Nonconvex compressed sensing with partially known support

We study recovering sparse and compressible signals using l_p minimization with p <; 1 when some part of the support of the signal is known a priori. Sparse reconstruction method based on l_p minimization with partially known set is proposed. Recovery conditions of l_p minimization with partially known support is given. Theoretical results show that l_p minimization with partially known set is stable and robust. Furthermore, numerical results show that l_p minimization with partially known support needs fewer measurements than the standard compressed sensing with partially known support.