Superpixel-based robust tensor low-rank approximation for multimedia data recovery

Recently, the low-rank matrix/tensor-based methods have attracted increasing attention for multi-dimensional multimedia data (e.g., image and video) recovery, which assumes the holistic data is low-rank. For most multimedia data, the low-rank assumption is usually violated due to their spatially diverse local similarity. The cube-based method, which breaks the holistic image into small local cubes with a fixed size, can alleviate this issue to some extent. However, cubes with a fixed size are not flexible to cover the regions of local similarity at different scales. Inspired by the superpixel, we suggest the size-adaptive super-tensor as the generic unit instead of the cube with the fixed spatial size, which allows us to flexibly exploit the local similarity at different scales. The super-tensor enjoys significant low-rankness and avoids excessive overlapped pixels as compared with cubes of fixed sizes. Empowering with the super-tensor, we propose a low-rank super-tensor approximation (LRSTA) model for multi-dimensional data recovery, which can fully exploit the local similarity and low-rankness at different scales. Moreover, we develop an efficient alternating direction method of multipliers (ADMM) algorithm to solve the proposed model. Extensive experiments on multimedia data, including color images, multispectral images (MSIs), and videos, verify that the proposed method outperforms the other competing methods.