Tensor restricted isometry property for multilinear sparse system of genomic interactions

We develop a tensor based multilinear system framework. We have shown that the TRIP gives the conditions for the sparse multilinear system to have a unique solution. We use this formulation to leverage existing theory from compressed sensing to efficiently infer the unknown coefficients. Moreover, we have also proven that the sparse signals can be recovered through the l₁ minimization. In our future work, we will provide some numerical methods based on l₁ minimization to approximate the solution to the multilinear system.