多小波构造方法研究及在图像处理中的应用
摘要
多小波优越的特性使得它广泛应用于信号和图像处理中,本文为解决如何从信号和图像内容本身和处理的目的出发,自适应地选择和构造多小波基的问题,研究了多小波、多小波预处理滤波器的构造方法及在图像处理中的应用。主要工作包括:
1.总结了描述多小波特性的5个表征量:正交性、对称性、近似特性、正则性和时频分辨率,给出了描述这些特性的具体方式,在多小波设计和具体应用间架构了一个桥梁,为有针对性的设计和应用多小波奠定了基础。
2.针对目前多小波构造方法繁多,选择困难的问题,从对多小波特性要求出发,详细介绍了正交、对称、紧支撑、高近似阶、最优时频分辨率的多小波构造方法,分析了方法的可行性、给出了具体设计方案,并对构造多小波过程中为了克服参数选择中计算量大和陷入局部极小的问题采用了优选初始值和变步长的解决办法。以设计长度为4的二重多小波为例,将整个设计过程有机的结合起来,使整个设计过程清晰明了,为应用者提供了一个方便的设计工具。
3.多小波预处理滤波器直接影响多小波滤波器组的工作性能,选择不当会破坏所设计的多小波的性质。针对这个问题,本文从对预处理滤波器要满足的要求出发,介绍了三种设计方法:矢量预处理滤波器、滤波器组、多小波平衡化的设计,分析了方法的特点,提出了具体的解决方案。尤其在矢量预处理滤波器设计中,提出了一种基于零空间的求取Q (0)的方法,克服了繁琐的计算和推导过程,大大提高了计算速度和准确性。这样,就可方便地根据具体要求来选择合适的设计方法设计多小波预处理滤波器。
4.针对基于多小波的多聚焦图像融合中多小波的选择问题,从多聚焦图像特点和对多聚焦图像的频谱内容的分析出发,在理论上提出了选择多小波的标准,即应选择小波函数频宽小,时频分辨率高的多小波,并通过实验验证了标准的准确性。对于融合过程中影响融合效果的另一个重要因素:融合规则,本文提出了对多小波系数不同频率分量采用不同的融合方案的融合规则,低频分量采用区域均方误差加权平均的方法,高频分量采用区域能量匹配度度量进行加权融合的方法进行融合,具有很好的融合效果。在实验中采用了原清晰图像与融合图像的均方根误差、融合图像的空间频率和清晰度作为融合效果的客观评价标准,并分析了评价标准的性能,一般均方根误差是最好的评价标准,但在实际应用中,常常没有原始清晰图像,在主观感觉融合效果较好的情况下,可采用空间频率和清晰度作为评价标准。
5.针对基于多小波图像去噪方法中的多小波选择问题,通过理论分析和实验验证,证明在相同的阈值函数和阈值条件下,选择具有较高的小波函数时频分辨率的多小波,会产生良好的去噪效果,为多小波去噪提供了选择多小波的依据。
6.基于多小波对常见浮游植物细胞图像进行了边缘和形状检测的初步研究,分析了细胞图像边缘特点,给出了具体的解决方法,实验证明,在边缘提取中取得了较好的效果,形状检测方法只适用于外形轮廓较好的情况。
To solve the question on correctly choosing the multiwavelets according signal and image contents and their processing intention, the construction methods and application of multiwavelets and prefilter are studied. The dissertation mainly included following aspects:
1. Five characteristics describing multiwavelets are summarized, which are orthogonality, symmetry, approximation, regularity and time-frequency resolution. A connection between the multiwaveles design and application are established by these characteristics.
2. The multiwavelets construction methods are introduced according the desire performance of the multiwavelets characteristics, which are orthogonal, symmetric, high approximation, good regularity and optimum time-frequency resolution. The feasibility of these methods is analyzed. The concrete means are given to construct wavelets. Correctly initializtion parameters and varying steps overcome the complexity of computation and local minimum. A convenient multiwavelets construction tool is provided for the practical design process.
3. The correct selection of prefilter is critical to the performance of the multiwavelets. Three design schemes of prfilters are introduced, which are vector prefilter, prefilter groop, balanced multiwavelets . The concrete realization methods are proposed. A null space method on computing Q (0) is present to boost the computation velocity and correctness.
4. A criterion of choosing multiwavelets in multi-focus image fuse is proposed, which is the wavelet functions should have narrow frequency width and high time frequency resolution. A new fusion rule is proposed for multi-focus image fusion. The object evaluation of fuse result is analyzed. The square root error between the original clarity image and the fusing result image is an excellent criterion for evaluating the fuse result. Without the original clarity image, the spatial frequency and definition can be used only when the fusing result image is good subjectively.
5. The selecting method of multiwaveletsin image denoising is present. At the same threshold function and threshold value conditions, the higher time frequency resolution, the better the denoising effect is.
6. The phytoplankton cell image edge and shape detecting method based on mu1tiwavelets is studied by analyzing the characteristics of the phytoplankton cell image edge. The experiments prove the validity of the methods.
1.总结了描述多小波特性的5个表征量:正交性、对称性、近似特性、正则性和时频分辨率,给出了描述这些特性的具体方式,在多小波设计和具体应用间架构了一个桥梁,为有针对性的设计和应用多小波奠定了基础。
2.针对目前多小波构造方法繁多,选择困难的问题,从对多小波特性要求出发,详细介绍了正交、对称、紧支撑、高近似阶、最优时频分辨率的多小波构造方法,分析了方法的可行性、给出了具体设计方案,并对构造多小波过程中为了克服参数选择中计算量大和陷入局部极小的问题采用了优选初始值和变步长的解决办法。以设计长度为4的二重多小波为例,将整个设计过程有机的结合起来,使整个设计过程清晰明了,为应用者提供了一个方便的设计工具。
3.多小波预处理滤波器直接影响多小波滤波器组的工作性能,选择不当会破坏所设计的多小波的性质。针对这个问题,本文从对预处理滤波器要满足的要求出发,介绍了三种设计方法:矢量预处理滤波器、滤波器组、多小波平衡化的设计,分析了方法的特点,提出了具体的解决方案。尤其在矢量预处理滤波器设计中,提出了一种基于零空间的求取Q (0)的方法,克服了繁琐的计算和推导过程,大大提高了计算速度和准确性。这样,就可方便地根据具体要求来选择合适的设计方法设计多小波预处理滤波器。
4.针对基于多小波的多聚焦图像融合中多小波的选择问题,从多聚焦图像特点和对多聚焦图像的频谱内容的分析出发,在理论上提出了选择多小波的标准,即应选择小波函数频宽小,时频分辨率高的多小波,并通过实验验证了标准的准确性。对于融合过程中影响融合效果的另一个重要因素:融合规则,本文提出了对多小波系数不同频率分量采用不同的融合方案的融合规则,低频分量采用区域均方误差加权平均的方法,高频分量采用区域能量匹配度度量进行加权融合的方法进行融合,具有很好的融合效果。在实验中采用了原清晰图像与融合图像的均方根误差、融合图像的空间频率和清晰度作为融合效果的客观评价标准,并分析了评价标准的性能,一般均方根误差是最好的评价标准,但在实际应用中,常常没有原始清晰图像,在主观感觉融合效果较好的情况下,可采用空间频率和清晰度作为评价标准。
5.针对基于多小波图像去噪方法中的多小波选择问题,通过理论分析和实验验证,证明在相同的阈值函数和阈值条件下,选择具有较高的小波函数时频分辨率的多小波,会产生良好的去噪效果,为多小波去噪提供了选择多小波的依据。
6.基于多小波对常见浮游植物细胞图像进行了边缘和形状检测的初步研究,分析了细胞图像边缘特点,给出了具体的解决方法,实验证明,在边缘提取中取得了较好的效果,形状检测方法只适用于外形轮廓较好的情况。
To solve the question on correctly choosing the multiwavelets according signal and image contents and their processing intention, the construction methods and application of multiwavelets and prefilter are studied. The dissertation mainly included following aspects:
1. Five characteristics describing multiwavelets are summarized, which are orthogonality, symmetry, approximation, regularity and time-frequency resolution. A connection between the multiwaveles design and application are established by these characteristics.
2. The multiwavelets construction methods are introduced according the desire performance of the multiwavelets characteristics, which are orthogonal, symmetric, high approximation, good regularity and optimum time-frequency resolution. The feasibility of these methods is analyzed. The concrete means are given to construct wavelets. Correctly initializtion parameters and varying steps overcome the complexity of computation and local minimum. A convenient multiwavelets construction tool is provided for the practical design process.
3. The correct selection of prefilter is critical to the performance of the multiwavelets. Three design schemes of prfilters are introduced, which are vector prefilter, prefilter groop, balanced multiwavelets . The concrete realization methods are proposed. A null space method on computing Q (0) is present to boost the computation velocity and correctness.
4. A criterion of choosing multiwavelets in multi-focus image fuse is proposed, which is the wavelet functions should have narrow frequency width and high time frequency resolution. A new fusion rule is proposed for multi-focus image fusion. The object evaluation of fuse result is analyzed. The square root error between the original clarity image and the fusing result image is an excellent criterion for evaluating the fuse result. Without the original clarity image, the spatial frequency and definition can be used only when the fusing result image is good subjectively.
5. The selecting method of multiwaveletsin image denoising is present. At the same threshold function and threshold value conditions, the higher time frequency resolution, the better the denoising effect is.
6. The phytoplankton cell image edge and shape detecting method based on mu1tiwavelets is studied by analyzing the characteristics of the phytoplankton cell image edge. The experiments prove the validity of the methods.
引文
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