A novel technique for radar-imaging inversions is proposed which leverages ideas from the emerging field of compressed sensing. This new method takes advantage of the transform sparsity inherent in natural images. Theoretical recovery results are promising and are borne out by simulations in which this technique outperforms Capon's method and the Maximum Entropy method. Preliminary results using data collected at the Jicamarca Radio Observatory are also presented. Key Points Compressed sensing theory can improve radar imaging experiments ©2013. American Geophysical Union. All Rights Reserved.