基于秩极小化理论的单幅图像超分辨率复原

发布时间：2019-03-23 20:18

【摘要】：图像超分辨率复原技术是当今图像处理领域一项极具挑战性且受到广泛关注的前沿研究课题。在图像的成像过程中，受硬件设备和成像系统的制约，最终获取的图像并不是原始场景的整体复原，不能保存原有的全部信息。超分辨率复原技术是成像的逆过程，主要是指利用一幅或者多幅低分辨率的图像来恢复高分辨率的图像。近几年，受信号处理领域压缩感知思想的启发，图像超分辨复原领域涌现出很多利用稀疏表示的方法，主要是基于向量的稀疏性进行研究的。本文从矩阵角度出发，利用秩极小化理论对单幅图像超分辨复原问题进行研究。首先，建立单幅图像超分辨率复原的压缩主成分追踪模型。模型中的近似低秩矩阵是根据图像的非局部自相似性构造的。本文采用增广拉格朗日乘子法将近似低秩矩阵分解成低秩矩阵和稀疏矩阵的和，，并将恢复的低秩矩阵作为高分辨率图像。其次，将压缩主成分追踪模型进行推广，建立了单幅图像超分辨率复原的Outlier Pursuit模型。该模型不仅考虑了恢复的低秩部分，也合理利用了恢复的稀疏差异部分，将两者共同作为复原的高分辨率图像。最后，通过实验进行仿真，实验结果表明，基于秩极小化理论建立的单幅图像超分辨复原模型是可行的，且采用低秩和稀疏部分联合的Outlier Pursuit模型所恢复的图像比只采用低秩部分的压缩主成分追踪模型更有效。
[Abstract]:Image super-resolution restoration technology is a very challenging and widely concerned frontier research topic in the field of image processing. In the image imaging process, because of the restriction of hardware equipment and imaging system, the acquired image is not the whole restoration of the original scene, and can not save all the original information. Super-resolution restoration is the inverse process of imaging, mainly refers to the use of one or more low-resolution images to restore high-resolution images. In recent years, inspired by the idea of compression perception in the field of signal processing, a lot of sparse representation methods have emerged in the field of image super-resolution restoration, mainly based on the sparsity of vectors. In this paper, the super-resolution restoration of single image is studied by using rank minimization theory from the angle of matrix. Firstly, a compressed principal component tracking model for super-resolution restoration of single image is established. The approximate low rank matrix in the model is constructed according to the nonlocal self-similarity of the image. In this paper, the augmented Lagrangian multiplier method is used to decompose the approximate low-rank matrix into the sum of low-rank matrix and sparse matrix, and the restored low-rank matrix is used as a high-resolution image. Secondly, the compressed principal component tracking model is generalized, and the Outlier Pursuit model of single image super-resolution restoration is established. The model not only considers the low rank part of the restoration, but also makes reasonable use of the sparse difference part of the restoration, and takes the two parts together as the restored high-resolution image. Finally, the simulation results show that the single image super-resolution restoration model based on rank minimization theory is feasible. The Outlier Pursuit model based on the combination of low rank and sparse parts is more efficient than the compressed principal component tracking model which only uses the low rank part.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TP391.41

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