For inverse synthetic aperture radar(ISAR),an ISAR signal in the cross-range direction has the characteristic of sparsity in the azimuth frequency domain.Due to this property,a Fourier basis is adopted as a kind of sparse basis,and high cross-range resolution imaging is achieved by using the compressed sensing(CS)method.However,the Fourier expanding for signal with finite length will result in energy leaking and spectrum widening.As a result,the Fourier basis cannot obtain the optimum sparse representation for signals of unknown frequencies in most cases.In this paper,we present an improved Fourier basis for sparse representation of the ISAR signal,which is constructed by frequency shift and weighting of the Fourier basis and available to obtain the robust recovery performance via CS.Simulation results show that the improved CS method outperforms conventional CS method that uses the Fourier basis. For inverse synthetic aperture radar (ISAR), an ISAR signal in the cross-range direction has the characteristic of sparsity in the azimuth frequency domain. Du to this property, a Fourier basis is adopted as a kind of sparse basis, and high cross- range resolution imaging is achieved by using the compressed sensing (CS) method. However, the Fourier expanding for signal with finite length will result in energy leaking and spectrum widening. As a result, the Fourier basis can not obtain the optimum sparse representation for signals of unknown frequencies in most cases.In this paper, we present an improved Fourier basis for sparse representation of the ISAR signal, which is constructed by frequency shift and weighting of the Fourier basis and available to obtain the robust recovery performance via CS.Simulation results show that the improved CS method outperforms conventional CS method that uses the Fourier basis.