基于Kronecker积的图像超分辨率快速算法

Fast Image Super-Resolution Reconstruction Algorithms Based on Kronecker Product of Matrices

本文提出了基于矩阵Kronecker积的图像超分辨率快速重构算法.基于观测模型的图像超分辨率重构算法是研究较多的方法,观测模型包含两个维数很大的降采样矩阵和模糊矩阵,这两个矩阵均可以表示为两个维数相对较低的矩阵的Kronecker积.因此图像降质可以分解为两个独立的过程,首先对行向降质,然后再对列向降质.根据这一观点,文章提出了一个与现有模型等价的新模型,并进一步证明用于克服逆向病态的正则化算子也可以作这样的分解.基于新的观测模型,文章提出了共轭梯度法来实现图像的超分辨率重构,与传统方法不同的是,本文算法直接使用矩阵而不是向量作为决策变量.文章给出了理论分析,实验结果证实新算法确实能显著的节省时间和存储空间开销.

This paper presents a fast algorithm for image super-resolution reconstruction based on the Kronecker product of matrices. In most iiteratures image super-resolution reconstruction algorithms are based on the observation model. This model contains a decimation matrix and blur matrix which have very large dimension. The two matrices can be represented respectively as the Kronecker product of two small matrices. So the degrading procedure can be accomplished first by the row-wise and then by the column-wise.Based on this decomposition, the original observation model can be transformed to an equivalent one.Further more we prove that the regularization operator can be decomposed by using the same technology. The conjugate-gradient optimization method that uses a matrix as decision variable is used to solve this new model. The proposed algorithm can extremely reduce the storage requirement and time consumption. We provide theoretic results and the simulations show they are valid.