非平稳信号的压缩算法研究
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摘要
信号分析在数据压缩等方面具有极其重要的意义,尤其是对非平稳信号有效的分析方法更是学术和工程界关注的热点问题之一。传统信号分析方法从单一的时域或频域对信号进行描述,不能提供准确的时间和频率的定位功能,也无法提供局部时间段的频域特征信息。而对于非平稳信号,其参数随时间在不断变化,因此单一的时域或频域分析法无法对其进行有效的处理。
本文从数值逼近理论的角度出发,针对具有缓慢变化趋势的非平稳信号进行了压缩算法及实现等内容的研究。论文主要工作包括：
1.提出了一种基于分类和曲线拟合的非平稳信号分解算法。针对具有缓慢单调变化趋势的非平稳信号,采用改进的经验模态分解算法对信号做预处理,以消去信号中的噪声,并利用曲线拟合对信号的主要规律进行描述。针对超光谱图像数据量大、谱线间数据相关性差等特点,提出分类算法将图像数据分为主光谱区域数据和非主光谱区域数据,不同类别数据采用不同的处理方法,最后获得数据的有效表达。
2.提出了经验数据分解算法。由非平稳数据的多项式描述引出经验数据分解算法的思想,利用局部区域数据的均值为基准,用函数表示数据的主要变化规律,从而将局部数据表示为函数与误差之和。建立了经验数据分解的一般结构,给出了经验数据分解结构中分解滤波器的设计准则。
3.给出了经验数据分解算法的实现思路,分别利用自适应优化法和三次样条插值法设计分解算法中的预测滤波器。针对连续色调图像数据和非连续色调图像数据的特点,提出了不同的分解结构,并通过仿真实验分析了经验数据分解算法的特点。
4.为了提高非平稳信号编译码系统的效率,对系统中的数据分解模块和比特平面编译码模块提出了并行算法,并给出了两模块实现并行算法的架构。仿真实验分析了编译码时间与内核数量之间的关系。
Finding an effective analytical method on non-stationary signal is one of the hot issues in both academia and engineering circle and it is of extremely important significance to signal analysis for data compression. Traditional signal processing methods describe the signals in the time or frequency domain separately. It provides neither precise time or frequency positioning nor information of frequency at any local time segment. Since parameters of non-stationary signals vary by time, the traditional approaches are less effective.
This thesis gives an intensive study on non-stationary signal compression algorithm and its implementation based on the theories of numerical approaching. The main work is summarized as follows:
1. Based on curve fitting and classification a non-stationary decomposition algorithm is presented. Studies on non-stationary signals with slow monotonic change have been performed. With the improved empirical mode decomposition algorithm, it is able to pre-process signals and to eliminate noise in the signals. The main rule of the change is described by the curve fitting. The classification algorithm is used to decompose the spectrum images into two categories as main or non-main spectrum domain, since the spectrum images have large volumes of data and the data correlation is poor. Different methods will be applied to each data domain and effective description of observation data will be obtained.
2. The empirical data decomposition algorithm is presented. The idea of the empirical data decomposition was extracted by polynomial description of the non-stationary data. The mean of the local area data is used as a benchmark and the main change rule of data is described by the function. The sum of the function and the error denotes the local area data. The general structure of the empirical data decomposition is founded, and the design rules of the analysis filter are presented.
3. The detailed implementation process of the empirical data decomposition is provided. The parameters of the predictive filter in the algorithm are designed by use of adaptive optimization and cubic spline interpolation functions, respectively. Different decomposition structures are presented for continuous-tone image data and non-continuous tone image data. The characteristics of empirical data decomposition algorithm are analyzed by simulation.
4. A parallel algorithm for data decomposition module and bit plane encoding and decoding module is proposed to improve efficiency of non-stationary signal encoding and decoding system. The parallel algorithm framework for the two modules is presented. Relations between the time of encoding and decoding and the number of kernel are analyzed by simulation.
本文从数值逼近理论的角度出发,针对具有缓慢变化趋势的非平稳信号进行了压缩算法及实现等内容的研究。论文主要工作包括：
1.提出了一种基于分类和曲线拟合的非平稳信号分解算法。针对具有缓慢单调变化趋势的非平稳信号,采用改进的经验模态分解算法对信号做预处理,以消去信号中的噪声,并利用曲线拟合对信号的主要规律进行描述。针对超光谱图像数据量大、谱线间数据相关性差等特点,提出分类算法将图像数据分为主光谱区域数据和非主光谱区域数据,不同类别数据采用不同的处理方法,最后获得数据的有效表达。
2.提出了经验数据分解算法。由非平稳数据的多项式描述引出经验数据分解算法的思想,利用局部区域数据的均值为基准,用函数表示数据的主要变化规律,从而将局部数据表示为函数与误差之和。建立了经验数据分解的一般结构,给出了经验数据分解结构中分解滤波器的设计准则。
3.给出了经验数据分解算法的实现思路,分别利用自适应优化法和三次样条插值法设计分解算法中的预测滤波器。针对连续色调图像数据和非连续色调图像数据的特点,提出了不同的分解结构,并通过仿真实验分析了经验数据分解算法的特点。
4.为了提高非平稳信号编译码系统的效率,对系统中的数据分解模块和比特平面编译码模块提出了并行算法,并给出了两模块实现并行算法的架构。仿真实验分析了编译码时间与内核数量之间的关系。
Finding an effective analytical method on non-stationary signal is one of the hot issues in both academia and engineering circle and it is of extremely important significance to signal analysis for data compression. Traditional signal processing methods describe the signals in the time or frequency domain separately. It provides neither precise time or frequency positioning nor information of frequency at any local time segment. Since parameters of non-stationary signals vary by time, the traditional approaches are less effective.
This thesis gives an intensive study on non-stationary signal compression algorithm and its implementation based on the theories of numerical approaching. The main work is summarized as follows:
1. Based on curve fitting and classification a non-stationary decomposition algorithm is presented. Studies on non-stationary signals with slow monotonic change have been performed. With the improved empirical mode decomposition algorithm, it is able to pre-process signals and to eliminate noise in the signals. The main rule of the change is described by the curve fitting. The classification algorithm is used to decompose the spectrum images into two categories as main or non-main spectrum domain, since the spectrum images have large volumes of data and the data correlation is poor. Different methods will be applied to each data domain and effective description of observation data will be obtained.
2. The empirical data decomposition algorithm is presented. The idea of the empirical data decomposition was extracted by polynomial description of the non-stationary data. The mean of the local area data is used as a benchmark and the main change rule of data is described by the function. The sum of the function and the error denotes the local area data. The general structure of the empirical data decomposition is founded, and the design rules of the analysis filter are presented.
3. The detailed implementation process of the empirical data decomposition is provided. The parameters of the predictive filter in the algorithm are designed by use of adaptive optimization and cubic spline interpolation functions, respectively. Different decomposition structures are presented for continuous-tone image data and non-continuous tone image data. The characteristics of empirical data decomposition algorithm are analyzed by simulation.
4. A parallel algorithm for data decomposition module and bit plane encoding and decoding module is proposed to improve efficiency of non-stationary signal encoding and decoding system. The parallel algorithm framework for the two modules is presented. Relations between the time of encoding and decoding and the number of kernel are analyzed by simulation.
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