Nonconvex compressed sensing with partially known signal support

We study recovering sparse and compressible signals using lp minimization with p<1p<1 when some part of the support of the signal is known a priori. Sparse reconstruction method based on lp minimization with partially known set is proposed and recovery conditions are given. Theoretical results show that lp minimization with partially known support is stable and robust. Experimental results are presented to expose the modification of lp minimization improves performance and need fewer samples to reconstruct the signal.