基于最优一维分解的图像超分辨方法

提出了一种用分离变量的一维函数乘积形式逼近二维图像数据的方法，通过在一维空间的超分辨处理，很容易实现对图像的超分辨处理。从理论上证明了这种表达是最优的。实际结果显示了超分辨的效果好，计算量小。这种方法也可应用于图像处理的其他领域和海量数据信息特征提取。

Image Superresolution Basing on the Optimum Discomposition

In this paper a novel method for image superresolution is proposed. The primary theory is proved that the 2-dimension image data can be approximated by the products of 1-dimension functions whose variables are separated from the image' s variables. Therefore, the image superresolution can proceed conveniently through the 1-dimension superresolution. Concretely, the digital image (M×N) can be expressed by the summation of the products ofM-dimension vectors andN-dimension vectors. So the image superresolution process can be converted to the M-dimension vector processing and theN-dimension vector processing easily. Thus the method is based on the eigenvectors. In the mean-square-error sense, this expression or decomposition is optimum. It is also proved to be identical with the literature3] when the hits go to infinite. At last the applications verify the theoretical result. Namely, this method has the better results and can reduce the calculations because the image can be adjusted adaptively and be expressed by the less parameters. In addition, this method can also be applied to other fields of image processing and the information processing of the great-capacity data.