We present an efficient and computationally simple approach for synthetic aperture radar (SAR) imaging in cases when the radar data have gaps, due to missing pulses and/or notches in the frequency band. Our method is a simple variation of gradient projection, in which the search path in each iteration is obtained by projecting the negative-gradient of the L1 norm onto a hyper-plane defining solutions which are consistent with the data. The computations are not complicated since the L1 gradient is simply equal to the sign() of the pixels in the image. Computational efficiency is obtained by incorporating the polar format algorithm, which accomplishes the projection operation using a fast Fourier transform. Sample results are presented using the AFRL Gotcha 2006 radar data set and the Space Dynamics Laboratory FlexSAR system.