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Sparse representation can be described in high dimensions and used in manyapplications, including MRI imaging and radar imaging. In some cases, methodshave 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 thispaper, the problem of high-dimensional sparse representation is formulatedgenerally based on the theory of tensors, and a method for solving it based onSL0 (Smoothed Least zero-nor) is presented. Also, the uniqueness conditions forsolution of the problem are considered in the high-dimensions. At the end ofthe paper, some numerical experiments are performed to evaluate the efficiencyof the proposed algorithm and the results are presented.

Fast and Robust High-Dimensional Sparse Representation Recovery Using Generalized SL0