Low-Rank Total Variation for Image Super-Resolution

Most natural images can be approximated using their low-rank components. This fact has been successfully exploited in recent advancements of matrix completion algorithms for image recovery. However, a major limitation of low-rank matrix completion algorithms is that they cannot recover the case where a whole row or column is missing. The missing row or column will be simply filled as an arbitrary combination of other rows or columns with known values. This precludes the application of matrix completion to problems such as super-resolution (SR) where missing values in many rows and columns need to be recovered in the process of up-sampling a low-resolution image. Moreover, low-rank regularization considers information globally from the whole image and does not take proper consideration of local spatial consistency. Accordingly, we propose in this paper a solution to the SR problem via simultaneous (global) low-rank and (local) total variation (TV) regularization. We solve the respective cost function using the alternating direction method of multipliers (ADMM). Experiments on MR images of adults and pediatric subjects demonstrate that the proposed method enhances the details of the recovered high-resolution images, and outperforms the nearest-neighbor interpolation, cubic interpolation, non-local means, and TV-based up-sampling.