  Sparse representation can be described in high dimensions and used in many
applications, including MRI imaging and radar imaging. In some cases, methods
have been proposed to solve the high-dimensional sparse representation problem,
but main solution is converting high-dimensional problem into one-dimension.
Solving the equivalent problem had very high computational complexity. In this
paper, the problem of high-dimensional sparse representation is formulated
generally based on the theory of tensors, and a method for solving it based on
SL0 (Smoothed Least zero-nor) is presented. Also, the uniqueness conditions for
solution of the problem are considered in the high-dimensions. At the end of
the paper, some numerical experiments are performed to evaluate the efficiency
of the proposed algorithm and the results are presented.
