基于变分法的遥感图像融合方法研究
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摘要
随着卫星遥感技术的发展,遥感图像融合技术研究吸引了越来越多研究者的目光。遥感图像融合是将多源遥感图像进行综合分析与合并,从而获得更为精确、全面和可靠的遥感图像的过程。本论文基于变分法理论提出四种遥感图像融合模型。特别地,其中三种模型针对遥感图像融合问题的一个分支——Pan-sharpening融合。本论文的基本思路是基于不同假设提出相应的能量泛函,并通过求解能量极小化问题得出融合结果。在数值计算上,本论文介绍了分裂Bregman快速算法,利用该算法进行数值处理,时间效率更高,得到的结果更稳定。具体地,本论文的研究内容包括：
·基于融合后图像的梯度信息应由原始图像最显著信息组成的假设,本论文提出一个像素级的变分融合模型。该模型首先提取原始图像的梯度,并将该梯度按一定规则合并,然后将合并后的梯度作为融合图像的梯度,并考虑到亮度均衡化等特征,建立一个能量泛函,从而提高图像融合的效果。本论文通过分裂Bregman迭代高效的实现模型的数值计算过程,并从定性、定量和效率等方面出发分析该模型的有效性。
·在Pan-sharpening问题上,基于融合结果需要同时保持空间信息、光谱信息和光谱相关度的特性,本论文首先提出三个假设,并据此建立一个变分模型：VP模型。进一步地,本论文从变分法理论上验证VP模型能量极小值的存在性,并利用分裂Bregman算法来实现数值计算。另外,为了更有效的对Pan-sharpening结果进行评价,本论文对现有评价标准进行合理的整理和分类。在实验方面,本论文采用QuickBird和IKONOS卫星提供的遥感数据来验证VP模型的有效性,并从定性、定量和效率等方面综合对实验结果进行评价。
·本论文将Framelet理论引入至Pan-sharpening问题当中,并据此建立两个基于Framelet的Pan-sharpening模型：FP和VFP模型。FP模型是简单的系数选择模型,该模型简单有效,但是结果唯一、不可调节。为适应多样性需求,本论文进一步提出一个基于Framelet的变分模型：VFP模型,该模型适应能力更强,在Pan-sharpening问题上更有效。本论文采用交替迭代和分裂Bregman实现数值计算,并采用Quickbird和IKONOS卫星数据从主观和客观上对实验结果进行总体评价,从而证实我们方法良好的实验效果和实用价值。最后,本论文分析比较VP和VFP模型,并给出各自的优缺点和适应范围。实验结果标明,在低噪声图像中,VP优于VFP,而在噪声明显的图像中,VFP则更优越。
With the rapid development of remote sensing techniques, remote sensing image fusion has been attracting more and more attention recently. Remote sensing image fusion aims to analyze and combine the remotely sensed images to obtain a single image which is more robust and informative. In this thesis, based on the variational theory, we propose four fusion models. Among them, three models are built for a branch of fusion: Pan-sharpening, which is a process of integrating a low resolution multi-spectral (MS) image with its corresponding panchromatic image to obtain a single high resolution MS image. The main idea of this thesis is to build the related energy functional based on some distinct hypotheses, and to obtain the final fusion result by minimizing the energy. In the numerical scheme, we use the split Bregman iteration to obtain the fusion results more stably, effectively and efficiently. Our main contributions are as follows:
●Firstly, we assume that the gradient of the fused image should be close to the most salient gradient in the multisource inputs. Based on this assumption, we develop a new pixel based variational model. In detail, we first extract the gradient of original images and combine them based on a certain rule, then treat this combined gradient as a term. By further take some features such as brightness equalization into account, an energy functional is built for enhancing the fusion effects. The model is implement by using the split Bregman iteration, and compared with many outstanding methods.
●Secondly, we assume that the pan-sharpened image should keep the spatial infor-mation, spectral information and spectral correction. Based on this assumption, we build an new variational model, named VP, for Pan-sharpening. We also discuss the existence of minimizer of our energy and describe the numerical procedure based on the split Bregman algorithm. For evaluating fusion results more effectively, we try to classify the existing measures into several categories. To verify the effectiveness of VP model, we compare it with some state-of-the-art schemes using QuickBird and IKONOS data. The results demonstrate the effectiveness and stability of VP. Besides, the computation efficiency comparison with other variational methods also shows that VP model is remarkable.
●We introduce the Framelet theory and propose two Pan-sharpening models, termed FP and VFP, based on the Framelet framework. The FP model is a coefficients choosing model, this model is simple and effective, but its results is unique which do not suitable for multifarious applications. To overcome this drawback, by combining the VP and other three fusion requirements, we build a Framelet based variational model:VFP. The alternating iteration algorithm and split Bregman iteration is further introduced to improve the numerical effect. We present the results of the two methods on the QuickBird and IKONOS images, and compare them with existing methods qualitatively and quantitatively. The comparison results demonstrate the superiority of our methods. Finally, we analyze and compare the VP and VFP, and show the advantages and disadvantages and specific scope of each model. The results show that VP outperforms VFP in low noise image, while VFP outperforms VP in high noise image.
·基于融合后图像的梯度信息应由原始图像最显著信息组成的假设,本论文提出一个像素级的变分融合模型。该模型首先提取原始图像的梯度,并将该梯度按一定规则合并,然后将合并后的梯度作为融合图像的梯度,并考虑到亮度均衡化等特征,建立一个能量泛函,从而提高图像融合的效果。本论文通过分裂Bregman迭代高效的实现模型的数值计算过程,并从定性、定量和效率等方面出发分析该模型的有效性。
·在Pan-sharpening问题上,基于融合结果需要同时保持空间信息、光谱信息和光谱相关度的特性,本论文首先提出三个假设,并据此建立一个变分模型：VP模型。进一步地,本论文从变分法理论上验证VP模型能量极小值的存在性,并利用分裂Bregman算法来实现数值计算。另外,为了更有效的对Pan-sharpening结果进行评价,本论文对现有评价标准进行合理的整理和分类。在实验方面,本论文采用QuickBird和IKONOS卫星提供的遥感数据来验证VP模型的有效性,并从定性、定量和效率等方面综合对实验结果进行评价。
·本论文将Framelet理论引入至Pan-sharpening问题当中,并据此建立两个基于Framelet的Pan-sharpening模型：FP和VFP模型。FP模型是简单的系数选择模型,该模型简单有效,但是结果唯一、不可调节。为适应多样性需求,本论文进一步提出一个基于Framelet的变分模型：VFP模型,该模型适应能力更强,在Pan-sharpening问题上更有效。本论文采用交替迭代和分裂Bregman实现数值计算,并采用Quickbird和IKONOS卫星数据从主观和客观上对实验结果进行总体评价,从而证实我们方法良好的实验效果和实用价值。最后,本论文分析比较VP和VFP模型,并给出各自的优缺点和适应范围。实验结果标明,在低噪声图像中,VP优于VFP,而在噪声明显的图像中,VFP则更优越。
With the rapid development of remote sensing techniques, remote sensing image fusion has been attracting more and more attention recently. Remote sensing image fusion aims to analyze and combine the remotely sensed images to obtain a single image which is more robust and informative. In this thesis, based on the variational theory, we propose four fusion models. Among them, three models are built for a branch of fusion: Pan-sharpening, which is a process of integrating a low resolution multi-spectral (MS) image with its corresponding panchromatic image to obtain a single high resolution MS image. The main idea of this thesis is to build the related energy functional based on some distinct hypotheses, and to obtain the final fusion result by minimizing the energy. In the numerical scheme, we use the split Bregman iteration to obtain the fusion results more stably, effectively and efficiently. Our main contributions are as follows:
●Firstly, we assume that the gradient of the fused image should be close to the most salient gradient in the multisource inputs. Based on this assumption, we develop a new pixel based variational model. In detail, we first extract the gradient of original images and combine them based on a certain rule, then treat this combined gradient as a term. By further take some features such as brightness equalization into account, an energy functional is built for enhancing the fusion effects. The model is implement by using the split Bregman iteration, and compared with many outstanding methods.
●Secondly, we assume that the pan-sharpened image should keep the spatial infor-mation, spectral information and spectral correction. Based on this assumption, we build an new variational model, named VP, for Pan-sharpening. We also discuss the existence of minimizer of our energy and describe the numerical procedure based on the split Bregman algorithm. For evaluating fusion results more effectively, we try to classify the existing measures into several categories. To verify the effectiveness of VP model, we compare it with some state-of-the-art schemes using QuickBird and IKONOS data. The results demonstrate the effectiveness and stability of VP. Besides, the computation efficiency comparison with other variational methods also shows that VP model is remarkable.
●We introduce the Framelet theory and propose two Pan-sharpening models, termed FP and VFP, based on the Framelet framework. The FP model is a coefficients choosing model, this model is simple and effective, but its results is unique which do not suitable for multifarious applications. To overcome this drawback, by combining the VP and other three fusion requirements, we build a Framelet based variational model:VFP. The alternating iteration algorithm and split Bregman iteration is further introduced to improve the numerical effect. We present the results of the two methods on the QuickBird and IKONOS images, and compare them with existing methods qualitatively and quantitatively. The comparison results demonstrate the superiority of our methods. Finally, we analyze and compare the VP and VFP, and show the advantages and disadvantages and specific scope of each model. The results show that VP outperforms VFP in low noise image, while VFP outperforms VP in high noise image.
引文
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