基于最优估计的SAR图像提高分辨率方法研究
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摘要
分辨率是表征与衡量SAR图像质量的重要指标,而利用参数模型与数据后处理技术提高SAR图像分辨率是缓解成像系统硬件水平与相关应用实际需求之间矛盾的一种重要手段。目前,在该领域,存在分辨率概念与提高分辨率机理并不完善,以及相关处理模型中含有待定模型参数造成其难以自适应求解的问题。
本文将SAR图像提高分辨率看作目标参数的高精度估计过程,基于最优估计准则与方法解决以上两个方面的问题。主要工作与创新点为:
(1)扩展了分辨率的内涵,得到了影响分辨率的因素,解释了提高分辨率机理
分析并指出了传统分辨率概念的不足之处。根据瑞利准则与点散射模型,通过理论推导研究了由目标幅度、位置等因素引起的相干性对分辨率的影响,指出由于相干性的存在,即使目标距离小于分辨率也可分辨,而目标距离大于分辨率时也可能不能分辨。这与名义分辨率的瑞利准则本质是相矛盾的,意味着它没有考虑相干性的影响。利用三次样条方法证明了“最高”测量分辨率的存在性,表明名义分辨率该受限于人类视觉感知能力。
提出了SAR图像域与频域上扩展的两点目标分辨率模型。基于点散射模型,利用分辨率原始定义及最优估计方法与准则,分别从假设检验与估计精度角度提出了SAR图像域与频域两点目标扩展分辨率标准与模型,得到简洁、客观合理的分辨率函数表达式,揭示了分辨率与重要的影响因素,如噪声、采样点数目(信号能量)之间的定量关系。相关结果与现有文献对分辨率的定性理解相一致,并克服了传统分辨率概念的缺陷与不足,在一定程度上完善了SAR图像提高分辨率机理。
(2)通过建立模型参数选择准则,实现了处理模型中参数的自适应最优估计
提出了复数域广义岭估计的直接求解方法。针对SAR频域上的病态线性模型,利用单调有界原理,得到复数域广义岭估计迭代初值的选取范围以达到收敛性,并构造了收敛解所需满足的二元方程组,从而得到该方法的解析解。对单位字典与l_k范数构成的正则化模型应用相似原理,并依据最小均方误差准则,得到最优模型参数以及模型解析解。结果证明了,当七取接近于0的较小正数时,该模型解是一类特殊的广义岭估计解。该类解析解的得出,在实现模型自适应求解的同时极大地提高了处理速度与估计精度。
提出了具有一稀疏约束项的正则化模型中的参数自适应最优估计方法。构造了具有变正则参数的l_k范数正则化处理模型,根据迭代过程的特点,以最小均方误差为准则,依据矩阵偏导原理,构造最优模型参数所需满足的矩阵方程,从而提出准最优模型参数的确定方法,建立了模型参数与真实目标参数值、噪声水平之间的联系,并设计了自适应迭代过程。实验结果表明该方法可使估计值达到较为理想的性能。并且,应用该方法对多幅SAR图像超分辨进行了初步研究。
在分析Fourier字典性质的基础上提出了快速自适应的基选择方法。通过详细的理论分析与实验验证过程,揭示了基于点散射模型所构造的Fourier字典的近似正交性,继而利用该特殊性质提出了一种快速自适应基选择方法,得到了强散射中心的位置与数目。该方法在一定程度上属于序贯基选择方法,但并非贪婪算法,且各基向量的选择互不影响。继而利用简便的最小二乘方法得到目标参数的无偏估计。并且,根据成像参数特点从节省计算量与存储量角度设计了计算过程。
The resolution is an important index to measure and represent the quality of SAR images, and improving the resolution via the data processing techniques and parametric models is a significant way to remission the contradiction between the hardware levels of imaging systems and practice requirements for the resolution. At present, there are two valuable problems to be solved in the resolution enhancement field of SAR image: one is the incomplete resolution concept and mechanism of resolution enhancement, and the other is the non-adaptive solving process for related models induced by the unknown model parameters.
This paper regards the resolution enhancement of SAR image as the estimation process of target parameters with high precision, and studies the above two problems based on the optimal estimation. The main contributions of this paper are listed as follows:
(1) The connotation of resolution concept is extended and its dominating factors are investigated, which explain the resolution enhancement mechanism
The faults of the traditional resolution are analyzed and pointed out. Based on the Rayleigh criterion and the parametric model of two point targets, it investigates the effect of the coherence resulting from the different amplitudes and positions of targets on the traditional resolution. It comes to the conclusions that the two targets may be resolved even if the distance is smaller than the resolution. This fact conflicts with the Rayleigh criterion itself. Moreover, the existence of the highest measured resolution is proved using the cubic spline method, which means the nominal resolution is limited by the human vision system.
The standard and model of extended resolutions in SAR image domain and frequency domain are proposed. To overcome these addressed faults, it utilizes the optimal estimation methodology, and proposes novel extended resolution concepts from the view of the hypothesis test and the estimation precision, based on the original resolution definition. Then, the compact and explicit expressions of the extended resolutions are obtained, which indicate the quantitative relationship between the resolution and the factors such as the noise level, signal power, etc. The obtained conclusions are coincident to the qualitative comprehension described in literatures and provide the explanation for existing resolution enhancement methods.
(2)The criterion for selecting optimal model parameter is established, and the adaptive optimal solving processes are implemented
The direct solution of the generalized ridge estimation method in the complex domain is put forward. The ranges of iterative initial values are analyzed based on the bounded monotonous principle, and a binary equation set that the convergence solution must be satisfied is constructed. Then, the analytic solution is obtained, which avoids the time-consuming iterative process, implement the adaptive solving processing, and improve the estimation performance. By applying the similar process and minimum mean-square error criterion, the optimal model parameters and the analytic solution of the regularization model with l_k norm and identity matrix is also gotten. The comparison results of these two solutions shows that this regularization model is a special form of the generalized ridge estimation method when k→0~+.
An adaptive optimal solving algorithm is proposed for the regularization model with l_k norm. A weighted regularization model with l_k norm is constructed based on the point target model. By analyzing the peculiarity of the iterative process and using the minimum mean-square error criterion, a matrix equation that the model parameters need to satisfy is constructed. Then, the suboptimal solution of it is obtained to design the adaptive iterative process, which establishes the relationship between model parameters, accurate values of target parameters and the noise level. Because it has not utilized the special property of the design matrix in the model, this method can be adopted directly to the generalized model such as the point enhancement model. Moreover, the superresolution imaging problem for multiple SAR images is studied preliminarily.
A fast and adaptive method for basis selection is presented based on the character analysis of Fourier dictionary. According to the theoretical derivation and experimental verification in detail, the approximate orthogonality of the reconstructed (over-)complete Fourier dictionary is exploited. Then, a novel fast and adaptive method for basis selection is developed and the unbiased estimators of target parameters can be obtained easily by using the least-square method. This method belongs to the sequential basis selection strategy, but it is not a greedy algorithm and the selected basis does not be affected mutually. Moreover, it designs a calculation process based on the character of imaging parameters, which decreases the load of the computation and memory.
本文将SAR图像提高分辨率看作目标参数的高精度估计过程,基于最优估计准则与方法解决以上两个方面的问题。主要工作与创新点为:
(1)扩展了分辨率的内涵,得到了影响分辨率的因素,解释了提高分辨率机理
分析并指出了传统分辨率概念的不足之处。根据瑞利准则与点散射模型,通过理论推导研究了由目标幅度、位置等因素引起的相干性对分辨率的影响,指出由于相干性的存在,即使目标距离小于分辨率也可分辨,而目标距离大于分辨率时也可能不能分辨。这与名义分辨率的瑞利准则本质是相矛盾的,意味着它没有考虑相干性的影响。利用三次样条方法证明了“最高”测量分辨率的存在性,表明名义分辨率该受限于人类视觉感知能力。
提出了SAR图像域与频域上扩展的两点目标分辨率模型。基于点散射模型,利用分辨率原始定义及最优估计方法与准则,分别从假设检验与估计精度角度提出了SAR图像域与频域两点目标扩展分辨率标准与模型,得到简洁、客观合理的分辨率函数表达式,揭示了分辨率与重要的影响因素,如噪声、采样点数目(信号能量)之间的定量关系。相关结果与现有文献对分辨率的定性理解相一致,并克服了传统分辨率概念的缺陷与不足,在一定程度上完善了SAR图像提高分辨率机理。
(2)通过建立模型参数选择准则,实现了处理模型中参数的自适应最优估计
提出了复数域广义岭估计的直接求解方法。针对SAR频域上的病态线性模型,利用单调有界原理,得到复数域广义岭估计迭代初值的选取范围以达到收敛性,并构造了收敛解所需满足的二元方程组,从而得到该方法的解析解。对单位字典与l_k范数构成的正则化模型应用相似原理,并依据最小均方误差准则,得到最优模型参数以及模型解析解。结果证明了,当七取接近于0的较小正数时,该模型解是一类特殊的广义岭估计解。该类解析解的得出,在实现模型自适应求解的同时极大地提高了处理速度与估计精度。
提出了具有一稀疏约束项的正则化模型中的参数自适应最优估计方法。构造了具有变正则参数的l_k范数正则化处理模型,根据迭代过程的特点,以最小均方误差为准则,依据矩阵偏导原理,构造最优模型参数所需满足的矩阵方程,从而提出准最优模型参数的确定方法,建立了模型参数与真实目标参数值、噪声水平之间的联系,并设计了自适应迭代过程。实验结果表明该方法可使估计值达到较为理想的性能。并且,应用该方法对多幅SAR图像超分辨进行了初步研究。
在分析Fourier字典性质的基础上提出了快速自适应的基选择方法。通过详细的理论分析与实验验证过程,揭示了基于点散射模型所构造的Fourier字典的近似正交性,继而利用该特殊性质提出了一种快速自适应基选择方法,得到了强散射中心的位置与数目。该方法在一定程度上属于序贯基选择方法,但并非贪婪算法,且各基向量的选择互不影响。继而利用简便的最小二乘方法得到目标参数的无偏估计。并且,根据成像参数特点从节省计算量与存储量角度设计了计算过程。
The resolution is an important index to measure and represent the quality of SAR images, and improving the resolution via the data processing techniques and parametric models is a significant way to remission the contradiction between the hardware levels of imaging systems and practice requirements for the resolution. At present, there are two valuable problems to be solved in the resolution enhancement field of SAR image: one is the incomplete resolution concept and mechanism of resolution enhancement, and the other is the non-adaptive solving process for related models induced by the unknown model parameters.
This paper regards the resolution enhancement of SAR image as the estimation process of target parameters with high precision, and studies the above two problems based on the optimal estimation. The main contributions of this paper are listed as follows:
(1) The connotation of resolution concept is extended and its dominating factors are investigated, which explain the resolution enhancement mechanism
The faults of the traditional resolution are analyzed and pointed out. Based on the Rayleigh criterion and the parametric model of two point targets, it investigates the effect of the coherence resulting from the different amplitudes and positions of targets on the traditional resolution. It comes to the conclusions that the two targets may be resolved even if the distance is smaller than the resolution. This fact conflicts with the Rayleigh criterion itself. Moreover, the existence of the highest measured resolution is proved using the cubic spline method, which means the nominal resolution is limited by the human vision system.
The standard and model of extended resolutions in SAR image domain and frequency domain are proposed. To overcome these addressed faults, it utilizes the optimal estimation methodology, and proposes novel extended resolution concepts from the view of the hypothesis test and the estimation precision, based on the original resolution definition. Then, the compact and explicit expressions of the extended resolutions are obtained, which indicate the quantitative relationship between the resolution and the factors such as the noise level, signal power, etc. The obtained conclusions are coincident to the qualitative comprehension described in literatures and provide the explanation for existing resolution enhancement methods.
(2)The criterion for selecting optimal model parameter is established, and the adaptive optimal solving processes are implemented
The direct solution of the generalized ridge estimation method in the complex domain is put forward. The ranges of iterative initial values are analyzed based on the bounded monotonous principle, and a binary equation set that the convergence solution must be satisfied is constructed. Then, the analytic solution is obtained, which avoids the time-consuming iterative process, implement the adaptive solving processing, and improve the estimation performance. By applying the similar process and minimum mean-square error criterion, the optimal model parameters and the analytic solution of the regularization model with l_k norm and identity matrix is also gotten. The comparison results of these two solutions shows that this regularization model is a special form of the generalized ridge estimation method when k→0~+.
An adaptive optimal solving algorithm is proposed for the regularization model with l_k norm. A weighted regularization model with l_k norm is constructed based on the point target model. By analyzing the peculiarity of the iterative process and using the minimum mean-square error criterion, a matrix equation that the model parameters need to satisfy is constructed. Then, the suboptimal solution of it is obtained to design the adaptive iterative process, which establishes the relationship between model parameters, accurate values of target parameters and the noise level. Because it has not utilized the special property of the design matrix in the model, this method can be adopted directly to the generalized model such as the point enhancement model. Moreover, the superresolution imaging problem for multiple SAR images is studied preliminarily.
A fast and adaptive method for basis selection is presented based on the character analysis of Fourier dictionary. According to the theoretical derivation and experimental verification in detail, the approximate orthogonality of the reconstructed (over-)complete Fourier dictionary is exploited. Then, a novel fast and adaptive method for basis selection is developed and the unbiased estimators of target parameters can be obtained easily by using the least-square method. This method belongs to the sequential basis selection strategy, but it is not a greedy algorithm and the selected basis does not be affected mutually. Moreover, it designs a calculation process based on the character of imaging parameters, which decreases the load of the computation and memory.
引文
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