  Exact recovery of tensor decomposition (TD) methods is a desirable property
in both unsupervised learning and scientific data analysis. The numerical
defects of TD methods, however, limit their practical applications on
real-world data. As an alternative, convex tensor decomposition (CTD) was
proposed to alleviate these problems, but its exact-recovery property is not
properly addressed so far. To this end, we focus on latent convex tensor
decomposition (LCTD), a practically widely-used CTD model, and rigorously prove
a sufficient condition for its exact-recovery property. Furthermore, we show
that such property can be also achieved by a more general model than LCTD. In
the new model, we generalize the classic tensor (un-)folding into reshuffling
operation, a more flexible mapping to relocate the entries of the matrix into a
tensor. Armed with the reshuffling operations and exact-recovery property, we
explore a totally novel application for (generalized) LCTD, i.e., image
steganography. Experimental results on synthetic data validate our theory, and
results on image steganography show that our method outperforms the
state-of-the-art methods.
