Nonlinear Transform Induced Tensor Nuclear Norm for Tensor Completion

The linear transform-based tensor nuclear norm (TNN) methods have recently obtained promising results for completion. main idea of these is exploiting the low-rank structure frontal slices targeted under transform along third mode. However, low-rankness not significant transforms family. To better pursue approximation, we propose a nonlinear TNN (NTTNN). More concretely, proposed composite consisting semi-orthogonal mode and element-wise on transform. two in are indispensable complementary to fully exploit underlying low-rankness. Based suggested metric, i.e., NTTNN, completion model. tackle resulting nonconvex optimization model, elaborately design proximal alternating minimization algorithm establish theoretical convergence guarantee. Extensive experimental hyperspectral images, multispectral videos show that our method outperforms state-of-the-art LRTC terms PSNR, SSIM, SAM values visual quality.