模糊推理最大熵图像恢复算法

与线性恢复算法相比,基于最大熵的图像恢复算法具有更好的图像恢复效果,但其收敛速度较慢。为了提高最大熵图像恢复算法的收敛速度,首先给出了算法的非周期反卷积模型,然后采用模糊推理系统在线确定算法的迭代步长。由于采用了可变步长,因此极大地提高了算法的收敛速度。仿真实验表明提出的算法收敛速度快,图像恢复效果好。     

基于最小二乘增量迭代正则化方法的图像复原

针对模糊图像的复原问题,从最小二乘算法出发,采用增量迭代的方法改善算法的收敛性,同时结合正则化技术克服问题的病态性质,研究了一种有效的图像复原方法。在运算中,采用最速下降法求解方程,并运用快速傅立叶变换(FFT)原理来减少计算复杂度,同时引入自适应的正则化参数,使其与图像复原的迭代运算同步进行并自动修正到最优值。计算机仿真结果表明,该方法可较好地再现原图像的重要信息,复原图像在峰值信噪比和主观视觉效果方面都有明显的提高。     

一种空间自适应正则化图象盲复原算法

图象盲复原所面临的主要问题是可利用信息的不足，所以必须充分利用图象本身及成像系统的先验信息，为此，结合模糊先验辨识的思想，给出了一种新的空间自适应正则化算法，该算法先用交替最小化的迭代方法对模糊进行先验辨识，然后利用辨识结果，用各向异性扩散进行图象复原，算法充分利用了图象及成像系统（或点扩散函数PSF）的分段平滑特性，同时又利用各向异性扩散的概念，使得正则化不仅在程度上，而且在方向上都是空间自适应的，从而能够有效地进行图象盲复原，仿真结果表明，该算法的复原效果优于空间自适应各向同性正则化（SAR）算法，其收敛性能优于空间自适应各向异性正则化（SAAR）算法。     

图像复原的Bregman迭代双正则化方法

正则化图像复原最终会导致一个大规模优化问题,提出了一种基于Bregman迭代双正则化的图像复原方法。该方法中目标函数同时考虑总变分正则化和小波域稀疏正则化,在Bregman框架下解决图像复原问题,并且给出了用于解该问题的分裂Bregman迭代算法。该算法将复杂的优化问题转化为几十次简单的迭代加以解决,每次迭代只需几次快速傅里叶变换和收缩操作即可。实验结果表明,提出的复原算法不论从客观改善信噪比还是主观视觉,都能取得很好的效果。同时与目前的复原算法相比,该算法有更快的收敛速度。     

On the iterative refinement of the solution of ill-conditioned linear system of equations

Recently, Salkuyeh and Fahim [A new iterative refinement of the solution of ill-conditioned linear system of equations, Int. Comput. Math. 88(5) (2011), pp. 950–956] have proposed a two-step iterative refinement of the solution of an ill-conditioned linear system of equations. In this paper, we first present a generalized two-step iterative refinement procedure to solve ill-conditioned linear system of equations and study its convergence properties. Afterward, it is shown that the idea of an orthogonal projection technique together with a basic stationary iterative method can be utilized to construct a new efficient and neat hybrid algorithm for solving the mentioned problem. The convergence of the offered hybrid approach is also established. Numerical examples are examined to demonstrate the feasibility of proposed algorithms and their superiority to some of existing approaches for solving ill-conditioned linear system of equations.     

Blind image deconvolution via dispersion minimization

In linear image restoration, the point spread function of the degrading system is assumed known even though this information is usually not available in real applications. As a result, both blur identification and image restoration must be performed from the observed noisy blurred image. This paper presents a computationally simple iterative blind image deconvolution method which is based on non-linear adaptive filtering. The new method is applicable to minimum as well as mixed phase blurs. The noisy blurred image is assumed to be the output of a two-dimensional linear shift-invariant system with an unknown point spread function contaminated by an additive noise. The method passes the noisy blurred image through a two-dimensional finite impulse response adaptive filter whose parameters are updated by minimizing the dispersion. When convergence occurs, the adaptive filter provides an approximate inverse of the point spread function. Moreover, its output is an estimate of the unobserved true image. Experimental results are provided.     

粒子群优化在图像最小误差阈值化中的应用

提出了一种基于粒子群优化（PSO）的图像最小误差阈值化方法。将粒子群优化算法应用于图像最小误差阈值化中,克服了常规最小误差阈值化计算量大的缺点。实验证明该算法能有效降低常规图像最小误差阈值化的计算量,与遗传算法相比,该方法有更好的收敛性和稳定性。     

基于压缩感知的超分辨率图像重建

压缩感知(CS)利用图像稀疏表示的先验知识,从少量的观测值中重建出原始图像。将CS理论应用于单幅图像超分辨率(SR),提出一种基于两步迭代收缩算法和全变分(TV)稀疏表示的图像重建方法。该方法无需任何训练集,仅需单幅低分辨率实现图像重建。算法在测量矩阵里加入下采样低通滤波器以使SR问题满足应用CS理论的有限等距性质;采用TV正则化函数,利用两步迭代法引入TV去噪算子,可以更好地重建图像边缘。实验结果证明,与已有的超分辨率方法相比,在不同的放大倍数下所提方法重建图像视觉效果更好,在峰值信噪比(PSNR)的评价指标上有显著的提高(4~6dB),且实验证实滤波器的引入决定算法的重建质量。     

A new social and momentum component adaptive PSO algorithm for image segmentation

In this paper, we present a new variant of Particle Swarm Optimization (PSO) for image segmentation using optimal multi-level thresholding. Some objective functions which are very efficient for bi-level thresholding purpose are not suitable for multi-level thresholding due to the exponential growth of computational complexity. The present paper also proposes an iterative scheme that is practically more suitable for obtaining initial values of candidate multilevel thresholds. This self iterative scheme is proposed to find the suitable number of thresholds that should be used to segment an image. This iterative scheme is based on the well known Otsu’s method, which shows a linear growth of computational complexity. The thresholds resulting from the iterative scheme are taken as initial thresholds and the particles are created randomly around these thresholds, for the proposed PSO variant. The proposed PSO algorithm makes a new contribution in adapting ‘social’ and ‘momentum’ components of the velocity equation for particle move updates. The proposed segmentation method is employed for four benchmark images and the performances obtained outperform results obtained with well known methods, like Gaussian-smoothing method (Lim, Y. K., & Lee, S. U. (1990). On the color image segmentation algorithm based on the thresholding and the fuzzy c-means techniques. Pattern Recognition, 23, 935–952; Tsai, D. M. (1995). A fast thresholding selection procedure for multimodal and unimodal histograms. Pattern Recognition Letters, 16, 653–666), Symmetry-duality method (Yin, P. Y., & Chen, L. H. (1993). New method for multilevel thresholding using the symmetry and duality of the histogram. Journal of Electronics and Imaging, 2, 337–344), GA-based algorithm (Yin, P. -Y. (1999). A fast scheme for optimal thresholding using genetic algorithms. Signal Processing, 72, 85–95) and the basic PSO variant employing linearly decreasing inertia weight factor.     

一种改进的Landweber迭代图像复原算法

为解决传统的Landweber迭代法收敛速度慢,且对噪声敏感的问题,本文针对几种常见的模糊,即大气湍流模糊以及运动模糊,分别研究讨论了图像模糊的产生机理,并提出了一种改进的Landweber迭代图像复原方法.通过将图像的信号域与噪声域分离,改进的方法只在信号域上进行迭代加速,抑制了噪声的扩大.实验对比结果表明本文提出的方法在加速收敛的同时仍可以提高图像复原的精度,并以遥感图像和高速铁路图像为例,进一步验证了该方法的实际应用效果.     

结合遗传算法的局部最小误差孔穴图像分割法

针对遗传算法和最小误差分割法各自的优缺点,将最小误差分割法与遗传算法进行改进并且相互结合,提出了一种结合遗传算法的局部最小误差孔穴图像分割法。该方法利用局部图像信息确定最佳阈值范围,并根据模拟退火思想对个体适应度进行自适应的调整,从而避免了早熟现象,提高了运算速度。实验结果表明:该方法不但能够准确地分割出孔穴图像,而且运算速度较快,是一种有效的孔穴图像分割方法。     

Fuzzy entropy based optimal thresholding using bat algorithm

Image segmentation is a very significant process in image analysis. Much effort based on thresholding has been made on this field as it is simple and intuitive, commonly used thresholding approaches are to optimize a criterion such as between-class variance or entropy for seeking appropriate threshold values. However, a mass of computational cost is needed and efficiency is broken down as an exhaustive search is utilized for finding the optimal thresholds, which results in application of evolutionary algorithm and swarm intelligence to obtain the optimal thresholds. This paper considers image thresholding as a constrained optimization problem and optimal thresholds for 1-level or multi-level thresholding in an image are acquired by maximizing the fuzzy entropy via a newly proposed bat algorithm. The optimal thresholding is achieved through the convergence of bat algorithm. The proposed method has been tested on some natural and infrared images. The results are compared with the fuzzy entropy based methods that are optimized by artificial bee colony algorithm (ABC), genetic algorithm (GA), particle swarm optimization (PSO) and ant colony optimization (ACO); moreover, they are also compared with thresholding methods based on criteria of between-class variance and Kapur's entropy optimized by bat algorithm. It is demonstrated that the proposed method is robust, adaptive, encouraging on the score of CPU time and exhibits the better performance than other methods involved in the paper in terms of objective function values.     

一种基于正则化参数自适应选择的快速近似求逆的图像恢复新算法

本文根据正则化恢复中正则化参数应具有的性质,提出了一种基于正则化参数自适选择方案的新的空域迭代恢复算法。     

一种改进的图像迭代盲反卷积算法

针对传统迭代盲反卷积算法收敛速度慢、容易出现解模糊等问题,提出一种改进的图像迭代盲反卷积算法。利用动量矩求解图像的有限支持域,在支持域中使频率域和空间域交替迭代,从而实现图像的盲复原。仿真结果表明,与传统迭代盲反卷积算法和基于小波变换的盲反卷积算法相比,该算法的收敛速度较快,具有较好的图像恢复效果。     

A fast higher degree total variation minimization method for image restoration

Based on the spectral decomposition theory, this paper presents a unified analysis of higher degree total variation (HDTV) model for image restoration. Under this framework, HDTV is reinterpreted as a family of weighted L₁–L₂ mixed norms of image derivatives. Due to the equivalent formulation of HDTV, we construct a modified functional for HDTV-based image restoration. Then, the minimization of the modified functional can be decoupled into two separate sub-problems, which correspond to the deblurring and denoising. Thus, we design a fast and efficient image restoration algorithm using an iterative Wiener deconvolution with fast projected gradient denoising (IWD-FPGD) scheme. Moreover, we show the convergence of the proposed IWD-FPGD algorithm for the special case of second-degree total variation. Finally, the systematic performance comparisons of the proposed IWD-FPGD algorithm demonstrate the effectiveness in terms of peak signal-to-noise ratio, structural similarity and convergence rate.     

Application of splitting scheme and multigrid method for TV-Stokes denoising

Based on some previous work on the connection between image restoration and fluid dynamics,we apply a two-step algorithm for image denoising.In the first step,using a splitting scheme to study a nonlinear Stokes equation,tangent vectors are obtained.In the second step,an image is restored to fit the constructed tangent directions.We apply a fixed point iteration to solve the total variation-based image denoising problem,and use algebraic multigrid method to solve the corresponding linear equations.Numerical...     

An improved binarization algorithm based on a water flow model for document image with inhomogeneous backgrounds

A segmentation algorithm using a water flow model [Kim et al., Pattern Recognition 35 (2002) 265–277] has already been presented where a document image can be efficiently divided into two regions, characters and background, due to the property of locally adaptive thresholding. However, this method has not decided when to stop the iterative process and required long processing time. Plus, characters on poor contrast backgrounds often fail to be separated successfully. Accordingly, to overcome the above drawbacks to the existing method, the current paper presents an improved approach that includes extraction of regions of interest (ROIs), an automatic stopping criterion, and hierarchical thresholding. Experimental results show that the proposed method can achieve a satisfactory binarization quality, especially for document images with a poor contrast background, and is significantly faster than the existing method.     

Image thresholding by variational minimax optimization

In this paper we introduce an adaptive image thresholding technique via minimax optimization of a novel energy functional that consists of a non-linear convex combination of an edge sensitive data fidelity term and a regularization term. While the proposed data fidelity term requires the threshold surface to intersect the image surface only at places with large image gradient magnitude, the regularization term enforces smoothness in the threshold surface. To the best of our knowledge, all the previously proposed energy functional-based adaptive image thresholding algorithms rely on manually set weighting parameters to achieve a balance between the data fidelity and the regularization terms. In contrast, we use minimax principle to automatically find this weighting parameter value, as well as the threshold surface. Our conscious choice of the energy functional permits a variational formulation within the minimax principle leading to a globally optimum solution. The proposed variational minimax optimization is carried out by an iterative gradient descent with exact line search technique that we experimentally demonstrate to be computationally far more attractive than the Fibonacci search applied to find the minimax solution. Our method shows promising results to preserve edge/texture structures in different benchmark images over other competing methods. We also demonstrate the efficacy of the proposed method for delineating lung boundaries from magnetic resonance imagery (MRI).     

高斯尺度空间下估计背景的自适应阈值分割算法

为有效分割非均匀光照图像,提出一种在高斯尺度空间下估计背景的自适应阈值分割算法. 首先,利用二维高斯函数对待处理图像进行卷积操作来构建一个高斯尺度空间,在此空间下进行背景估计,并采用背景差法来消除非均匀光照干扰,从而提取出目标图像;然后,采用 矫正进行增强处理以突出较暗目标信息;最后,经强调谷底的最大类间方差法进行全局分割得到最终结果. 为验证算法的有效性,对非均匀光照条件下文本图像以及非文本图像进行了测试,并与基于偏移场的模糊C均值方法、灰度波动变换自适应阈值分割算法和自适应最小误差阈值分割算法,在错误分割率和运行时间上进行了对比. 实验结果表明,对比以上三种方法,该算法的分割结果更为理想.     

Modified bacterial foraging algorithm based multilevel thresholding for image segmentation

Multilevel thresholding is one of the most popular image segmentation techniques. In order to determine the thresholds, most methods use the histogram of the image. This paper proposes multilevel thresholding for histogram-based image segmentation using modified bacterial foraging (MBF) algorithm. To improve the global searching ability and convergence speed of the bacterial foraging algorithm, the best bacteria among all the chemotactic steps are passed to the subsequent generations. The optimal thresholds are found by maximizing Kapur's (entropy criterion) and Otsu's (between-class variance) thresholding functions using MBF algorithm. The superiority of the proposed algorithm is demonstrated by considering fourteen benchmark images and compared with other existing approaches namely bacterial foraging (BF) algorithm, particle swarm optimization algorithm (PSO) and genetic algorithm (GA). The findings affirmed the robustness, fast convergence and proficiency of the proposed MBF over other existing techniques. Experimental results show that the Otsu based optimization method converges quickly as compared with Kapur's method.