Simultaneous iterative image restoration and evaluation of theregularization parameter

A nonlinear regularized iterative image restoration algorithm is proposed, according to which only the noise variance is assumed to be known in advance. The algorithm results from a set theoretic regularization approach, where a bound of the stabilizing functional, and therefore the regularization parameter, are updated at each iteration step. Sufficient conditions for the convergence of the algorithm are derived and experimental results are shown     

Regularized adaptive high-resolution image reconstruction considering inaccurate subpixel registration

We propose a high-resolution image reconstruction algorithm considering inaccurate subpixel registration. A regularized iterative reconstruction algorithm is adopted to overcome the ill-posedness problem resulting from inaccurate subpixel registration. In particular, we use multichannel image reconstruction algorithms suitable for applications with multiframe environments. Since the registration error in each low-resolution image has a different pattern, the regularization parameters are determined adaptively for each channel. We propose two methods for estimating the regularization parameter automatically. The proposed algorithms are robust against registration error noise, and they do not require any prior information about the original image or the registration error process. Information needed to determine the regularization parameter and to reconstruct the image is updated at each iteration step based on the available partially reconstructed image. Experimental results indicate that the proposed algorithms outperform conventional approaches in terms of both objective measurements and visual evaluation.     

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.     

基于Poisson-Markov场的超分辨力图像复原算法

图像的超分辨力复原和信噪比的提高是图像复原追求的目标.Poisson-ML图像复原方法(PML)具有很强的超分辨力复原能力,但在复原过程中会产生振荡条纹且对带噪较大的图像不能取得理想的复原效果.在Poisson和Markov分布假设的基础上,提出基于Poisson-Markov场的超分辨力图像复原算法及其正则化参数的自适应选择方法(MPML).实验表明,MPML算法不但具有很好的超分辨力复原能力,而且能有效减少和去除复原图像中的振荡条纹,对于带噪较大的图像也能取得理想的复原效果,因此其图像复原质量明显好于PML算法.正则化参数能被自动优化地选择且与图像复原的迭代运算同步进行.     

二阶Hopfield型神经网络的稳定性 分析及收敛速度的估计

本文讨论二阶连续Hopfield型神经网络平衡点的全局稳定性问题,利用LMI方法和Lyapunov方法得到了网络平衡点全局渐近稳定和全局指数稳定的几个充分条件,并对其指数收敛速度进行了估计.     

SAR图像目标超分辨的变范数正则化算法

 基于正则化变分的框架,提出了SAR图像目标超分辨的变范数算法.考虑目标在成像区域中的稀疏特性,利用广义高斯分布对目标区域的幅度进行建模,在Bayes估计的框架下,推导了l_p范数约束的正则化变分模型和广义高斯分布形状参数的关系.采用迭代的方法在逐次估计真实图像的过程中,将p的取值与逐次估计结果相关联,逐步估计目标区域分布的形状参数,并修正l_p范数的具体形式,由此得到变范数的正则化模型.该方法克服了通过经验选取p值的局限,以及由观测数据估计p值的误差.仿真和实测SAR图像的处理结果表明了该方法的有效性.     

基于残差图像的迭代终止条件及其在NCSR算法中的应用

现有图像去模糊(deblurring)算法多依赖于 正则化技术以迭代逼近求解最优目标函数 方式实现关于原图像的最佳估计,由于缺乏迭代终止判定条件(ITC),这些算法通常采用固 定迭代 次数实现以至执行效率不高,同时所获得图像的质量在很多时候也未必是最佳的。鉴于在迭 代过程中每一步所获得的中间估计图像经与模糊核卷积后和模糊图像之间残差图像的亮度 值具有显著的高斯分布特点,提出使用广义高斯分布(GGD)模型为迭代过程中的残差图像建 模并以GGD模型参数值作为衡量去模糊效果的度量 (DM,deblurring measure)。基于DM,在保障去模糊图像质量的前提下,设计了ITC自适应 地终止迭代过程以提高去模糊算法的计算 效率。在经典的非局部集中稀疏表示(NCSR,nonlocally centralized sparse representat ion)去模糊算法上完成的大量 的实验表明,对于运动、高斯和失焦3种典型的模糊失真,新提出的ITC能 够有效判定在每一步迭代过程中所获得的估计图像是否已达到最佳的图像质量,从而实现 在保障去模糊图像质量的前提下大幅度提高NCSR算法计算效率的目的。所提出的ITC判定方 法具有普适性,调整相关参数后也可以应用于其它迭代型的去模糊算法。     

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     

一种新的正规自适应边缘保护的超分辨率算法

主要提出了一个新的正规自适应超分辨率算法.正规项只惩罚图像中可能包含有大量噪声的低频部分,同时保护图像中可能包含有锐利边缘的高频部分,其中,惩罚阈值自动地被一个线性函数决定.对于正规参数的选择,这里不采用固定的正规参数而是提出一个对数函数在每次迭代时自适应地选择正规参数.该算法经过仿真实验和真实的红外图像测试,实验结果显示该算法鲁棒性好,可以有效复原图像细节.     

A restoration–segmentation algorithm based on flexible Arnoldi–Tikhonov method and Curvelet denoising

In this paper, we illustrate a two-stage algorithm consisting of restoration and segmentation to reach binary segmentation from the noisy and blurry image. The results of our method can be applied in main fields of the image processing such as object extraction. In the first stage, we have a linear discrete ill-posed problem with a noise-contaminated right-hand side, arising from the image restoration. We consider problems in which the coefficient matrix is the sum of Kronecker products of matrices and present a global flexible Arnoldi–Tikhonov method coupled with the generalized cross-validation for the computation of the regularization parameter at each iteration. The proposed algorithm is based on the global Arnoldi method that allows using a more flexible solution subspace. In the second stage, we segment the restored image in order to reach a binary image in which the target object is emphasized. In our segmentation method, we use Gaussian scale-space technique to compute discrete gradients of the restored image for pre-segmenting. Also, in order to denoise, we use a tight frame of Curvelet transforms and thresholding which is based on the principle obtained by minimizing Stein’s unbiased risk estimate. This algorithm has an iterative part based on the iterative part of TFA (Cai et al. in SIAM J Imaging 6(1):464–486, 2013), but we use eigenvectors of Hessian matrix of image for improving this part. Theoretical properties of the method of both stages and numerical experiments are presented.     

基于粒子群优化的正则化水下图像盲复原

水下图像恢复的难点在于缺少海水的点扩展函数的足够信息,而导致病态的问题.为了提高水下激光成像系统的成像质量,提出了用粒子群优化正则化参量的盲图像复原算法.该方法结合Tikhonov正则化和改进的全变分正则化的技术特点,使用一种交替迭代方法,分别估计点扩展函数和估计复原图像,同时用粒子群算法优化正则化参量.结果表明,该方法对水下图像复原具有较好的鲁棒性,算法收敛稳定.     

基于TwIST-TV 约束的图像去模糊方法

传统的基于频域和小波域的去模糊算法所得的复原图像总是存在比较明显的边缘振铃及模糊效应,而较为有效的空域迭代优化去模糊算法速度通常比较慢。为了解决上述问题,提出了基于二步迭代阈值收缩（TwIST）与总变分（TV）约束相结合的图像去模糊算法（TwIST-TV）。首先在去模糊目标函数中加入对图像的TV 正则化约束,其次在对图像小波系数的每次二步迭代之前,加入对图像的TV 优化去噪约束,最后迭代获取去模糊图像。实验结果表明:相对于基于频域和小波域的模糊图像恢复算法,TwIST-TV 能有效抑制边缘模糊和振铃效应,复原图像的信噪比（SNR）、峰值信噪比（PSNR）高出1~7 dB,平均结构相似度指标（MSSIM）可高出0.05,相对于空域解卷积算法在保证求解精度相当的情况下具备6 倍以上的速度优势。     

Novel cooperative neural fusion algorithms for image restoration and image fusion.

To deal with the problem of restoring degraded images with non-Gaussian noise, this paper proposes a novel cooperative neural fusion regularization (CNFR) algorithm for image restoration. Compared with conventional regularization algorithms for image restoration, the proposed CNFR algorithm can relax need of the optimal regularization parameter to be estimated. Furthermore, to enhance the quality of restored images, this paper presents a cooperative neural fusion (CNF) algorithm for image fusion. Compared with existing signal-level image fusion algorithms, the proposed CNF algorithm can greatly reduce the loss of contrast information under blind Gaussian noise environments. The performance analysis shows that the proposed two neural fusion algorithms can converge globally to the robust and optimal image estimate. Simulation results confirm that in different noise environments, the proposed two neural fusion algorithms can obtain a better image estimate than several well known image restoration and image fusion methods.     

基于噪声与图像同步迭代来确定时间步进法的规整化参数

为了在反卷积过程中正确地估计噪声的方差,该文构造一幅纯噪声图像跟实际的观测图像同步进行反卷积计算,并把纯噪声图像的方差作为观测图像中噪声方差的估计值来辅助计算规整化参数。针对规整化的各项异性,该文提出了能够保持两种噪声同步变化的特殊的规整化项。新的规整化项在迭代纯粹噪声图像时使用,这样确保每次迭代都可以保持人工噪声与实际图像噪声的统计特性相一致。在能够准确知道迭代过程中图像包含噪声的方差的时候,该文建立了规整化参数与图像噪声方差之间的关系式并转化成简单的解一元二次方程问题。实验证明新的算法不但更好地抑制了噪声而且避免了过平滑,基于时间步进法计算变分图像恢复的适应性被明显的提高了。     

A Gaussian Mixture Model-based regularization method in adaptive image restoration

A GMM （Gaussian Mixture Model） based adaptive image restoration is proposed in this paper. The feature vectors of pixels are selected and extracted. Pixels are clustered into smooth, edge or detail texture region according to variance-sum criteria function of the feature vectors. Then parameters of GMM are calculated by using the statistical information of these feature vectors. GMM predicts the regularization parameter for each pixel adaptively. Hopfield Neural Network （Hopfield-NN） is used to optimize the objective function of image restoration, and network weight value matrix is updated by the output of GMM. Since GMM is used, the regularization parameters share properties of different kind of regions. In addition, the regularization parameters are different from pixel to pixel. GMM-based regularization method is consistent with human visual system, and it has strong generalization capability. Comparing with non-adaptive and some adaptive image restoration algorithms, experimental results show that the proposed algorithm obtains more preferable restored images.     

带总观测误差约束的模糊图像恢复

模糊图像恢复是数字图像处理领域的研究热点之一,总变差(Total Variation, TV)规整化可以很好的保持图像的细节,然而,传统的TV图像恢复模型需要考虑最优的正则化参数,由此,提出了一族包含不同规整化因子,带总观测误差约束的模糊图像恢复模型,并分为去模糊和去噪两步求解此模型。在去模糊过程中,利用共轭梯度法求出一个满足总观测误差约束的初始恢复图像;在去噪过程中,首先,以去模糊的结果作为初始估计;其次,针对 范数最小化问题,利用优化—最小化(Majoriziation-Minimization, MM)算法的思想,将原问题转化为一系列容易求解的优化子问题;最后,极小化优化子问题,得到最终的恢复图像。实验结果表明,该算法对模糊图像的恢复效果是显著地。      

Noninvasive myocardial activation time imaging: a novel inverse algorithm applied to clinical ECG mapping data

Linear approaches like the minimum-norm least-square algorithm show insufficient performance when it comes to estimating the activation time map on the surface of the heart from electrocardiographic (ECG) mapping data. Additional regularization has to be considered leading to a nonlinear problem formulation. The Gauss-Newton approach is one of the standard mathematical tools capable of solving this kind of problem. To our experience, this algorithm has specific drawbacks which are caused by the applied regularization procedure. In particular, under clinical conditions the amount of regularization cannot be determined clearly. For this reason, we have developed an iterative algorithm solving this nonlinear problem by a sequence of regularized linear problems. At each step of iteration, an individual L-curve is computed. Subsequent iteration steps are performed with the individual optimal regularization parameter. This novel approach is compared with the standard Gauss-Newton approach. Both methods are applied to simulated ECG mapping data as well as to single beat sinus rhythm data from two patients recorded in the catheter laboratory. The proposed approach shows excellent numerical and computational performance, even under clinical conditions at which the Gauss-Newton approach begins to break down.     

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.     

Hopfield neural network based algorithms for image restoration andreconstruction. II. Performance analysis

For pt. I see ibid., vol.48, no.7, p.2105-18 (2000). In this paper, we analyze four typical sequential Hopfield (1982) neural network (HNN) based algorithms for image restoration and reconstruction, which are the modified HNN (PK) algorithm, the HNN (ZCVJ) algorithm with energy checking, the eliminating-highest-error (EHE) algorithm, and the simulated annealing (SA) algorithm. A new measure, the correct transition probability (CTP), is proposed for the performance of iterative algorithms and is used in this analysis. The CTP measures the correct transition probability for a neuron transition at a particular time and reveals the insight of the performance at each iteration. The general properties of the CTP are discussed. Derived are the CTP formulas of these four algorithms. The analysis shows that the EHE algorithm has the highest CTP in all conditions of the severity of blurring, the signal-to-noise ratio (SNR) of a blurred noisy image, and the regularization term. This confirms the result in many previous simulations that the EHE algorithms can converge to more accurate images with much fewer iterations, have much higher correct transition rates than other HNN algorithms, and suppress streaks in restored images. The analysis also shows that the CTPs of all these algorithms decrease with the severity of blurring, the severity of noise, and the degree of regularization, which also confirms the results in previous simulations. This in return suggests that the correct transition probability be a rational performance measure