  In this paper, we study multi-dimensional image recovery. Recently,
transform-based tensor nuclear norm minimization methods are considered to
capture low-rank tensor structures to recover third-order tensors in
multi-dimensional image processing applications. The main characteristic of
such methods is to perform the linear transform along the third mode of
third-order tensors, and then compute tensor nuclear norm minimization on the
transformed tensor so that the underlying low-rank tensors can be recovered.
The main aim of this paper is to propose a nonlinear multilayer neural network
to learn a nonlinear transform via the observed tensor data under
self-supervision. The proposed network makes use of low-rank representation of
transformed tensors and data-fitting between the observed tensor and the
reconstructed tensor to construct the nonlinear transformation. Extensive
experimental results on tensor completion, background subtraction, robust
tensor completion, and snapshot compressive imaging are presented to
demonstrate that the performance of the proposed method is better than that of
state-of-the-art methods.
