Fast Blind Image Super Resolution Using Matrix-Variable Optimization

Super resolution image reconstruction under unknown Gaussian blur has been a challenging topic. Advanced optimization-based works for blind image super-resolution (SR) were reported to be effective, but there exist both large data space storage and time consuming due to vector-variable optimization. This paper proposes a matrix-variable optimization method for fast blind image SR. We first present an accurate blur kernel estimation-based matrix decomposition method. Then we propose minimizing a matrix-variable optimization problem with sparse representation and TV regularization terms. The proposed method can exactly estimate the unknown blur kernel and blur matrix. Compared with vector-variable optimization based methods for blind image SR, the proposed method can greatly reduce their data space storage and computation time. Compared with deep learning methods, the proposed method can directly deal with multiframe SR problem without training and learning task. Experimental results show that the proposed algorithm is superior to conventional optimization-based method in terms of solution quality and computation time. Moreover, the proposed method can obtain higher reconstruction quality than the deep learning methods, specially in the case of large blur kernels.