图像复原的Contourlet收缩与广义全变分正则化方法

建立了广义全变分(total variation,TV)模型,分析正则项在复原算法中的作用.分别从图像的平坦区域和边缘区域入手,在平坦区域图像各向同性扩散,在边缘区域则要满足各向异性扩散,从理论上对两种情形下的扩散做深入分析,推导出广义TV模型满足的一些条件,为了防止高噪声情形下复原模型失效以及克服方块效应,在正则项中引入了 Contourlet收缩,它是一种多分辨的、局域的、多方向的更稀疏的图像表示方法,正则项中引入的Contourlet收缩具有去噪和提取图像重要信息的作用,Contourlet收缩与广义TV正则化相结合,兼顾了图像的光滑性和边缘保持,特别是在图像严重模糊、噪声越多的情形下,更加体现了这种算法比改进的TV模型有效.     

Relations Between Regularization and Diffusion Filtering

Regularization may be regarded as diffusion filtering with an implicit time discretization where one single step is used. Thus, iterated regularization with small regularization parameters approximates a diffusion process. The goal of this paper is to analyse relations between noniterated and iterated regularization and diffusion filtering in image processing. In the linear regularization framework, we show that with iterated Tikhonov regularization noise can be better handled than with noniterated. In the nonlinear framework, two filtering strategies are considered: the total variation regularization technique and the diffusion filter technique of Perona and Malik. It is shown that the Perona-Malik equation decreases the total variation during its evolution. While noniterated and iterated total variation regularization is well-posed, one cannot expect to find a minimizing sequence which converges to a minimizer of the corresponding energy functional for the Perona–Malik filter. To overcome this shortcoming, a novel regularization technique of the Perona–Malik process is presented that allows to construct a weakly lower semi-continuous energy functional. In analogy to recently derived results for a well-posed class of regularized Perona–Malik filters, we introduce Lyapunov functionals and convergence results for regularization methods. Experiments on real-world images illustrate that iterated linear regularization performs better than noniterated, while no significant differences between noniterated and iterated total variation regularization have been observed.     

非线性微分代数系统的稳定性

本文发展了微分代数系统的稳定性理论,讨论了微分代数系统在平衡点近旁的正则性问题、给出了在平衡点处的受限形式,建立了受限系统Ｌｙａｐｕｎｏｖ稳定性的基本定理,得到了微分代数系统平凡解渐近稳定的判别准则。     

A weighted H1 seminorm regularization method for Fredholm integral equations of the first kind

Many problems in mathematics and engineering lead to Fredholm integral equations of the first kind, e.g. signal and image processing. These kinds of equations are difficult to solve numerically since they are ill-posed. Therefore, regularization is required to obtain a reasonable approximate solution. This paper presents a new regularization method based on a weighted H¹ seminorm. Details of numerical implementation are given. Numerical examples, including one-dimensional and two-dimensional integral equations, are presented to illustrate the efficiency of the proposed approach. Numerical results show that the proposed regularization method can restore edges as well as details.     

基于非局部均值的单帧图像超分辨率重建算法

为了解决单帧低分辨率图像获得高分辨率图像的问题,提出了一种基于非局部均值滤波的单帧图像超分辨率算法,将图像超分辨率重建视为反问题,建立正则化模型,充分考虑图像的局部结构信息和自然图像中不同尺度的相似性冗余,加入非局部滤波.实验结果表明,文中算法从单帧图像重建的图像边缘轮廓和纹理较传统算法清楚,有效抑制了人工伪影,同时对噪声具有鲁棒性.在视觉效果及峰值信噪比上都取得良好的结果.     

Novel reconstruction method for frequency-hopping signals

The reconstruction of the Frequency Hopping(FH) signal is studied in the noise environment. After analyzing the sparse characteristics of the FH signal at the receiving end, an atomic decomposition is constructed based on the parameters of the FH signal.Then a signal reconstruction method for the FH signal is presented based on the Generalized Regularized FOCUSS Algorithm. By choosing the proper regular parameter, the FH signal is reconstructed in the noise environmet. Simulation results demonstrate that the method is correct and effective.     

基于明暗信息的胶囊内镜图像三维形状恢复

利用明暗恢复形状技术,将视频胶囊内镜二维图像的明暗信息重构小肠内腔表面的三维场景信息。针对传统的明暗恢复形状技术的约束条件,提出了一种针对胶囊内镜图像的预处理方法,利用预处理后的图像恢复出更为平滑的视觉场景,同时保留被检查对象的结构信息。基于临床数据的实验结果表明,三维形状恢复技术可以增强胶囊内镜视频的可读性,提高小肠疾病的诊断准确率。     

采用测地线活动轮廓模型检测与跟踪运动目标

水平集几何活动轮廓模型能较好地适应曲线的拓扑变化.为了跟踪和获取刚体和非刚体运动目标的轮廓信息,提出了一种基于改进测地线活动轮廓(GAC)模型和Kalman滤波相结合的算法以检测和跟踪运动目标.该算法首先采用高斯混合模型和背景差分获取目标的运动区域,在运动区域内采用引入距离规则化项的GAC模型进行曲线演化,使改进GAC模型在运动目标的真实轮廓处收敛;然后通过结合Kalman滤波预测目标下一帧的位置,实现对目标轮廓跟踪.实验结果表明,该方法适用于刚体和非刚体目标,在部分遮挡的情况下也能保持良好的检测和跟踪效果.     

一种改进的双项自适应总体变差去噪模型

研究经典总体变差去噪模型及其改进的自适应去噪模型,提出一种基于预处理图像局部信息的双项自适应模型。利用空间自适应保真项缓解二阶非线性滤波对细节的过度平滑,通过自适应正则化项减少阶梯效应,使数值更稳定和收敛。实验结果表明,与原方法相比,改进方法具有更好的鲁棒性,在噪声较高的情况下仍能取得较好的去噪效果。     

非均匀损伤介质中利用波传播理论对损伤参数的反演

介绍了波在非均匀损伤介质中的传播的反问题,根据波的响应来反演介质的损伤。首先应用Newton迭代法把非线性问题化为线性问题,得到一组不适定的线性方程式组,采用Tikhonov正则化求解,对于正则参数选取采用L线曲线准则,求出了原问题的稳定的、有效的解,获得了与真实损伤度较为吻合的反演参数。工程实例的模拟分析计算证明了上述算法的有效性。