基于稀疏约束正则化模型的图像提高分辨率技术研究
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摘要
获取高分辨率的SAR和光学遥感侦察监视图像,是目前成像系统发展的主要方向之一,而成本、研制周期和硬件技术水平等因素在一定程度上限制了当前我国部分遥感观测图像的分辨率。因此,研究图像数据处理方法,改进图像的质量,提高图像的分辨率,具有重要的理论和实际意义。
论文以SAR图像与光学图像提高分辨率的不适定问题为背景,针对图像稀疏先验约束在提高分辨率处理中的有效应用,解决稀疏约束正则化模型处理的有关问题。本文的主要工作如下:
1)从多个角度系统揭示了SAR图像目标强散射中心的稀疏性机理
研究了SAR图像目标强散射中心稀疏性的成因。首先,从目标散射中心概念出发,根据电磁散射理论,通过理论研究与实验分析了目标散射中心的稀疏性。其次,从场景粗糙屈光面对后向散射强度的影响机理出发,揭示了SAR图像中多数场景表现为“近黑”的统计特性和物理原因。最后,从人类视觉稀疏分解的角度出发,对比分析了SAR图像与光学图像稀疏结构的异同。
2)利用SAR图像数据的Cauchy先验,建立了Lorentz函数稀疏约束正则化提高分辨率模型,并给出其快速求解算法
建立了Lorentz(洛伦茨)函数稀疏约束正则化提高分辨率模型,该模型对应于SAR图像数据的Cauchy分布的先验信息。给出了一种较快的求解算法,分析了该稀疏约束正则化模型的稳健性、压缩性和解的广义稀疏性,及其在SAR图像处理中的应用。
3)提出了一种变拟范数稀疏约束的正则化SAR图像提高分辨率模型,并建立了交互迭代的求解算法
目前,提高分辨率的正则化模型通常采用预先固定的l p拟范数的方式。在此基础上,提出了一种正则化约束项随着数据而变化的正则化模型。本文将其称为变拟范数约束的正则化模型。根据稀疏约束拟范数与广义高斯分布形状参数的关系,研究了模型稀疏约束项的确定方法,给出了一种交互迭代求解的方法,并将其应用于SAR图像目标提高分辨率处理。
4)建立了拟范数稀疏约束正则化模型与解的稀疏性之间的关系,并提出一种对SAR图像幅度进行部分压缩的提高分辨率算法
采用不同的拟范数约束项,正则化模型的解会具有不同的稀疏性。研究了拟范数的形式与模型最优稀疏解的关系,指出了l p拟范数中p的取值特点。推导了拟范数正则化约束模型的阈值特性,给出了阈值与拟范数以及正则化参数的关系。并推导了观测数据噪声水平和解的稀疏性的关系,由此得到了模型对解的稀疏性的决定机制。推导了拟范数约束正则化模型的压缩性质,并提出了一种部分压缩算法,以保持目标散射中心的幅度。
5)针对广义高斯和泊松分布噪声条件下提高分辨率处理,给出了非二次数据度量和稀疏约束的正则化模型与求解算法
针对光学图像,研究了非高斯噪声条件下图像提高分辨率的正则化方法,分别从Bayes估计和正则化变分的角度研究了正则化模型的构造问题,得到了具有不同形式非二次数据度量项的正则化模型。为该正则化模型引入了边缘稀疏约束,并研究了求解方法。考虑了两类典型的非高斯噪声,即广义高斯分布噪声(涵盖了均匀分布、Laplace分布、重尾分布等多种情况)和泊松分布噪声,主要采用了光学遥感图像来进行实验分析。
To acquire high resolution synthetic aperture radar (SAR) images and optical remote sensing images is one of the main development directions of remote reconnaissance and surveillance. But the high cost and the current hardware techniques limit the improvement of resolution of remote images. Therefore, it is of theoretical and practical significance to study relative data processing methods to improve image qualities and enhance the resolution.
This thesis works on the background of ill-posed problems of resolution enhancement of SAR and optical images. The thesis has studied the effective application of sparsity constraints to resolution enhancement, and relative problems of sparsity constrained regularization. The main contributions of this thesis are listed as follows:
1) The thesis systematically reveals the sparsity mechanism of target scattering centers in the SAR images from multiple perspectives.
The causes of sparsity of strong scattering centers in the SAR imaging scene are investigated. Firstly, according to the conception of target scattering centers and the electromagnetic scattering theory, the theoretical and experimental analyses show the physical reason of the sparse property of scattering centers, which are brighter points in the image. Secondly, considering the mechanism of influence of backscattering intensity by the rough refraction surface of imaging area, the paper reveals the statistical property and physical reason the“near-black”characteristic of most scenes in SAR images. Finally, the thesis compares the different sparsity configurations of SAR and optical images, in view of the sparse decomposition properties of human visual system.
2) The thesis exploits Lorentzian function to the domain of SAR image resolution enhancement.
Based on the Cauchy distribution of the amplitude of SAR image, the thesis presents a regularization model with Lorentzian function as a sparsity constraint term. A fast algorithm is proposed to solve the regularization model. The robustness and the shrinkage property of the model are analyzed. At last, the paper concludes that the solution is general sparse, i.e. most data of the acquired solution are near-zero, few are far from zero. The experimental results with SAR images proof the above properties.
3) The thesis presents a new sparsity constraint regularization model with variable l p quasi-norms with application to resolution enhancement.
Generally, the current resolution enhancement regularization models take a fixed l p quasi-norm term as the regularization term, and keep it invariant in the model-solving process. This presents a new regularization model, whose l p quasi-norm term is not fixed and changes in accordance of the image data. We call it a regularization model with variable l p quasi-norms. According to the relation between l p quasi-norm term and the shape parameter of generalized Gaussian distributed data, the paper proposes a method to determine this regularization term. The regularization model leads to an alternating iterative algorithm to seek the optimal solution.
4) The thesis deduces the relations of quasi-norm sparsity constraint regularization models and the sparsity property of solution, and presents a partial shrinkage algorithm.
Taking different l p quasi-norm regularization term, the solution of regularization model will be of different degree of sparsity. The thesis studies the relations of sparse regularization term and the solution, and form the determination property of parameter p of the l p quasi-norm constraint regularization model. The thesis deduces the threshold of the model, and points out the relation of the threshold and l p quasi-norm regularization term and the regularization parameter, and proposes of partial shrinkage algorithm to protect the intensity of SAR images scattering centers. The relation between noise and the sparsity of solution is also deduced. The above works form a foundation of the determination mechanism of the sparsity of solution by the regularization model.
5) The thesis studies the resolution enhancement methods of optical images under the non-Gaussian noise, presents a framework of regularization with non-quadratic data measurements and sparsity constraint terms.
According to the Bayesian estimation and variation method, the thesis construct different regularization models with non-quadratic regularization terms with application to blurred optical images with different non-Gaussian noise, i.e. generalized Gaussian distributed noise and Poisson distributed noise. The sparsity of the edges is considered in the regularization model. The thesis discusses different algorithm for each regularization model. The thesis demonstrates the resolution enhancement abilities of different models with remote sensing images and common optical images, and the results show the effectiveness of the algorithms.
论文以SAR图像与光学图像提高分辨率的不适定问题为背景,针对图像稀疏先验约束在提高分辨率处理中的有效应用,解决稀疏约束正则化模型处理的有关问题。本文的主要工作如下:
1)从多个角度系统揭示了SAR图像目标强散射中心的稀疏性机理
研究了SAR图像目标强散射中心稀疏性的成因。首先,从目标散射中心概念出发,根据电磁散射理论,通过理论研究与实验分析了目标散射中心的稀疏性。其次,从场景粗糙屈光面对后向散射强度的影响机理出发,揭示了SAR图像中多数场景表现为“近黑”的统计特性和物理原因。最后,从人类视觉稀疏分解的角度出发,对比分析了SAR图像与光学图像稀疏结构的异同。
2)利用SAR图像数据的Cauchy先验,建立了Lorentz函数稀疏约束正则化提高分辨率模型,并给出其快速求解算法
建立了Lorentz(洛伦茨)函数稀疏约束正则化提高分辨率模型,该模型对应于SAR图像数据的Cauchy分布的先验信息。给出了一种较快的求解算法,分析了该稀疏约束正则化模型的稳健性、压缩性和解的广义稀疏性,及其在SAR图像处理中的应用。
3)提出了一种变拟范数稀疏约束的正则化SAR图像提高分辨率模型,并建立了交互迭代的求解算法
目前,提高分辨率的正则化模型通常采用预先固定的l p拟范数的方式。在此基础上,提出了一种正则化约束项随着数据而变化的正则化模型。本文将其称为变拟范数约束的正则化模型。根据稀疏约束拟范数与广义高斯分布形状参数的关系,研究了模型稀疏约束项的确定方法,给出了一种交互迭代求解的方法,并将其应用于SAR图像目标提高分辨率处理。
4)建立了拟范数稀疏约束正则化模型与解的稀疏性之间的关系,并提出一种对SAR图像幅度进行部分压缩的提高分辨率算法
采用不同的拟范数约束项,正则化模型的解会具有不同的稀疏性。研究了拟范数的形式与模型最优稀疏解的关系,指出了l p拟范数中p的取值特点。推导了拟范数正则化约束模型的阈值特性,给出了阈值与拟范数以及正则化参数的关系。并推导了观测数据噪声水平和解的稀疏性的关系,由此得到了模型对解的稀疏性的决定机制。推导了拟范数约束正则化模型的压缩性质,并提出了一种部分压缩算法,以保持目标散射中心的幅度。
5)针对广义高斯和泊松分布噪声条件下提高分辨率处理,给出了非二次数据度量和稀疏约束的正则化模型与求解算法
针对光学图像,研究了非高斯噪声条件下图像提高分辨率的正则化方法,分别从Bayes估计和正则化变分的角度研究了正则化模型的构造问题,得到了具有不同形式非二次数据度量项的正则化模型。为该正则化模型引入了边缘稀疏约束,并研究了求解方法。考虑了两类典型的非高斯噪声,即广义高斯分布噪声(涵盖了均匀分布、Laplace分布、重尾分布等多种情况)和泊松分布噪声,主要采用了光学遥感图像来进行实验分析。
To acquire high resolution synthetic aperture radar (SAR) images and optical remote sensing images is one of the main development directions of remote reconnaissance and surveillance. But the high cost and the current hardware techniques limit the improvement of resolution of remote images. Therefore, it is of theoretical and practical significance to study relative data processing methods to improve image qualities and enhance the resolution.
This thesis works on the background of ill-posed problems of resolution enhancement of SAR and optical images. The thesis has studied the effective application of sparsity constraints to resolution enhancement, and relative problems of sparsity constrained regularization. The main contributions of this thesis are listed as follows:
1) The thesis systematically reveals the sparsity mechanism of target scattering centers in the SAR images from multiple perspectives.
The causes of sparsity of strong scattering centers in the SAR imaging scene are investigated. Firstly, according to the conception of target scattering centers and the electromagnetic scattering theory, the theoretical and experimental analyses show the physical reason of the sparse property of scattering centers, which are brighter points in the image. Secondly, considering the mechanism of influence of backscattering intensity by the rough refraction surface of imaging area, the paper reveals the statistical property and physical reason the“near-black”characteristic of most scenes in SAR images. Finally, the thesis compares the different sparsity configurations of SAR and optical images, in view of the sparse decomposition properties of human visual system.
2) The thesis exploits Lorentzian function to the domain of SAR image resolution enhancement.
Based on the Cauchy distribution of the amplitude of SAR image, the thesis presents a regularization model with Lorentzian function as a sparsity constraint term. A fast algorithm is proposed to solve the regularization model. The robustness and the shrinkage property of the model are analyzed. At last, the paper concludes that the solution is general sparse, i.e. most data of the acquired solution are near-zero, few are far from zero. The experimental results with SAR images proof the above properties.
3) The thesis presents a new sparsity constraint regularization model with variable l p quasi-norms with application to resolution enhancement.
Generally, the current resolution enhancement regularization models take a fixed l p quasi-norm term as the regularization term, and keep it invariant in the model-solving process. This presents a new regularization model, whose l p quasi-norm term is not fixed and changes in accordance of the image data. We call it a regularization model with variable l p quasi-norms. According to the relation between l p quasi-norm term and the shape parameter of generalized Gaussian distributed data, the paper proposes a method to determine this regularization term. The regularization model leads to an alternating iterative algorithm to seek the optimal solution.
4) The thesis deduces the relations of quasi-norm sparsity constraint regularization models and the sparsity property of solution, and presents a partial shrinkage algorithm.
Taking different l p quasi-norm regularization term, the solution of regularization model will be of different degree of sparsity. The thesis studies the relations of sparse regularization term and the solution, and form the determination property of parameter p of the l p quasi-norm constraint regularization model. The thesis deduces the threshold of the model, and points out the relation of the threshold and l p quasi-norm regularization term and the regularization parameter, and proposes of partial shrinkage algorithm to protect the intensity of SAR images scattering centers. The relation between noise and the sparsity of solution is also deduced. The above works form a foundation of the determination mechanism of the sparsity of solution by the regularization model.
5) The thesis studies the resolution enhancement methods of optical images under the non-Gaussian noise, presents a framework of regularization with non-quadratic data measurements and sparsity constraint terms.
According to the Bayesian estimation and variation method, the thesis construct different regularization models with non-quadratic regularization terms with application to blurred optical images with different non-Gaussian noise, i.e. generalized Gaussian distributed noise and Poisson distributed noise. The sparsity of the edges is considered in the regularization model. The thesis discusses different algorithm for each regularization model. The thesis demonstrates the resolution enhancement abilities of different models with remote sensing images and common optical images, and the results show the effectiveness of the algorithms.
引文
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