多尺度分析与压缩感知理论在图像处理中的应用研究
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摘要
多尺度几何分析理论一直是信号处理的重点内容,它通过时域和频域来联合表示信号,是分析非平稳信号的有力工具。它通过基函数的伸缩、平移等运算对信号进行有效多尺度细化分析,是一种非常灵活、快速和有效的高维信号处理方法,能高效从信号中提取有用信息。多尺度几何分析主要分为非自适应多尺度几何分析与自适应多尺度几何分析两类。其中,非自适应多尺度几何分析主要包括Ridgelet变换、Curvelet变换以及Contourlet变换；自适应多尺度几何分析主要包括Brushlet变换、Wedgelet变换、Beamlet变换、Bandelet变换、Directionlet变换、Shearlet变换、Chordlet变换和Tetrolet变换等。由于多尺度几何分析具有诸多优良特征,所以它非常适合用于去噪、压缩、增强、恢复和特征提取等多方面的图像处理任务。
压缩感知(Compressing Sensing, CS)理论与目前仍然在信息理论中占统治地位的Shannon-Nyquist理论不同,它提出将信号的采样与压缩同时进行,使得在某种基上有稀疏或者压缩表示的信号采样率大大降低,并能将稀疏信号从高度不完整的测量中以极高的概率进行恢复。目前,CS理论已经被广泛应用在诸如各种压缩成像(医学成像、高光谱成像等)、模数转换、生物计算、数据通信、几何数据分析及遥感等领域,并且还呈现出迅速发展的趋势。
论文针对多尺度几何分析以及压缩感知技术在图像分析及处理中的应用与研究展开。并在图像滤波、图像融合以及纹理图像分类三个方面分别进行研究。
首先,分析了多尺度几何分析和压缩感知理论的成因以及基本原理,并介绍了Contourlet变换、非下采样Contourlet变换、Beamlet变换、Directionlet变换、Shearlet变换等几种重要多尺度几何分析方法的特点和基本理论构造。
然后,在多尺度几何分析与压缩感知理论的基础上提出三种图像滤波算法。分别为：基于平移不变Contourlet变换的图像滤波算法、基于Shearlet-SURE的图像滤波算法、基于NSCT-Wave Atom混合域去噪模型的图像滤波算法。这几种方法都能极其稀疏的表示待滤波图像,并且较低的计算复杂度,能够很好的实现对图像的有效去噪与细节增强。最后通过仿真实验,验证了这几种滤波方法的有效性和优越性。
再次,为了有效减少待融合图像中噪声的干扰,增强图像融合后的线性表达能力并提高信息量,提出一种基于NSCT-Beamlet的多尺度融合方法,使用Beamlet变换具有的线检测特性对NSCT变换后的高频成分进行边缘检测,然后通过聚类边缘密度差值来确定其系数的融合规则。接下来在多尺度几何分析理论的基础上结合压缩感知理论,分别提出基于NSCT变换、Directionlet变换和Shearlet变换稀疏表示后观测值融合的图像融合方法,它们恢复的结果图像有极高概率比一般多尺度几何分析融合方法具有更多的信息量和更好的清晰度。并且,观测值是原始分解系数通过随机线性降维的结果,在很大程度上减少了融合所需的数据信息量,所以在计算复杂度上也有一定降低。实验结果表明,提出的融合方法均能有效和极为快速的对图像进行融合,并且能在融合过程中增强图像细节。
最后,在纹理图像分类的研究中,首先对基于多尺度几何分析的散射变换(Scattering Transformation)理论进行了详细阐述,并就其在纹理分类上的性能作了详细的对比和分析。然后,针对目前很多特征算子不能兼具平移不变性和旋转不变性的问题,在二代曲波的基础上,对每个尺度上曲波系数的均值和方差进行旋转规范化以保持特征的旋转不变性,然后结合具有平移不变性和利普希茨连续性的散射向量特征对纹理图像进行分类。另外,提出一种基于压缩感知理论的图像分类方法。在特征提取阶段,从局部图像块中提取随机特征,然后将随机特征嵌入到“词袋”(Bag-of-words, BoW)模型,不经过恢复算法进行重构,直接在压缩域内进行学习和分类,该方法在性能和复杂度上都优于传统的特征提取方法。
综上所述,本文研究了基于多尺度几何分析和压缩感知理论在图像处理中的应用,并针对目前该领域中存在的不足,设计相应的算法进行改进,仿真实验证实,本文所应用的算法和提出的改进方案,均能获得较好的效果。
Multi-scale analysis technology has been the key content of signal processing, it joints the time domain and frequency domain to present signal, is a powerful tool for the analysis of non-stationary signals. It is mainly through the basis function expansion, translation and other operations to the effective signal multi-scale analysis, it is a very flexible, fast, efficient high dimensional signal processing method, can effectively extract useful information from signal. Multi-scale analysis is divided into non-adaptive multi-scale geometric analysis and adaptive multi-scale set analysis. Among them, the adaptive multi-scale geometric analysis includes a recently proposed Ridgelet, Curvelet and Contourlet transform; Adaptive multi-scale geometric analysis including Brushlet, Wedgelet, Wedgelet, Beamlet, Bandlet, Directionlet, Shearlet and Tetrolet transform. As a result of multiscale analysis of many excellent characteristics, so it is very suitable for denoising, compression, restoration, enhancement, feature extraction and other aspects of image processing tasks. But they still existing many problems and need to be further studied.
Compressed sensing (CS) theory is different from Shannon/Nyquist theorem which is currently still the dominant theory in the information, it will signal sampling and compression at the same time, made in a substrate having sparse or compressed representation of the signal sampling rate is greatly reduced, and the sparse signal from was previously considered to be highly incomplete measurement with high probability of recovery. The current CS theory has been widely used in applications such as various compression imaging, analog-to-digital conversion, biological computing, geometric data analysis, remote sensing and other fields, and is continuing to develop quickly.
This paper mainly studies the multi-scale geometric analysis and compressed sensing theory in image processing applications.Mainly in the form three aspects of filter, image fusion and classification.
First, we analysis the theory of multi-scale analysis and compressed sensing, and introduces the downsampling Contourlet transform, Beamlet transform, Directionlet transform, Shearlet transform and the characteristics of transform coefficients distribution.
Secondly, we put forward three kinds of image filtering algorithm based on the multiscale geometric analysis and compressed sensing theory. Respectively:Based on translation invariant Contourlet transform algorithm、based on Shearlet-SURE image, the image filtering algorithm based on NSCT-Wave atom domain framework, atom mixture of compressed sensing image filtering algorithm. These methods can be extremely sparse representation for filtering image, and the computational complexity is low, can be very good to achieve the right image effective denoising and detail enhancement. And through the simulation experiments, the denoising method is effective and superior.
Again, in order to be able to effectively reduce the noise on the fusion image interference, enhanced fusion linear expression ability, increase the amount of information, we proposed one kind multi-scale fusion method based on the NSCT-Beamlet, using the Beamlet transform for line detection characteristics on NSCT transform the frequency components for edge detection, and then the cluster edge density difference is used to determine the coefficient fusion rule. And in the multi-scale geometric analysis based on the combination of compressed sensing theory, we put forward three kinds of observation data fusion based on image fusion method. They have a high probability of recovery than ordinary multi-scale analysis of fusion method has more information content and sharpness of the image, and as a result of observation value relative to the primary decomposition coefficient is greatly reduced, so the proposed method in computational complexity also has much lower. The experimental results show that, the two kinds of fusion methods are both effective and extremely fast image fusion, and in the process of fusion of detail enhancement.
Finally, in view of many characteristic operators cannot both translational and rotational invariance problem at the present, in the two generation of curved wave foundation, through rotating the standardization to the mean and variance of each scale curve let coefficient, in order to maintain the characteristics of rotational invariance, and then combining with translational invariance and Lipchitz continuity of the scattering vector characteristics for image classification. In addition, we proposed one kind image classification method based on compressed sensing. In the feature extraction stage, extract random features from the local image block, then the random characteristics of embedded into the "Bag of words"(BoW) model, and optimized algorithm for reconstruction, directly in the compressed domain learning and classification. The test results show that, the method performance and complexity than traditional feature extraction method.
To sum up, this paper studies is based on multi-scale analysis and compressed sensing theory in image processing applications, and in view of the present problems in the field, design the corresponding algorithm, simulation results show that, all the algorithm and the improved scheme can obtain very good results.
压缩感知(Compressing Sensing, CS)理论与目前仍然在信息理论中占统治地位的Shannon-Nyquist理论不同,它提出将信号的采样与压缩同时进行,使得在某种基上有稀疏或者压缩表示的信号采样率大大降低,并能将稀疏信号从高度不完整的测量中以极高的概率进行恢复。目前,CS理论已经被广泛应用在诸如各种压缩成像(医学成像、高光谱成像等)、模数转换、生物计算、数据通信、几何数据分析及遥感等领域,并且还呈现出迅速发展的趋势。
论文针对多尺度几何分析以及压缩感知技术在图像分析及处理中的应用与研究展开。并在图像滤波、图像融合以及纹理图像分类三个方面分别进行研究。
首先,分析了多尺度几何分析和压缩感知理论的成因以及基本原理,并介绍了Contourlet变换、非下采样Contourlet变换、Beamlet变换、Directionlet变换、Shearlet变换等几种重要多尺度几何分析方法的特点和基本理论构造。
然后,在多尺度几何分析与压缩感知理论的基础上提出三种图像滤波算法。分别为：基于平移不变Contourlet变换的图像滤波算法、基于Shearlet-SURE的图像滤波算法、基于NSCT-Wave Atom混合域去噪模型的图像滤波算法。这几种方法都能极其稀疏的表示待滤波图像,并且较低的计算复杂度,能够很好的实现对图像的有效去噪与细节增强。最后通过仿真实验,验证了这几种滤波方法的有效性和优越性。
再次,为了有效减少待融合图像中噪声的干扰,增强图像融合后的线性表达能力并提高信息量,提出一种基于NSCT-Beamlet的多尺度融合方法,使用Beamlet变换具有的线检测特性对NSCT变换后的高频成分进行边缘检测,然后通过聚类边缘密度差值来确定其系数的融合规则。接下来在多尺度几何分析理论的基础上结合压缩感知理论,分别提出基于NSCT变换、Directionlet变换和Shearlet变换稀疏表示后观测值融合的图像融合方法,它们恢复的结果图像有极高概率比一般多尺度几何分析融合方法具有更多的信息量和更好的清晰度。并且,观测值是原始分解系数通过随机线性降维的结果,在很大程度上减少了融合所需的数据信息量,所以在计算复杂度上也有一定降低。实验结果表明,提出的融合方法均能有效和极为快速的对图像进行融合,并且能在融合过程中增强图像细节。
最后,在纹理图像分类的研究中,首先对基于多尺度几何分析的散射变换(Scattering Transformation)理论进行了详细阐述,并就其在纹理分类上的性能作了详细的对比和分析。然后,针对目前很多特征算子不能兼具平移不变性和旋转不变性的问题,在二代曲波的基础上,对每个尺度上曲波系数的均值和方差进行旋转规范化以保持特征的旋转不变性,然后结合具有平移不变性和利普希茨连续性的散射向量特征对纹理图像进行分类。另外,提出一种基于压缩感知理论的图像分类方法。在特征提取阶段,从局部图像块中提取随机特征,然后将随机特征嵌入到“词袋”(Bag-of-words, BoW)模型,不经过恢复算法进行重构,直接在压缩域内进行学习和分类,该方法在性能和复杂度上都优于传统的特征提取方法。
综上所述,本文研究了基于多尺度几何分析和压缩感知理论在图像处理中的应用,并针对目前该领域中存在的不足,设计相应的算法进行改进,仿真实验证实,本文所应用的算法和提出的改进方案,均能获得较好的效果。
Multi-scale analysis technology has been the key content of signal processing, it joints the time domain and frequency domain to present signal, is a powerful tool for the analysis of non-stationary signals. It is mainly through the basis function expansion, translation and other operations to the effective signal multi-scale analysis, it is a very flexible, fast, efficient high dimensional signal processing method, can effectively extract useful information from signal. Multi-scale analysis is divided into non-adaptive multi-scale geometric analysis and adaptive multi-scale set analysis. Among them, the adaptive multi-scale geometric analysis includes a recently proposed Ridgelet, Curvelet and Contourlet transform; Adaptive multi-scale geometric analysis including Brushlet, Wedgelet, Wedgelet, Beamlet, Bandlet, Directionlet, Shearlet and Tetrolet transform. As a result of multiscale analysis of many excellent characteristics, so it is very suitable for denoising, compression, restoration, enhancement, feature extraction and other aspects of image processing tasks. But they still existing many problems and need to be further studied.
Compressed sensing (CS) theory is different from Shannon/Nyquist theorem which is currently still the dominant theory in the information, it will signal sampling and compression at the same time, made in a substrate having sparse or compressed representation of the signal sampling rate is greatly reduced, and the sparse signal from was previously considered to be highly incomplete measurement with high probability of recovery. The current CS theory has been widely used in applications such as various compression imaging, analog-to-digital conversion, biological computing, geometric data analysis, remote sensing and other fields, and is continuing to develop quickly.
This paper mainly studies the multi-scale geometric analysis and compressed sensing theory in image processing applications.Mainly in the form three aspects of filter, image fusion and classification.
First, we analysis the theory of multi-scale analysis and compressed sensing, and introduces the downsampling Contourlet transform, Beamlet transform, Directionlet transform, Shearlet transform and the characteristics of transform coefficients distribution.
Secondly, we put forward three kinds of image filtering algorithm based on the multiscale geometric analysis and compressed sensing theory. Respectively:Based on translation invariant Contourlet transform algorithm、based on Shearlet-SURE image, the image filtering algorithm based on NSCT-Wave atom domain framework, atom mixture of compressed sensing image filtering algorithm. These methods can be extremely sparse representation for filtering image, and the computational complexity is low, can be very good to achieve the right image effective denoising and detail enhancement. And through the simulation experiments, the denoising method is effective and superior.
Again, in order to be able to effectively reduce the noise on the fusion image interference, enhanced fusion linear expression ability, increase the amount of information, we proposed one kind multi-scale fusion method based on the NSCT-Beamlet, using the Beamlet transform for line detection characteristics on NSCT transform the frequency components for edge detection, and then the cluster edge density difference is used to determine the coefficient fusion rule. And in the multi-scale geometric analysis based on the combination of compressed sensing theory, we put forward three kinds of observation data fusion based on image fusion method. They have a high probability of recovery than ordinary multi-scale analysis of fusion method has more information content and sharpness of the image, and as a result of observation value relative to the primary decomposition coefficient is greatly reduced, so the proposed method in computational complexity also has much lower. The experimental results show that, the two kinds of fusion methods are both effective and extremely fast image fusion, and in the process of fusion of detail enhancement.
Finally, in view of many characteristic operators cannot both translational and rotational invariance problem at the present, in the two generation of curved wave foundation, through rotating the standardization to the mean and variance of each scale curve let coefficient, in order to maintain the characteristics of rotational invariance, and then combining with translational invariance and Lipchitz continuity of the scattering vector characteristics for image classification. In addition, we proposed one kind image classification method based on compressed sensing. In the feature extraction stage, extract random features from the local image block, then the random characteristics of embedded into the "Bag of words"(BoW) model, and optimized algorithm for reconstruction, directly in the compressed domain learning and classification. The test results show that, the method performance and complexity than traditional feature extraction method.
To sum up, this paper studies is based on multi-scale analysis and compressed sensing theory in image processing applications, and in view of the present problems in the field, design the corresponding algorithm, simulation results show that, all the algorithm and the improved scheme can obtain very good results.
引文
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