Fourier domain methods are fast algorithms for SAR imaging. They typically involve an interpolation in the frequency domain to re-grid non-uniform data so inverse fast Fourier transforms can be performed. In this paper, we apply a frame reconstruction algorithm, extending the non-uniform fast Fourier transform, to stripmap SAR data. Further, we present an improved thresholded frame reconstruction algorithm for robust performance and improved computational efficiency. We demonstrate compelling results on real stripmap SAR data.