First of all, a novel reconstruction method in compressed sensing(CS) theory is proposed based on genetic
algorithm(GA), and its concrete flow is designed. In the method, the genetically iterative idea is adopted to reconstruct the
original signal exactly on the condition that the sparsity degree is unknown, which avoids the subspace pursuit. Furthermore,
the proposed reconstruction method is employed in high resolution range profile(HRRP) reconstruction in synthetic aperture
radar(SAR) imaging, and related SAR application model is established. In this model, the effective sparsity transform matrix
and measurement matrix are designed successfully. The simulation results not only show the effectiveness of the proposed
reconstruction method, but also verify that the reconstruction of SAR HRRP by using the proposed method is feasible and
robust.