粒子群优化及其在图像处理中的应用研究
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摘要
粒子群优化(Particle Swarm Optimization, PSO)是群体智能中的一个重要分支,为解决那些难以建立严格的理论模型,传统优化方法难以奏效甚至根本无法解决的问题提供了新的思路。粒子群优化以其算法实现简单,对软硬件要求较低,适用性强的优点获得了广泛应用。PSO优化过程中粒子多样性的丧失可能会使算法陷入局部极值。近年来,人们依据不同的物理或生物模型引入的多子群结构对克服陷入局部极值有积极作用,但由于这些研究多针对具体应用提出,多子群优化算法尚缺乏统一的理论框架。
本文主要围绕粒子群优化理论和应用技术展开研究,对粒子群优化的算法改进、理论框架、基于粒子群优化的小波神经网络和PSO在图像去噪、图像融合等实际应用做了较为深入系统的研究。本文的主要研究内容和贡献如下:
(1)把生态进化策略中的r-选择和K-选择的概念引入到粒子群优化中,提出了一种基于r-选择和K-选择的r/KPSO(r-selection and K-selection based Particle Swarm Optimization, r/KPSO)算法。r/KPSO把整个种群分为r-子群和K-子群,r-子群偏重以数量见长r-选择的进化策略,用于保持种群的多样性,是广度意义上的搜索;而K-子群偏重以质量见长的K-选择策略,在已知最优点的附近做精细搜索,是深度意义上的搜索。两个子群通过群内竞争和群间竞争,优势互补,共同达到优化的目的。为了定量衡量算法收敛的速度,提出了收敛起始代这一指标,用于表明算法开始收敛的代次。在对若干典型函数的极值优化的实验中,r/KPSO获得了较高的优化精度,并在“收敛起始代”意义下获得了更快的收敛速度。
(2)在r/KPSO的基础上对多子群的概念加以扩展,提出了一种多子群多策略(Multi-Subswarms Multi-Strategies, MSMS)的广义粒子群优化结构框架。在MSMS框架下,不同的子群采用不同的策略,并提出了策略偏重度的概念,用于衡量各个策略对子群进化的影响程度。在MSMS框架下,各子群可以同步地或者异步地执行优化更新过程。以已有文献中的OPSO(Optimized Particle Swarm Optimization)和QSO(Quantum Swarm Optimization)两个典型多子群算法为例分别分析了MSMS框架的异步型和同步型。在MSMS框架下,进一步总结了r/KPSO,并在其指导下提出对r/KPSO的改进设想。几个典型实例的分析表明,MSMS架构能够适合于对多子群结构的粒子群优化进行分析总结,对改进已有算法和设计新算法有指导意义。
(3)把粒子群优化和小波神经网络相结合,提出了基于粒子群优化的小波神经网络(Particle Swarm Optimized Wavelet Neural Network, PSOWNN),克服了Sigmoid前馈神经网络的缺点。PSOWNN在训练时采用“双循环”结构,在结构调整规则中指定期望的收敛速度和精度后,可以依据结构调整规则,自动地调整神经元个数,而小波神经元的权值和相关参数通过粒子群优化确定。通过对脉冲噪声去除中的像素分类问题,验证了PSOWNN的性能。
(4)针对中值滤波存在较严重过度滤波的现象,提出了基于改进型中值滤波和分类(Modified Median Filtering and Classifying, MMFC)的两种去除脉冲噪声的方案,每个方案在滤波前都用PSOWNN对像素是否受到污染做出判断。在方案1中,PSOWNN从含噪图像中区分出未受污染的像素,并在滤波结果中把这些像素还原为其在原噪声图像中的值,其余像素采用采用滤波结果;在方案2中,PSOWNN从含噪图像中区分出那些未被污染的像素,在这些像素上执行滤波,而其余像素保持不变。由于增加了PSOWNN的分类判断,MMFC滤波的准确度和针对性得到提高,在脉冲噪声去除中有较好的主客观性能表现。
(5)针对全局阈值无法体现子带系数分布差异的问题,提出了分级子带收缩算法(Hierarchical Subbands Shrinking, HSS),并针对硬阈值函数和软阈值函数的小波系数的过度扼杀的现象,提出了一种新的阈值函数——光滑阈值函数(Smooth Thresholding,ST)。HSS充分考虑到不同尺度、不同方向上的高频子带小波系数分布的差异,对每个子带采用不同的阈值;ST函数能够合理地收缩幅值较小的小波系数,而当小波系数较大时则拥有逼近于软阈值的收缩结果;此外ST函数还具有实数范围内全局可导的特性,便于数学处理。HSS采用ST函数作为阈值函数,并把粒子群优化用于确定各子带的阈值,获得了较好的去噪效果。
(6)针对基于小波的多源图像融合中的若干阈值和参数仅凭主观经验进行设定难以达到最佳融合效果的问题,结合人眼的视觉特性提出了基于粒子群优化的小波区域(Particle Swarm Optimized Wavelet Region, PSOWR)图像融合算法。PSOWR算法用局部能量和区域对比度来指导小波系数融合过程,并把粒子群优化引入到图像融合之中,用于确定融合规则中的相关阈值和参数。遥感图像和医学图像的融合实验结果表明,PSOWR算法不论是从主观视觉质量还是客观数据指标上都有良好表现。
As a member of swarm intelligence, Particle Swarm Optimization (PSO) provides new ideas to sovle those difficult problems for those traditional optimization methods. For its easy implementation, low requirement and cheap cost, PSO has used in wide engineering fields. Similar to other optimization algorithms, diversity loss in optimization procedure may cause local minima. Inspired by biological or physical models, multi-subswarms optimization could do well in avoiding local minima. But most multi-subswarms optimization algorithms are proposed for sovling special problem, general frame is useful to analyze or design multi-subswarms optimization.
The main research work in the dissertation is as follows:
(1) The r-selection and K-selection strategies in Ecology are introduced into particle swarm, and the r/KPSO is proposed (r-selection and K-selection based Particle Swarm Optimization, r/KPSO). The swarm is devided into two subswarms, r-subswarm favoring r-selection strategy and K-subswarm favoring K-selection strategy. The main task of r-subswarm is to explore the search space in quite high speed and r-paricles can breed many progencies. K-paritlces only breed few offsprings, and the offspring exploit the search space around their parent. The two subswarms compete and collaborate for the purpose of optimization. To evaluate the speed of convergence quantitatively, fisrt converging generation (FCG) is introduced to tell the first genertation where convergence begins. Some experiments on type benchmark functions showed that r/KPSO did well in most cases.
(2) Based on r/KPSO, a PSO frame named Multi-Subswarms Multi-Strategies (MSMS) is provided for the analysis of multiswarm optimization. MSMS allows subswarms adopte various strategies, and the strategy favoring degree (SFD) can be used for evaluate the weight of certain strategy for the subswarm. All subswarms in MSMS can update synchronizingly or asynchronously. MSMS frame can be used for PSO structure analysis or design. As two examples, the OPSO and QSO are analyzed under MSMS frame. In the view of MSMS, r/KPSO is summarized and the ideas to improve it are also discussed.
(3) Combining the PSO algorithm and wavelet neural network, the PSOWNN (Particle Swarm Optimized Wavelet Neural Network) is presented. PSOWNN can adjust its own structure by adding new neuron according to the network structure update principles. In the WNN training, PSO adoptes so-called“double cycles”structure, one for particle optimizing and another for structure adjusting. The test of pixles classifying proved the approximation performance of PSOWNN.
(4) A noval denoising algorithm named MMFC (Modified Median Filtering and Classifying) is used to remove pulse noise. Two approaches (App1 and App2) of MMFC are provided and both of which adopte PSOWNN to classifying the pixels. If PSOWNN distinguishes the uncorrupted pixcels in the result image, App1 sets them as the values in noisy image. If PSOWNN distinguishes the corrupted pixels, App2 filters them and keeps others as before. For the classifying of PSOWNN, MMFC can process those pixels more properly than traditional median filtering.
(5) Hierarchical Subbands Shrinking (HSS) is proposed for Gaussian noise removal. HSS adoptes special threshold determined by PSO for every subband. A noval thresholding function, smooth-thresholding (ST) is proposed and adopted by HSS. The ST function is suite for mathematic processing for it is continuous and derivatable for all real numbers.
(6) Many variables need to be determined in image fusion based on wavelet region local statistics. A noval image fusion algorithm named PSOWR (Particle Swarm Optimized Wavelet Region) is proposed. The thresholds and other parameters used by image fusion are all determined by PSO and the fusion rules like local energy, contrast, weighted average and selection are combined with“region”idea for coefficient selection in the low- and high-pass subbands. The experiments on remote sense and medical images showed PSOWR can provide a more satisfactory fusion outcome.
本文主要围绕粒子群优化理论和应用技术展开研究,对粒子群优化的算法改进、理论框架、基于粒子群优化的小波神经网络和PSO在图像去噪、图像融合等实际应用做了较为深入系统的研究。本文的主要研究内容和贡献如下:
(1)把生态进化策略中的r-选择和K-选择的概念引入到粒子群优化中,提出了一种基于r-选择和K-选择的r/KPSO(r-selection and K-selection based Particle Swarm Optimization, r/KPSO)算法。r/KPSO把整个种群分为r-子群和K-子群,r-子群偏重以数量见长r-选择的进化策略,用于保持种群的多样性,是广度意义上的搜索;而K-子群偏重以质量见长的K-选择策略,在已知最优点的附近做精细搜索,是深度意义上的搜索。两个子群通过群内竞争和群间竞争,优势互补,共同达到优化的目的。为了定量衡量算法收敛的速度,提出了收敛起始代这一指标,用于表明算法开始收敛的代次。在对若干典型函数的极值优化的实验中,r/KPSO获得了较高的优化精度,并在“收敛起始代”意义下获得了更快的收敛速度。
(2)在r/KPSO的基础上对多子群的概念加以扩展,提出了一种多子群多策略(Multi-Subswarms Multi-Strategies, MSMS)的广义粒子群优化结构框架。在MSMS框架下,不同的子群采用不同的策略,并提出了策略偏重度的概念,用于衡量各个策略对子群进化的影响程度。在MSMS框架下,各子群可以同步地或者异步地执行优化更新过程。以已有文献中的OPSO(Optimized Particle Swarm Optimization)和QSO(Quantum Swarm Optimization)两个典型多子群算法为例分别分析了MSMS框架的异步型和同步型。在MSMS框架下,进一步总结了r/KPSO,并在其指导下提出对r/KPSO的改进设想。几个典型实例的分析表明,MSMS架构能够适合于对多子群结构的粒子群优化进行分析总结,对改进已有算法和设计新算法有指导意义。
(3)把粒子群优化和小波神经网络相结合,提出了基于粒子群优化的小波神经网络(Particle Swarm Optimized Wavelet Neural Network, PSOWNN),克服了Sigmoid前馈神经网络的缺点。PSOWNN在训练时采用“双循环”结构,在结构调整规则中指定期望的收敛速度和精度后,可以依据结构调整规则,自动地调整神经元个数,而小波神经元的权值和相关参数通过粒子群优化确定。通过对脉冲噪声去除中的像素分类问题,验证了PSOWNN的性能。
(4)针对中值滤波存在较严重过度滤波的现象,提出了基于改进型中值滤波和分类(Modified Median Filtering and Classifying, MMFC)的两种去除脉冲噪声的方案,每个方案在滤波前都用PSOWNN对像素是否受到污染做出判断。在方案1中,PSOWNN从含噪图像中区分出未受污染的像素,并在滤波结果中把这些像素还原为其在原噪声图像中的值,其余像素采用采用滤波结果;在方案2中,PSOWNN从含噪图像中区分出那些未被污染的像素,在这些像素上执行滤波,而其余像素保持不变。由于增加了PSOWNN的分类判断,MMFC滤波的准确度和针对性得到提高,在脉冲噪声去除中有较好的主客观性能表现。
(5)针对全局阈值无法体现子带系数分布差异的问题,提出了分级子带收缩算法(Hierarchical Subbands Shrinking, HSS),并针对硬阈值函数和软阈值函数的小波系数的过度扼杀的现象,提出了一种新的阈值函数——光滑阈值函数(Smooth Thresholding,ST)。HSS充分考虑到不同尺度、不同方向上的高频子带小波系数分布的差异,对每个子带采用不同的阈值;ST函数能够合理地收缩幅值较小的小波系数,而当小波系数较大时则拥有逼近于软阈值的收缩结果;此外ST函数还具有实数范围内全局可导的特性,便于数学处理。HSS采用ST函数作为阈值函数,并把粒子群优化用于确定各子带的阈值,获得了较好的去噪效果。
(6)针对基于小波的多源图像融合中的若干阈值和参数仅凭主观经验进行设定难以达到最佳融合效果的问题,结合人眼的视觉特性提出了基于粒子群优化的小波区域(Particle Swarm Optimized Wavelet Region, PSOWR)图像融合算法。PSOWR算法用局部能量和区域对比度来指导小波系数融合过程,并把粒子群优化引入到图像融合之中,用于确定融合规则中的相关阈值和参数。遥感图像和医学图像的融合实验结果表明,PSOWR算法不论是从主观视觉质量还是客观数据指标上都有良好表现。
As a member of swarm intelligence, Particle Swarm Optimization (PSO) provides new ideas to sovle those difficult problems for those traditional optimization methods. For its easy implementation, low requirement and cheap cost, PSO has used in wide engineering fields. Similar to other optimization algorithms, diversity loss in optimization procedure may cause local minima. Inspired by biological or physical models, multi-subswarms optimization could do well in avoiding local minima. But most multi-subswarms optimization algorithms are proposed for sovling special problem, general frame is useful to analyze or design multi-subswarms optimization.
The main research work in the dissertation is as follows:
(1) The r-selection and K-selection strategies in Ecology are introduced into particle swarm, and the r/KPSO is proposed (r-selection and K-selection based Particle Swarm Optimization, r/KPSO). The swarm is devided into two subswarms, r-subswarm favoring r-selection strategy and K-subswarm favoring K-selection strategy. The main task of r-subswarm is to explore the search space in quite high speed and r-paricles can breed many progencies. K-paritlces only breed few offsprings, and the offspring exploit the search space around their parent. The two subswarms compete and collaborate for the purpose of optimization. To evaluate the speed of convergence quantitatively, fisrt converging generation (FCG) is introduced to tell the first genertation where convergence begins. Some experiments on type benchmark functions showed that r/KPSO did well in most cases.
(2) Based on r/KPSO, a PSO frame named Multi-Subswarms Multi-Strategies (MSMS) is provided for the analysis of multiswarm optimization. MSMS allows subswarms adopte various strategies, and the strategy favoring degree (SFD) can be used for evaluate the weight of certain strategy for the subswarm. All subswarms in MSMS can update synchronizingly or asynchronously. MSMS frame can be used for PSO structure analysis or design. As two examples, the OPSO and QSO are analyzed under MSMS frame. In the view of MSMS, r/KPSO is summarized and the ideas to improve it are also discussed.
(3) Combining the PSO algorithm and wavelet neural network, the PSOWNN (Particle Swarm Optimized Wavelet Neural Network) is presented. PSOWNN can adjust its own structure by adding new neuron according to the network structure update principles. In the WNN training, PSO adoptes so-called“double cycles”structure, one for particle optimizing and another for structure adjusting. The test of pixles classifying proved the approximation performance of PSOWNN.
(4) A noval denoising algorithm named MMFC (Modified Median Filtering and Classifying) is used to remove pulse noise. Two approaches (App1 and App2) of MMFC are provided and both of which adopte PSOWNN to classifying the pixels. If PSOWNN distinguishes the uncorrupted pixcels in the result image, App1 sets them as the values in noisy image. If PSOWNN distinguishes the corrupted pixels, App2 filters them and keeps others as before. For the classifying of PSOWNN, MMFC can process those pixels more properly than traditional median filtering.
(5) Hierarchical Subbands Shrinking (HSS) is proposed for Gaussian noise removal. HSS adoptes special threshold determined by PSO for every subband. A noval thresholding function, smooth-thresholding (ST) is proposed and adopted by HSS. The ST function is suite for mathematic processing for it is continuous and derivatable for all real numbers.
(6) Many variables need to be determined in image fusion based on wavelet region local statistics. A noval image fusion algorithm named PSOWR (Particle Swarm Optimized Wavelet Region) is proposed. The thresholds and other parameters used by image fusion are all determined by PSO and the fusion rules like local energy, contrast, weighted average and selection are combined with“region”idea for coefficient selection in the low- and high-pass subbands. The experiments on remote sense and medical images showed PSOWR can provide a more satisfactory fusion outcome.
引文
[1]王俊伟粒子群优化算法的改进及应用东北大学博士论文[D], 2006.01
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