priors such as the generalized Gaussian Markov random field prior and the Huber prior, even though those priors are not everywhere twice continuously differentiable.     

On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering.

In this paper, we focus on the problem of speckle removal by means of anisotropic diffusion and, specifically, on the importance of the correct estimation of the statistics involved. First, we derive an anisotropic diffusion filter that does not depend on a linear approximation of the speckle model assumed, which is the case of a previously reported filter, namely, SRAD. Then, we focus on the problem of estimation of the coefficient of variation of both signal and noise and of noise itself. Our experiments indicate that neighborhoods used for parameter estimation do not need to coincide with those used in the diffusion equations. Then, we show that, as long as the estimates are good enough, the filter proposed here and the SRAD perform fairly closely, a fact that emphasizes the importance of the correct estimation of the coefficients of variation.     

Variational Bayesian Blind Deconvolution Using a Total Variation Prior

In this paper, we present novel algorithms for total variation (TV) based blind deconvolution and parameter estimation utilizing a variational framework. Using a hierarchical Bayesian model, the unknown image, blur, and hyperparameters for the image, blur, and noise priors are estimated simultaneously. A variational inference approach is utilized so that approximations of the posterior distributions of the unknowns are obtained, thus providing a measure of the uncertainty of the estimates. Experimental results demonstrate that the proposed approaches provide higher restoration performance than non-TV-based methods without any assumptions about the unknown hyperparameters.      

Performance study of the minimax robust phased array for wireless communications

In this paper, new robust M-estimation techniques are developed for combating impulsive noise and multiple-access interference in communication systems. Power functions of the proposed robust estimators are obtained by minimizing a nonquadratic residual function derived from the Huber's minimax robust estimation theory. Maximum peaks of these power functions are used for estimation of communication signals as well as direction of arrival. A strong advantage of the proposed robust M-estimation algorithms is a decreased sensitivity of the estimates with respect to an actual unknown distribution of random noises and interferences. Simulation results demonstrate that the proposed robust algorithms, the robust median, and robust Huber estimators, offer significant performance gain over the conventional and minimum-variance distortionless-response estimators, with the best results given by the robust Huber estimator.     

A combined order selection and parameter estimation algorithm forundamped exponentials

We propose an approximate maximum likelihood parameter estimation algorithm, combined with a model order estimator for superimposed undamped exponentials in noise. The algorithm combines the robustness of Fourier-based estimators and the high-resolution capabilities of parametric methods. We use a combination of a Wald (1945) statistic and a MAP test for order selection and initialize an iterative maximum likelihood descent algorithm recursively based on estimates at higher candidate model orders. Experiments using simulated data and synthetic radar data demonstrate improved performance over MDL, MAP, and AIC in places of practical interest     

First-order fusion of volumetric medical imagery

A novel fusion scheme for volumetric medical imagery based on first-order local variational information is presented. The authors first define the contrast of a volumetric image with an arbitrary number of bands, which corresponds with the 3D gradient in the special case of a single-band image with a Euclidean metric. This contrast of multi-band image is regarded as the target contrast field. The next step is to look for a single-band volumetric image as the fusion result, which will have the closest gradient field to the contrast of the input multi-band image. It is a functional extremum problem. Using the variational approach, it leads directly to its Euler-Lagrange equation. By iteration of gradient descent, the final result can be obtained. Experimental results are presented to support the performance of the method.     

A robust auto‐adaptive approach for serial acquisition of generalized multi‐carrier spread spectrum in multipath fading mobile channels

In this paper, a new robust auto‐adaptive approach for pseudo‐noise (PN) code acquisition is proposed. It is applied to the generalized multi‐carrier direct‐sequence code‐division multiple‐access (MC DS‐CDMA) systems communicating over frequency‐selective multipath Rayleigh fading channels. This new approach is based on the constant false alarm rate (CFAR) detection algorithm, referred here as automatic selection partial sum ordered statistics (ASPSOS)‐CFAR. The proposed approach does not require any prior information about the background environment and uses maximum likelihood estimation (MLE) method to detect the interfering signals group in the ranked cells for the full reference window. Once this group is identified and censored, the remaining smaller ranked cells are combined to form an estimate of the background noise level to compute the adaptive threshold. Through simulations, the performance of the proposed detector is analyzed and compared with traditional CFAR detectors based on fixed or automatic censoring algorithms. The obtained results show that the proposed detector eliminates the drawbacks of the previously related detectors and offers a robust detection performance to enhance the acquisition process in heterogeneous background environments.     

Robust Competitive Estimation With Signal and Noise Covariance Uncertainties

Robust estimation of a random vector in a linear model in the presence of model uncertainties has been studied in several recent works. While previous methods considered the case in which the uncertainty is in the signal covariance, and possibly the model matrix, but the noise covariance is assumed to be completely specified, here we extend the results to the case where the noise statistics may also be subjected to uncertainties. We propose several different approaches to robust estimation, which differ in their assumptions on the given statistics. In the first method, we assume that the model matrix and both the signal and the noise covariance matrices are uncertain, and develop a minimax mean-squared error (MSE) estimator that minimizes the worst case MSE in the region of uncertainty. The second strategy assumes that the model matrix is given and tries to uniformly approach the performance of the linear minimum MSE estimator that knows the signal and noise covariances by minimizing a worst case regret measure. The regret is defined as the difference or ratio between the MSE attainable using a linear estimator, ignorant of the signal and noise covariances, and the minimum MSE possible when the statistics are known. As we show, earlier solutions follow directly from our more general results. However, the approach taken here in developing the robust estimators is considerably simpler than previous methods