Basis Pursuit is a novel method of signal sparse representation.It seeks sparse representation from over-complete dictionaries.That is to use the fewest dictionary elements to represent the signal exactly.Then the intrinsic feature of the signal can be captured.We extend the application of the Basis Pursuit method to SAR super-resolution processing.Firstly

based on the SAR attributed scattering model

a new type compacted Dictionary is designed in phase history domain.By this way

the dimension of the desired problem is even smaller.Secondly

a new and fast iterative algorithm is proposed

the fine feature parameter estimation of the scatter in SAR image is obtained.Finally

in terms of SAR attributed scattering model in the phase history domain

larger scale phase history data is built.By FFT imaging

higher resolution image is obtained.Simulation experiments and computational results of measured MSTAR data demonstrate that Basis Pursuit can be implemented speedy and stably

it can provide super-resolution at the same time.