Recovery of Real-Valued Sparse Models in the Multi-Dimensional Spectral Domain

The objective of this work is to present different approaches for recovering a sensed real-valued sparse model in the spectral domain and its embed frequency parameters. We address compressed sensing approaches based on
$\ell_{A,0}$
and
$\ell_{A,3}$
atomic norms, showing the conditions to recover these models and presenting the corresponding methodology to solve the norms. As an application scenario, the proposed methodology is validated with 2-D images representing different weaving patterns in canvases, that allow a sparse representation in the spectral domain. The results show that the proposed methodology allow an error free recovery of the number of threads in the cloth.