Image Interpolation via Low-Rank Matrix.pdf

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 25, NO. 8, AUGUST 2015 1261 Image Interpolation via Low-Rank Matrix Completion and Recovery Feilong Cao, Miaomiao Cai, and Yuanpeng Tan Abstract— Methods of achieving image super-resolution (SR) have been the object of research for some time. These approaches suggest that when a low-resolution (LR) image is directly downsampled from its corresponding high-resolution (HR) image without blurring, i.e., the blurring kernel is the Dirac delta function, the reconstruction becomes an image-interpolation problem. Hence, this is a pervasive way to explore the linear relationship among neighboring pixels to reconstruct a HR image from a LR input image. This paper seeks an efficient method to determine the local order of the linear model implicitly. According to the theory of low-rank matrix completion and recovery, a method for performing single-image SR is proposed by formulating the reconstruction as the recovery of a low-rank matrix, which can be solved by the augmented Lagrange multiplier method. In addition, the proposed method can be used to handle noisy data and random perturbations robustly. The experimental results show that the proposed method is effective and competitive compared with other methods. Index Terms— Augmented Lagrange multiplier (ALM), image interpolation, low-rank matrix recovery, reconstruction, super- resolution (SR). I. INTRODUCTION IMAGE super-resolution (SR) technology is always desir-able in visual information processing to obtain more detail in an image. It aims to reconstruct a high-resolution (HR) image from one or more low-resolution (LR) images [1], [2]. This task essentially can be converted into an inverse problem of the image degradation process. However, the SR problem is inherently ill-posed because many HR images can generate the same LR image by downsampling. Therefore, prior knowl- edge and fundamental assumptions are necessary to obtain high-quality HR images fro