基于小波分析的测量信号处理技术研究
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摘要
在实际生产生活中,人们经常要面对大量的动态测量信号处理问题,实时高效准确的处理结果一直是人们所追求的目标。小波分析理论由于自身所具有的分时分频精细表达和多尺度多分辨率分析等独特优势,已经逐渐发展成为动态测量信号处理领域中的重要技术手段。
然而,小波分析理论在实际应用中仍旧存在着一些限制和缺陷,其中比较突出的有:如何选择最合适的小波基函数;如何选择有用信号小波系数的适当阈值;如何解决经典DWT导致的方向性差以及平移不变性的缺失等等。对这些问题的妥善解决是保证小波分析理论在实际工程中得以实用化的关键,具有重要的理论价值和工程意义。
本文在大量查阅国内外相关文献的基础上,对小波函数的特性、小波变换的性质以及相关动态测量信号的特点进行了深入研究,提出了一些有成效的解决措施,通过数值计算证明了设计思路的正确性,并在实际工程的应用中取得了满意效果。
在详细分析各种常见小波的特性,深入研究选择小波基函数的七种测量标准基础之上,提出了一种优化方案,通过设计最大化能量-Shannon熵比和最小化极值信息测量指标,来用于评价最合适小波基函数的选择。在充分发挥原有七种选择标准的优点同时,也很好的解决了它们之间的冲突。数值实验表明,所设计的综合标准简单实用,易于理解,符合小波基函数的选择要求。
通过详细分析小波变换去噪的机理,针对经典小波去噪技术的过程和特点展开讨论。鉴于小波阈值去噪法在最小均方误差意义下可达近似最优,且框架小波可借助相关信息来补偿因噪声干扰而丢失的某些含有重要信息的小波系数,提出了一种基于小波阈值去噪法的改进SURE- LET框架小波去噪技术,数值实验表明,该技术能自适应寻找全局最优,避免过早收敛,在保证恢复信号全貌的同时实现去噪。在实际工程中的应用也取得了较好效果。
详细研究和分析各种基于小波变换模极大值的信号检测技术,发现了这类技术对于弱态信号检测能力很差,且对方向性的较高要求导致二维图像检测结果产生伪边界现象。通过对小波系数相关性去噪法的分析,将小波熵引入到信号检测技术领域,选择复Morlet小波作为小波基函数,提出了一种适用于检测微弱信号边缘特性的复Morlet小波熵检测技术,数值试验和工程应用均表明,对于微弱信号的检测效果明显好于小波变换模极大值信号检测法。
通过详细研究和分析各种基于标准线性小波变换的图像信号融合技术,提出了一种基于无下采样极值提升方案的非线性离散小波变换的融合技术。首先基于小波变换模极大值去噪思想,设计了极值提升小波方案,在此基础上利用等效易位定理进行无下采样移不变扩展,最后确定了相应的融合规则。数值试验表明,该技术计算复杂度小、构造简单易实现、具有较好的去噪效果和融合稳定性,对系统测量精度的提高帮助更大。
通过对各类图像信号质量评价标准的详细分析和研究,基于人类视觉系统的要求,提出一个基于小波系数的图像质量评价标准,即小波子带的加权归一化均方差,借助每个图像子带中小波系数的加权归一化均方差的总和来评价图像的质量。所选择的每一个图像子带的权重都反映了其在图像上的感知刺激,可自适应地测量图像的整体和局部变形。数值试验表明,该标准与HVS评价效果相一致,是一种较好的全参考客观质量评价标准。
To get an accurate and real-time process result is always a best target what people hope. The Wavelet analysis theory is gradually developing to become one of important technology in the dynamic measurement signal process field by its advantage of multiresolution and multidimension analysis on time-frequent.
However, there are many problems which still limit the practice application of Wavelet analysis theory, such as the problem how choose the rightist Wavelet base function and the best threshold value, shortage of the directionality and the shift invariance due to classics DWT, and so on. How to solve these problems has been the key that ensure the Wavelet analysis theory to become utility in practical applications. It must show great academic value and practical importance.
Through collecting and studying of many documents about Wavelet analysis theory, this thesis makes studies of the characteristic of Wavelet base function, the character of Wavelet Transform and the property of correlation dynamic measurement signal. Then, some effective resolving methods and the accurate real-time improvement algorithms are proposed, the correctness of this idea is testified by some numerical experiments.
The basis properties of various wavelet families are first introduced. Seven measures are then studied for base wavelet selection. To resolve a conflict that the results obtained from these measures are not consistent, two comprehensive optimization index, namely the maximum energy-to-Shannon entropy ratio and the minimum minmax information measure, are developed and evaluated for appropriate base wavelet selection. Numerical experiment shows they properly meet with need of base wavelet selection.
The denoising mechanism of Wavelet Transform is detailed analysis, process and characteristic of the classics Wavelet-based denoising technology is studied. Because the Wavelet-based Threshold value deniosing can reach similar optimum on minimum mean square error, and framelet transform can remedy some wavelet coefficients with vital information. So a framelet denoising technology with the improvement SURE-LET based on Wavelet-based Threshold value deniosing is proposed. Numerical experiment shows it can seek global optimum by self- adapting and imply denoising based on keep the signal completeness.
The various maximum-modulus of Wavelet Transform-based signal detection technology are detailedly studied and found not to detect for faint signal. Following coefficient correlation of Wavelet Transform-based, Wavelet entropy is lead into signal detection technology field, and choosing complex Morlet as the rightest Wavelet base function. So a complex Morlet Wavelet-based Wavelet entropy detection technology for faint signal is proposed. Numerical experiment shows the effects of this algorithm obvious surpass over maximum-modulus of Wavelet Transform-based signal detection technology.
By studying and analysing the various standard linearity Wavelet-based image signal fusion technology detailedly, a maximum lifting scheme-based undecima- ted nonlinearity discrete wavelet transform signal fusion technology is proposed. First maximum lifting scheme is designed according to maximum-modulus of Wavelet Transform. Then the shift invariance expansion is carried out by Noble Identities theorem based on maximum lifting scheme. At last fusion rule is settled. The numerical experiment shows the merit of this algorithm is only involving in integer calculation, and better for the hardware realization.
According to the concepts of Human Visual System(HVS), the weight for each subband is chosen to reflect its perceptual impact on the image, which measures the distortions in the global structure and local details of an image in a more balanced way automatically. So a Image Quality Metric(IQM)called Weighted Normalized Mean Square Error of wavelet subbands(WNMSE)is proposed. WNMSE uses the weighted sum of the normalized mean square errors of wavelet coefficients to assess the quality of an image, and can be calculated in the middle of compression without reconstructing the image. Numerical experiment shows that WNMSE has better performance than both the legacy Peak Signal-to- Noise Ratio(PSNR)and the well referenced Structural SIMilarity(SSIM).
然而,小波分析理论在实际应用中仍旧存在着一些限制和缺陷,其中比较突出的有:如何选择最合适的小波基函数;如何选择有用信号小波系数的适当阈值;如何解决经典DWT导致的方向性差以及平移不变性的缺失等等。对这些问题的妥善解决是保证小波分析理论在实际工程中得以实用化的关键,具有重要的理论价值和工程意义。
本文在大量查阅国内外相关文献的基础上,对小波函数的特性、小波变换的性质以及相关动态测量信号的特点进行了深入研究,提出了一些有成效的解决措施,通过数值计算证明了设计思路的正确性,并在实际工程的应用中取得了满意效果。
在详细分析各种常见小波的特性,深入研究选择小波基函数的七种测量标准基础之上,提出了一种优化方案,通过设计最大化能量-Shannon熵比和最小化极值信息测量指标,来用于评价最合适小波基函数的选择。在充分发挥原有七种选择标准的优点同时,也很好的解决了它们之间的冲突。数值实验表明,所设计的综合标准简单实用,易于理解,符合小波基函数的选择要求。
通过详细分析小波变换去噪的机理,针对经典小波去噪技术的过程和特点展开讨论。鉴于小波阈值去噪法在最小均方误差意义下可达近似最优,且框架小波可借助相关信息来补偿因噪声干扰而丢失的某些含有重要信息的小波系数,提出了一种基于小波阈值去噪法的改进SURE- LET框架小波去噪技术,数值实验表明,该技术能自适应寻找全局最优,避免过早收敛,在保证恢复信号全貌的同时实现去噪。在实际工程中的应用也取得了较好效果。
详细研究和分析各种基于小波变换模极大值的信号检测技术,发现了这类技术对于弱态信号检测能力很差,且对方向性的较高要求导致二维图像检测结果产生伪边界现象。通过对小波系数相关性去噪法的分析,将小波熵引入到信号检测技术领域,选择复Morlet小波作为小波基函数,提出了一种适用于检测微弱信号边缘特性的复Morlet小波熵检测技术,数值试验和工程应用均表明,对于微弱信号的检测效果明显好于小波变换模极大值信号检测法。
通过详细研究和分析各种基于标准线性小波变换的图像信号融合技术,提出了一种基于无下采样极值提升方案的非线性离散小波变换的融合技术。首先基于小波变换模极大值去噪思想,设计了极值提升小波方案,在此基础上利用等效易位定理进行无下采样移不变扩展,最后确定了相应的融合规则。数值试验表明,该技术计算复杂度小、构造简单易实现、具有较好的去噪效果和融合稳定性,对系统测量精度的提高帮助更大。
通过对各类图像信号质量评价标准的详细分析和研究,基于人类视觉系统的要求,提出一个基于小波系数的图像质量评价标准,即小波子带的加权归一化均方差,借助每个图像子带中小波系数的加权归一化均方差的总和来评价图像的质量。所选择的每一个图像子带的权重都反映了其在图像上的感知刺激,可自适应地测量图像的整体和局部变形。数值试验表明,该标准与HVS评价效果相一致,是一种较好的全参考客观质量评价标准。
To get an accurate and real-time process result is always a best target what people hope. The Wavelet analysis theory is gradually developing to become one of important technology in the dynamic measurement signal process field by its advantage of multiresolution and multidimension analysis on time-frequent.
However, there are many problems which still limit the practice application of Wavelet analysis theory, such as the problem how choose the rightist Wavelet base function and the best threshold value, shortage of the directionality and the shift invariance due to classics DWT, and so on. How to solve these problems has been the key that ensure the Wavelet analysis theory to become utility in practical applications. It must show great academic value and practical importance.
Through collecting and studying of many documents about Wavelet analysis theory, this thesis makes studies of the characteristic of Wavelet base function, the character of Wavelet Transform and the property of correlation dynamic measurement signal. Then, some effective resolving methods and the accurate real-time improvement algorithms are proposed, the correctness of this idea is testified by some numerical experiments.
The basis properties of various wavelet families are first introduced. Seven measures are then studied for base wavelet selection. To resolve a conflict that the results obtained from these measures are not consistent, two comprehensive optimization index, namely the maximum energy-to-Shannon entropy ratio and the minimum minmax information measure, are developed and evaluated for appropriate base wavelet selection. Numerical experiment shows they properly meet with need of base wavelet selection.
The denoising mechanism of Wavelet Transform is detailed analysis, process and characteristic of the classics Wavelet-based denoising technology is studied. Because the Wavelet-based Threshold value deniosing can reach similar optimum on minimum mean square error, and framelet transform can remedy some wavelet coefficients with vital information. So a framelet denoising technology with the improvement SURE-LET based on Wavelet-based Threshold value deniosing is proposed. Numerical experiment shows it can seek global optimum by self- adapting and imply denoising based on keep the signal completeness.
The various maximum-modulus of Wavelet Transform-based signal detection technology are detailedly studied and found not to detect for faint signal. Following coefficient correlation of Wavelet Transform-based, Wavelet entropy is lead into signal detection technology field, and choosing complex Morlet as the rightest Wavelet base function. So a complex Morlet Wavelet-based Wavelet entropy detection technology for faint signal is proposed. Numerical experiment shows the effects of this algorithm obvious surpass over maximum-modulus of Wavelet Transform-based signal detection technology.
By studying and analysing the various standard linearity Wavelet-based image signal fusion technology detailedly, a maximum lifting scheme-based undecima- ted nonlinearity discrete wavelet transform signal fusion technology is proposed. First maximum lifting scheme is designed according to maximum-modulus of Wavelet Transform. Then the shift invariance expansion is carried out by Noble Identities theorem based on maximum lifting scheme. At last fusion rule is settled. The numerical experiment shows the merit of this algorithm is only involving in integer calculation, and better for the hardware realization.
According to the concepts of Human Visual System(HVS), the weight for each subband is chosen to reflect its perceptual impact on the image, which measures the distortions in the global structure and local details of an image in a more balanced way automatically. So a Image Quality Metric(IQM)called Weighted Normalized Mean Square Error of wavelet subbands(WNMSE)is proposed. WNMSE uses the weighted sum of the normalized mean square errors of wavelet coefficients to assess the quality of an image, and can be calculated in the middle of compression without reconstructing the image. Numerical experiment shows that WNMSE has better performance than both the legacy Peak Signal-to- Noise Ratio(PSNR)and the well referenced Structural SIMilarity(SSIM).
引文
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