Rong Chen

Chencheng Cai, Rong Chen, Han Xiao

We consider the problem of matrix approximation and denoising induced by the Kronecker product decomposition. Specifically, we propose to approximate a given matrix by the sum of a few Kronecker products of matrices, which we refer to as the Kronecker product approximation (KoPA). Because the Kronecker product is an extension of the outer product from vectors to matrices, KoPA extends the low rank matrix approximation, and includes it as a special case. Comparing with the latter, KoPA also offers a greater flexibility, since it allows the user to choose the configuration, which are the dimensions of the two smaller matrices forming the Kronecker product. On the other hand, the configuration to be used is usually unknown, and needs to be determined from the data in order to achieve the optimal balance between accuracy and parsimony. We propose to use extended information criteria to select the configuration. Under the paradigm of high dimensional analysis, we show that the proposed procedure is able to select the true configuration with probability tending to one, under suitable conditions on the signal-to-noise ratio. We demonstrate the superiority of KoPA over the low rank approximations through numerical studies, and several benchmark image examples.

Xiaotong Luo, Rong Chen, Yuan Xie et al.

Image quality measurement is a critical problem for image super-resolution (SR) algorithms. Usually, they are evaluated by some well-known objective metrics, e.g., PSNR and SSIM, but these indices cannot provide suitable results in accordance with the perception of human being. Recently, a more reasonable perception measurement has been proposed in [1], which is also adopted by the PIRM-SR 2018 challenge. In this paper, motivated by [1], we aim to generate a high-quality SR result which balances between the two indices, i.e., the perception index and root-mean-square error (RMSE). To do so, we design a new deep SR framework, dubbed Bi-GANs-ST, by integrating two complementary generative adversarial networks (GAN) branches. One is memory residual SRGAN (MR-SRGAN), which emphasizes on improving the objective performance, such as reducing the RMSE. The other is weight perception SRGAN (WP-SRGAN), which obtains the result that favors better subjective perception via a two-stage adversarial training mechanism. Then, to produce final result with excellent perception scores and RMSE, we use soft-thresholding method to merge the results generated by the two GANs. Our method performs well on the perceptual image super-resolution task of the PIRM 2018 challenge. Experimental results on five benchmarks show that our proposal achieves highly competent performance compared with other state-of-the-art methods.