  The problem of recovering a low $n$-rank tensor is an extension of sparse
recovery problem from the low dimensional space (matrix space) to the high
dimensional space (tensor space) and has many applications in computer vision
and graphics such as image inpainting and video inpainting. In this paper, we
consider a new tensor recovery model, named as minimum $n$-rank approximation
(MnRA), and propose an appropriate iterative hard thresholding algorithm with
giving the upper bound of the $n$-rank in advance. The convergence analysis of
the proposed algorithm is also presented. Particularly, we show that for the
noiseless case, the linear convergence with rate $\frac{1}{2}$ can be obtained
for the proposed algorithm under proper conditions. Additionally, combining an
effective heuristic for determining $n$-rank, we can also apply the proposed
algorithm to solve MnRA when $n$-rank is unknown in advance. Some preliminary
numerical results on randomly generated and real low $n$-rank tensor completion
problems are reported, which show the efficiency of the proposed algorithms.
