图像盲源分离的多尺度几何分析方法
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摘要
图像在采集、使用和保存等过程中会出现污损、杂斑、噪声和叠加等退化现象,退化图像可以认为是由不同的、相互独立的图像信号经未知的混合过程(混合方式)形成的混合图像,对混合图像的分离过程与盲源分离(Blind Source Separation, BSS)问题模型的假设是一致的。为此,BSS技术在图像处理方面有着广阔的应用前景,是图像处理的有力工具。
与此同时,当前不同研究领域的学者针对信号处理提出了图像多尺度几何分析理论(Multiscale Geometry Analysis, MGA)这一新的数学工具,其能稀疏表示图像。将多尺度几何分析理论应用于图像盲源分离,丰富了图像盲源分离算法,有效地推进盲源分离技术的实际应用。
为此,本论文紧密围绕当前盲源分离方法研究的热点和难点,充分利用图像多尺度几何分析理论,提出了图像盲源分离的多尺度几何分析方法,并重点研究基于第二代Curvelet多尺度几何分析的图像盲源分离方法。具体研究内容及取得的成果如下:
1.针对实际接收到的图像信号不稀疏的一般情况,研究图像多尺度几何分析理论。着重研究第二代Curvelet多尺度几何分析,对信号进行稀疏表示。通过仿真实验对Curvelet的分解过程进行了分析,表明Curvelet能达到对图像信号最稀疏的表示。
2.针对适定情况,提出了基于Curvelet多尺度几何分析的图像盲源分离方法。该方法以Curvelet分解后的子图像的峭度作为信号稀疏性判据,选取最稀疏子图像,在稀疏域中实施盲源分离。仿真实验证明该方法可行和有效,并很大程度上提高了盲源分离算法的收敛速度和分离精度。
3.针对图像盲源分离的初始化问题,提出了基于Curvelet多尺度几何分析的盲源分离初始化方法。该方法利用Curvelet多尺度几何分析后信号的稀疏性特点,采用了C-means聚类方法寻求混合矩阵估计值,把该估计值作为算法初始值。该方法克服了盲源分离算法初始值选取的随意性,避免算法陷入局部最小,提高了分离精度。
4.针对欠定情况,提出了基于Curvelet多尺度几何分析的欠定-适定联合盲源分离方法。该方法利用稀疏化后信号的一些特性,构造中间混合矩阵,取得预分离信号,把欠定问题转化为适定问题。仿真实验表明,该方法使欠定情况下的盲源分离取得了良好的效果。
5.针对含噪情况,提出了基于Curvelet多尺度几何分析的含噪图像盲源分离方法。该方法利用Curvelet多尺度几何分析良好的降噪性能,以及Curvelet稀疏化后高频子图像服从拉普拉斯分布的特点,构造了位置相关的自适应数学形态学降噪算子,对含噪混合图像进行降噪预处理,然后采用传统盲源分离算法实施分离。仿真实验表明,该方法取得了良好的分离效果,提高了盲源分离方法对噪声环境的适应性。
本论文对推进盲源分离技术在图像处理中的实际应用具有重要的研究意义,研究成果可应用于图像增强、图像去噪、图像识别和图像分离等图像处理领域。
In real life, the image degenerate problem surely exists during using and conserving, for example: blurred, parti-colored, noised and mixed, etc. Those degenerated images can be looked as the mixed images by mutually independent images without mixing performance. The image separation processing is in accordance with the model of blind source separation (BSS). Therefore, BSS technology has a wide application prospects in the field of image processing.
Just like current, scholars in different researching fields have put forward novel ideas and algorithms on account of signal processing, for example: image multiscale geometry analysis (MGA). Images have better sparsity in transform domain. Image sparsity has become a new mathematic tool for BSS, and breathes new vitality into BSS research. BSS algorithms become more and more diversified, and shall be applied in real life.
Therefore, those research results of image multiscale geometry analysis would be utilized fully in this dissertation. Tightly couple with the hotspot and difficult point of BSS, extensively research multiscale geometry analysis, and focus on image BSS based on the second generation Curvelet sparse representation. Detail research contents as follows:
1. In accordance with the general conditions that those received image signals are non-sparse, utilize image multiscale geometry analysis to make image signals sparse. And focus on researching the second generation Curvelet sparse representation. Analyse the decomposition process of Curvelet transform, certify that it can representate image signals most sparse.
2. Research on image BSS based on Curvelet sparse representation in determined conditions. BSS can be implemented in sparse domain. The algorithm uses the kurtosis of sub-images as sparsity criterion, then the most sparse sub-imges can be selected. Simulation experiments certify that the algorithm is feasible and effective.
3. Research on image BSS initialization problem. According to signals sparsity by Curvelet transform, the mixed matrix can be estimated with C-means cluster analysis, and the estimated value is looked as initial value of BSS algorithm. The initialization algorithm improves separation rate of convergence and separation pricision.
4. Research on image BSS based on Curvelet sparse representation in underdetermined circumstance. According to signals sparsity by Curvelet transform, underdetermined-determined union separation algorithm has been put forward. The algorithm constructs an intermediate mixed matrix, and turns the underdetermined problem into determinted problem. Simulation experiments certify that the algorithm has a good separation result.
5. Research on noised-image BSS based on Curvelet sparse representation. Construct an adaptive noise operator with mathematical morphology, and pre-process noised mixed images wjth the noise operator, then separate mixed images with traditional BSS algorithm. The novel algorithm promotes BSS suit to noising circumstance.
The research results in this diseertation can be applied to image processing field, for example: image enhancement, image denosing, image identification, and image separation, etc.
与此同时,当前不同研究领域的学者针对信号处理提出了图像多尺度几何分析理论(Multiscale Geometry Analysis, MGA)这一新的数学工具,其能稀疏表示图像。将多尺度几何分析理论应用于图像盲源分离,丰富了图像盲源分离算法,有效地推进盲源分离技术的实际应用。
为此,本论文紧密围绕当前盲源分离方法研究的热点和难点,充分利用图像多尺度几何分析理论,提出了图像盲源分离的多尺度几何分析方法,并重点研究基于第二代Curvelet多尺度几何分析的图像盲源分离方法。具体研究内容及取得的成果如下:
1.针对实际接收到的图像信号不稀疏的一般情况,研究图像多尺度几何分析理论。着重研究第二代Curvelet多尺度几何分析,对信号进行稀疏表示。通过仿真实验对Curvelet的分解过程进行了分析,表明Curvelet能达到对图像信号最稀疏的表示。
2.针对适定情况,提出了基于Curvelet多尺度几何分析的图像盲源分离方法。该方法以Curvelet分解后的子图像的峭度作为信号稀疏性判据,选取最稀疏子图像,在稀疏域中实施盲源分离。仿真实验证明该方法可行和有效,并很大程度上提高了盲源分离算法的收敛速度和分离精度。
3.针对图像盲源分离的初始化问题,提出了基于Curvelet多尺度几何分析的盲源分离初始化方法。该方法利用Curvelet多尺度几何分析后信号的稀疏性特点,采用了C-means聚类方法寻求混合矩阵估计值,把该估计值作为算法初始值。该方法克服了盲源分离算法初始值选取的随意性,避免算法陷入局部最小,提高了分离精度。
4.针对欠定情况,提出了基于Curvelet多尺度几何分析的欠定-适定联合盲源分离方法。该方法利用稀疏化后信号的一些特性,构造中间混合矩阵,取得预分离信号,把欠定问题转化为适定问题。仿真实验表明,该方法使欠定情况下的盲源分离取得了良好的效果。
5.针对含噪情况,提出了基于Curvelet多尺度几何分析的含噪图像盲源分离方法。该方法利用Curvelet多尺度几何分析良好的降噪性能,以及Curvelet稀疏化后高频子图像服从拉普拉斯分布的特点,构造了位置相关的自适应数学形态学降噪算子,对含噪混合图像进行降噪预处理,然后采用传统盲源分离算法实施分离。仿真实验表明,该方法取得了良好的分离效果,提高了盲源分离方法对噪声环境的适应性。
本论文对推进盲源分离技术在图像处理中的实际应用具有重要的研究意义,研究成果可应用于图像增强、图像去噪、图像识别和图像分离等图像处理领域。
In real life, the image degenerate problem surely exists during using and conserving, for example: blurred, parti-colored, noised and mixed, etc. Those degenerated images can be looked as the mixed images by mutually independent images without mixing performance. The image separation processing is in accordance with the model of blind source separation (BSS). Therefore, BSS technology has a wide application prospects in the field of image processing.
Just like current, scholars in different researching fields have put forward novel ideas and algorithms on account of signal processing, for example: image multiscale geometry analysis (MGA). Images have better sparsity in transform domain. Image sparsity has become a new mathematic tool for BSS, and breathes new vitality into BSS research. BSS algorithms become more and more diversified, and shall be applied in real life.
Therefore, those research results of image multiscale geometry analysis would be utilized fully in this dissertation. Tightly couple with the hotspot and difficult point of BSS, extensively research multiscale geometry analysis, and focus on image BSS based on the second generation Curvelet sparse representation. Detail research contents as follows:
1. In accordance with the general conditions that those received image signals are non-sparse, utilize image multiscale geometry analysis to make image signals sparse. And focus on researching the second generation Curvelet sparse representation. Analyse the decomposition process of Curvelet transform, certify that it can representate image signals most sparse.
2. Research on image BSS based on Curvelet sparse representation in determined conditions. BSS can be implemented in sparse domain. The algorithm uses the kurtosis of sub-images as sparsity criterion, then the most sparse sub-imges can be selected. Simulation experiments certify that the algorithm is feasible and effective.
3. Research on image BSS initialization problem. According to signals sparsity by Curvelet transform, the mixed matrix can be estimated with C-means cluster analysis, and the estimated value is looked as initial value of BSS algorithm. The initialization algorithm improves separation rate of convergence and separation pricision.
4. Research on image BSS based on Curvelet sparse representation in underdetermined circumstance. According to signals sparsity by Curvelet transform, underdetermined-determined union separation algorithm has been put forward. The algorithm constructs an intermediate mixed matrix, and turns the underdetermined problem into determinted problem. Simulation experiments certify that the algorithm has a good separation result.
5. Research on noised-image BSS based on Curvelet sparse representation. Construct an adaptive noise operator with mathematical morphology, and pre-process noised mixed images wjth the noise operator, then separate mixed images with traditional BSS algorithm. The novel algorithm promotes BSS suit to noising circumstance.
The research results in this diseertation can be applied to image processing field, for example: image enhancement, image denosing, image identification, and image separation, etc.
引文
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