In existing sparsity-driven inverse synthetic aperture radar (ISAR) imaging framework a sparse recovery (SR) algorithm is usually applied to azimuth compression to achieve high resolution in the cross-range direction. For range compression, however, direct application of an SR algorithm is not very effective because the scattering centers resolved in the high resolution range profiles at different view angles always exhibit irregular range cell migration (RCM), especially for complex targets, which will blur the ISAR image. To alleviate the sparse recovery-induced RCM in range compression, a sparsity-driven framework for ISAR imaging named Fourier-sparsity integrated (FSI) method is proposed in this paper, which can simultaneously achieve better focusing performance in both the range and cross-range domains. Experiments using simulated data and real data demonstrate the superiority of our proposed framework over existing sparsity-driven methods and range-Doppler methods.