Compressive Sensing Reconstruction With Prior Information by Iteratively Reweighted Least-Squares

Iteratively reweighted least-squares (IRLS) algorithms have been successfully used in compressive sensing to reconstruct sparse signals from incomplete linear measurements taken in nonsparse domains. The underlying optimization problem corresponds to finding the vector that solves the ${\ell _{p}}$ minimization while explaining the measurements, and IRLS allows to easily control the used value of ${p}$, with effect on the number of required measurements. In this paper, we propose a weighting strategy in the reconstruction method based on IRLS in order to add prior information on the support of the sparse domain. Our simulation results show that the use of prior knowledge about positions of at least some of the nonzero coefficients in the sparse domain leads to a reduction in the number of linear measurements required for unambiguous reconstruction. This reduction occurs for all values of ${p}$ , so that a further reduction can be achieved by decreasing ${p}$ and using prior information. The proposed weighting scheme also reduces the computational complexity with respect to the IRLS with no prior information, both in terms of number of iterations and computation time.