各向异性扩散及其在电磁数据处理中的应用研究
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摘要
基于偏微分方程的各向异性扩散图像处理方法由于具有良好的定向扩散能力自上世纪九十年代以来图像领域得到了广泛应用。尤其是在图像的去噪与增强及图像的分割处理方面,作为一种非线性处理技术,不仅计算简单,而且对于连续信号,偏微分方程可视为具有微小邻域局部滤波的迭代,可与已有的滤波方法相结合,形成新的滤波方法。本文把各向异性扩散的定向扩散能力引入到地球物理的数据处理中,实现了电磁信号处理的非线性化处理。
首先通过热扩散及热扩散方程、基于能量流的扩散方程,导出了向异性扩散模型与图像能量的变化过程之间的关系,并证明了利用能量流方法获得的图像处理过程同样满足极大极小原理。也证明了若能量有限的图像,灰度均值为零,则图像平均能量的变化等于图像灰度均方差的变化。研究了在图像的扩散处理中,图像和噪声的能量变化过程与特征。然后把热物理扩散中的扩散平衡引入到图像处理的各向异性扩散中,定义了图像扩散平衡的概念,实现了最佳扩散时间尺度的稳定有效估计。模拟测试表明本文提出的方法能在保护信号特征的同时在噪声的压制也能达到较好的可视效果,即特征的保护与噪声压制上能达到一个合理的平衡。相对MSE及其它方法不需估计噪声强度(方差),能自适应于图像,运行简单稳定,即使在低信噪比下也能获得很好的估计效果。
其次利用贝叶斯统计、稳健统计与各向异性扩散联系,把各向异性扩散引入到电磁观测的阻抗估计中去,修改了适于阻抗估计的各向异性扩散方程,提高了阻抗估计的稳定性。证明了常规Robust估计的收敛值是只是ADR估计中解之一。
第三通过把各向异性扩散和局部单调扩散引入到地球物理领域中,提出了基于各向异性扩散的曲线平滑方法。为了使消除随机噪声与“飞点”噪声能够在扩散中同时进行,并消除“飞点”噪声引起的扩散行为的不稳定性,研究有理函数在信号平滑处理中的应用,以及它与线性滤波和非线性滤波区别及其特点。并通过改变梯度估计的方式,不仅提高了扩散行为的稳定性,还能有效地压制“飞点”的影响。
第四针对平滑滤波过程时间尺度对滤波结果的影响,利用扩散平滑过程中信号与噪声能量的变化特点,提出了利用扩散平衡确定扩散时间尺度的方法。模拟与实测数据显示:(1)利用扩散平滑与扩散平衡时间尺度能使含噪模拟曲线平滑后曲线高精度地逼近了原始曲线;(2)在各向异性扩散平滑中存在明显的DB极小值或零值点。
第五针对浅层不均匀体电磁观测的影响,我们利用各向异性扩散的定向扩散能力以及浅层不均匀体干扰的特性(高频特征),研究利用各向异性扩散的静态效应改正方法,并提出了新的扩散模型和扩散系数函数,研究讨论了在电磁观测处理中的梯度算子与拉氏算子的计算方法。实测数据测试表明本文方法优于经典的EMAP方法,有效地压制了浅层不均匀体的干扰,并提取到深部的趋势信息与浅部的局部信息,而EMAP方法虽然也能提取到深部的趋势信息,但在浅部仍然可以看到还有许多干扰存在。
The anisotropic diffusion(AD) based on the partial differential equations is one of the extensive used method in the image processing due to possess the directional diffusivity from twenty century ninety years. Especially the anisotropic diffusion, as a nonlinear method, possesses of computing facility, moreover, the partial differential equations can be regard as local filter iteration of exiguity neighbour, and make a new filter method by combined with existing filter method in the image de-noise and segment processing. The directional diffusivity of anisotropic diffusion is introduced to geophysical data processing, and achieves the nonlinear processing of electromagnetic signal.
The first the relation of AD model and the energy variety of image is educed by thermal diffusion and the diffusion equations based energy flux, and proves the image processing by energy flux sufficing maximum-minimum principle, the variety of image energy is equivalent to that of image intensity. The variety character of image and noise energy are studied. The concept of image diffusion balance is defined and achieves the efficient estimation of diffusion time scale by diffusion balance of thermal diffusion introduced to anisotropic diffusion. The result of simulation test indicates the method proposed in the paper can remove noise and protects the character of signal and achieves preferable vision effect. The novel method need not estimate intensity of noise and can adapt image relatively with MSE method. The results of test indicate its validity.
The second the anisotropic diffusion is introduced to the impedance estimation of electromagnetic measurement by the relation of Bayes statistic, Robust statistic and anisotropic diffusion, the anisotropic diffusion equation is modified to adapt to impedance estimation, the modification equation improves the stability of estimation, and the convergence of general Robust estimation is one of ADR result.
The third the curve smoothing of electromagnetic measurement based anisotropic diffusion and local monotony diffusion is proposed. In order to remove "outliers" noise and instability in the diffusion, the application of rational function in the signal smoothing and the relation with linear and nonlinear filter is studies, the stability of diffusion and the ability of removing outliers noise is improved by altering grads estimation method.
The fourth estimation method of diffusion time scale is proposed in order to remove the effect of time scale to filter result. The results of simulation and field data test indicate: (1) the noisy simulation curve can approach to the free curve highly precision by diffusion time scale. (2)the DB minimum or zero value point is existence obviously in the anisotropic diffusion smoothing.
The fifth the correction method of station effect in electromagnetic measurement is studied by the directional diffusivity of anisotropic diffusion and the character of asymmetry in the shallow earth, and a new diffusion model and diffusion coefficient function are proposed. The computer method of grads operator is discussed. The field data test indicates that the proposed method can remove the interference of shallow asymmetry, extract trend information in deep earth and local information shallow earth and precede the classical EMAP method.
首先通过热扩散及热扩散方程、基于能量流的扩散方程,导出了向异性扩散模型与图像能量的变化过程之间的关系,并证明了利用能量流方法获得的图像处理过程同样满足极大极小原理。也证明了若能量有限的图像,灰度均值为零,则图像平均能量的变化等于图像灰度均方差的变化。研究了在图像的扩散处理中,图像和噪声的能量变化过程与特征。然后把热物理扩散中的扩散平衡引入到图像处理的各向异性扩散中,定义了图像扩散平衡的概念,实现了最佳扩散时间尺度的稳定有效估计。模拟测试表明本文提出的方法能在保护信号特征的同时在噪声的压制也能达到较好的可视效果,即特征的保护与噪声压制上能达到一个合理的平衡。相对MSE及其它方法不需估计噪声强度(方差),能自适应于图像,运行简单稳定,即使在低信噪比下也能获得很好的估计效果。
其次利用贝叶斯统计、稳健统计与各向异性扩散联系,把各向异性扩散引入到电磁观测的阻抗估计中去,修改了适于阻抗估计的各向异性扩散方程,提高了阻抗估计的稳定性。证明了常规Robust估计的收敛值是只是ADR估计中解之一。
第三通过把各向异性扩散和局部单调扩散引入到地球物理领域中,提出了基于各向异性扩散的曲线平滑方法。为了使消除随机噪声与“飞点”噪声能够在扩散中同时进行,并消除“飞点”噪声引起的扩散行为的不稳定性,研究有理函数在信号平滑处理中的应用,以及它与线性滤波和非线性滤波区别及其特点。并通过改变梯度估计的方式,不仅提高了扩散行为的稳定性,还能有效地压制“飞点”的影响。
第四针对平滑滤波过程时间尺度对滤波结果的影响,利用扩散平滑过程中信号与噪声能量的变化特点,提出了利用扩散平衡确定扩散时间尺度的方法。模拟与实测数据显示:(1)利用扩散平滑与扩散平衡时间尺度能使含噪模拟曲线平滑后曲线高精度地逼近了原始曲线;(2)在各向异性扩散平滑中存在明显的DB极小值或零值点。
第五针对浅层不均匀体电磁观测的影响,我们利用各向异性扩散的定向扩散能力以及浅层不均匀体干扰的特性(高频特征),研究利用各向异性扩散的静态效应改正方法,并提出了新的扩散模型和扩散系数函数,研究讨论了在电磁观测处理中的梯度算子与拉氏算子的计算方法。实测数据测试表明本文方法优于经典的EMAP方法,有效地压制了浅层不均匀体的干扰,并提取到深部的趋势信息与浅部的局部信息,而EMAP方法虽然也能提取到深部的趋势信息,但在浅部仍然可以看到还有许多干扰存在。
The anisotropic diffusion(AD) based on the partial differential equations is one of the extensive used method in the image processing due to possess the directional diffusivity from twenty century ninety years. Especially the anisotropic diffusion, as a nonlinear method, possesses of computing facility, moreover, the partial differential equations can be regard as local filter iteration of exiguity neighbour, and make a new filter method by combined with existing filter method in the image de-noise and segment processing. The directional diffusivity of anisotropic diffusion is introduced to geophysical data processing, and achieves the nonlinear processing of electromagnetic signal.
The first the relation of AD model and the energy variety of image is educed by thermal diffusion and the diffusion equations based energy flux, and proves the image processing by energy flux sufficing maximum-minimum principle, the variety of image energy is equivalent to that of image intensity. The variety character of image and noise energy are studied. The concept of image diffusion balance is defined and achieves the efficient estimation of diffusion time scale by diffusion balance of thermal diffusion introduced to anisotropic diffusion. The result of simulation test indicates the method proposed in the paper can remove noise and protects the character of signal and achieves preferable vision effect. The novel method need not estimate intensity of noise and can adapt image relatively with MSE method. The results of test indicate its validity.
The second the anisotropic diffusion is introduced to the impedance estimation of electromagnetic measurement by the relation of Bayes statistic, Robust statistic and anisotropic diffusion, the anisotropic diffusion equation is modified to adapt to impedance estimation, the modification equation improves the stability of estimation, and the convergence of general Robust estimation is one of ADR result.
The third the curve smoothing of electromagnetic measurement based anisotropic diffusion and local monotony diffusion is proposed. In order to remove "outliers" noise and instability in the diffusion, the application of rational function in the signal smoothing and the relation with linear and nonlinear filter is studies, the stability of diffusion and the ability of removing outliers noise is improved by altering grads estimation method.
The fourth estimation method of diffusion time scale is proposed in order to remove the effect of time scale to filter result. The results of simulation and field data test indicate: (1) the noisy simulation curve can approach to the free curve highly precision by diffusion time scale. (2)the DB minimum or zero value point is existence obviously in the anisotropic diffusion smoothing.
The fifth the correction method of station effect in electromagnetic measurement is studied by the directional diffusivity of anisotropic diffusion and the character of asymmetry in the shallow earth, and a new diffusion model and diffusion coefficient function are proposed. The computer method of grads operator is discussed. The field data test indicates that the proposed method can remove the interference of shallow asymmetry, extract trend information in deep earth and local information shallow earth and precede the classical EMAP method.
引文
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