【作者】 张文成；

【导师】 赵春晖；

【作者基本信息】 哈尔滨工程大学 ， 通信与信息系统， 2004， 硕士

【摘要】 层叠滤波理论是80年代中期逐渐兴起的一种非线性数字滤波技术。层叠滤波理论优点在于：采用了阈值分解结构，有利于并行处理和通过VLSI技术实现；在理论上概括了许多非线性数字滤波器，成为研究非线性数字滤波器的一种重要工具。因此，层叠滤波器的研究具有重要的理论价值和实际意义。本文从层叠滤波器的基本理论入手，在建立最优层叠滤波器优化模型的基础上，研究了层叠滤波器优化算法及其在图像处理中的应用。本文的主要研究内容和取得的成果包括以下几个方面： 依据层叠滤波器输出信号满足层叠性这一前提，提出了一种输出信号快速重建算法，此算法有利于在无法进行并行处理时重建输出信号。该算法能在普通计算机上较快地重建输出信号，较之传统的重建算法，速度得到了较大提高，有利于在普通计算机上进行层叠滤波处理仿真时，重建输出信号。 由正布尔函数的表示方法及其定义和性质，提出了一种正布尔函数随机生成算法，使应用全局化优化算法，如遗传算法优化层叠滤波器成为可能。 讨论了基于MAE准则的最优层叠滤波器优化模型，借助于正布尔函数随机生成算法，用简单遗传算法实现了基于MAE准则层叠滤波器的最优化。 在MAE准则下，用遗传算法虽然可以有效地最优化层叠滤波器，但是优化速度很慢。为了克服这一缺点，本文讨论了一种快速自适应最优层叠滤波算法。仿真实验表明，用遗传算法优化的基于MAE准则的最优层叠滤波器能在有效地保持图像细节的同时，较好地去除噪声；而快速自适应最优层叠滤波算法具有与遗传算法相同的优化效果却大大地提高了优化速度。 由于基于MAE准则的最优层叠滤波器不能很好地去除图像噪声，本文建立了基于MSE准则的最优层叠滤波器优化模型，并且利用自适应遗传算法实现了其优化。在图像处理领域，计算机仿真结果表明，基于MSE准则的最优层叠滤波器去除噪声能力明显优于基于MAE准则的最优层叠滤波器，但细节保持能力稍差些。 对于非线性滤波器，噪声消除和细节保持为一对矛盾。为了避免细节保哈尔滨工程大学硕士学位论文持和噪声消除之间的冲突，本文提出了一种新型的最优层叠滤波器—基于细节检测的最优层叠滤波器，进一步改善了层叠滤波器的性能，折衷了层叠滤波器的细节保持和噪声消除能力。计算机仿真实验结果证明:通过对图像的细节和平滑部分分别用不同的正布尔函数处理，能使基于细节检测最优层叠滤波器在有效地滤除图像噪声的同时很好地保持图像细节。 基于细节检测最优层叠滤波器虽然可以很好地在保持图像细节和滤除图像噪声方面找到一折衷点，但是需要区分噪声图像的细节部分和平滑部分，这无疑使滤波过程变得更为复杂。为了解决这一问题，本文提出了一种基于邻域加权平均绝对值误差(NWMAE)准则，用于优化层叠滤波器。仿真实验表明，基于领域加权平均绝对值误差准则最优层叠滤波器也能在细节保持和滤除噪声方面寻找到比较合适的折衷点。关键词:层叠滤波器;图像处理:遗传算法;自适应算法;邻域加权平均绝对值误差准则更多还原

【Abstract】 Stack filters which are a kind of nonlinear digital filters, have received considerable attention during recent years since 1986 when their theory was presented. Stack filters virtues lie in: applying the architecture of threshold decomposition, suitable to parallel processing and VLSI realization; including many kinds of nonlinear filters, being an important tool for nonlinear research. Therefore, researching on stack filters has important theoretical and practical values. Beginning with stack filters’ fundamental theory, optimization algorithms and their application in image processing of stack filters are studied in this dissertation. The main contents and contributions of this paper are showed as following:A fast output signal restoration algorithm is presented according to the rule that the output signal satisfies stacking property. This algorithm can be used to restore output signal on a universal computer fast when parallel machine is unavailable.An algorithm for generating positive Boolean function (PBF) randomly is also presented in this paper based on the definition and representation methods of PBF. This algorithm makes using genetic algorithms to optimize stack filters possible. These two algorithms are simulated in Matlab environment. The experimental results show the fast output signal restoration algorithm restores output signal much faster on an ordinary computer than traditional algorithm.Using the algorithm for generating positive Boolean function randomly and the optimization model of stack filters based on MAE criteria, optimal stack filters are searched by simple genetic algorithms.The optimization speed of genetic algorithms is unacceptable, though it finds optimal stack filers effectively. In order to overcome this drawback, a fast adaptive algorithm for optimal stack filters is presented in this paper.Experimental results show that optimal stack filters based on MAE criteria, which are found by genetic algorithms preserve details of images perfectly and suppress noise passably. The fast algorithm has the same performance as the genetic algorithms but the time spending on optimizing is much less than genetic algorithms.The optimization model based on MSE criteria is presented in this paper because optimal stack filters base on MAE criterion cannot suppress noise of images perfectly. Adaptive genetic algorithms are used to optimize optimal stack filters based on MSE criterion. Computer simulated experiments show that the noise suppressing capability of this kind of optimal stack filters is better than the optimal stack filters based on MAE criterion but the detail preserving capability is little worse.For nonlinear filters, noise suppressing and detail preserving is a pair of contradictions. In order to calm down the confliction between them, a new kind of optimal stack filters-optimal stack filters based on detail detection is presented in this paper. The performance of stack filters is improved by this kind stack filters and get a good tradeoff between noise suppressing and detail preserving. Experimental results show that optimal stack filters based on detail detection can suppress noise perfectly as well as preserving details of an image effectively through processing the detail and smooth parts by different positive Boolean functions.Although optimal stack filters based on detail detection can reach a good tradeoff between noise suppressing and detail preservation, the processing procedure is more complicated. In order to overcome this drawback, a new kind of criterion-neighboring weighted mean absolute error criterion is presented as an optimality criterion of stack filters. Simulated experiments show that optimal stack filters based on neighboring weighted mean absolute criterion can also reach a good tradeoff between noise suppressing and detail preservation.更多还原