Fast image super-resolution reconstruction algorithms based on Kronecker product of matrices

This paper presents a fast algorithm for image super-resolution reconstruction based on the Kronecker product of matrices. In most literatures 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.