An effective LRTC model integrated with total α ‐order variation and boundary adjustment for multichannel visual data inpainting

Abstract

Restoring damaged multichannel visual data with high loss ratio is quite a challenging task. To address this problem, an effective LRTC (low-rank tensor completion) model integrated with total α-order variation (TVα) in the fractional bounded variation space BVα is proposed to perform superior fractional-in-space regularization. Based on using LR constraint to restore global patterns, TVα regularization is integrated to exploit nonlocally-correlated information on each channel to infer the lost data and simultaneously effectively deal with complex details due to the powerful fractional calculus. Then, a nonlocal fractional regularization strategy for multi-dimensional data and an effective numerical optimization method are creatively designed to solve this problem. Two novel fractional derivative matrix approximations are derived and applied to the first two unfolding modes of the tensor respectively to conveniently solve the fractional regularization subproblem by using an element-wise shrinkage-thresholding operation. In addition, boundary extension and adjustment strategy are designed for the unfolded matrices to alleviate the influence of inaccurate boundary conditions in fractional derivative computations. Experiments are conducted to illustrate its performance and efficiency for YUV video, RGB and HSI restoration, especially its ability to effectively recover complex structures and the details of multi-component visual data with relatively high missing rate.