Abstract: Synthetic aperture interferometric radiometers (SAIRs) are an important detector in the field of passive microwave remote sensing. The imaging inversion process in SAIRs is an ill-conditioned inverse problem mathematically. Although the traditional regularization methods can effectively overcome its ill-condition, there are the problems of large reconstruction errors and poor robustness to interference noise. Compared with traditional regularization methods, the LSQR iterative method has the advantages of high calculation accuracy and good numerical stability. However, the convergence speed for the LSQR method is not fast enough. With regards to this, a subspace preconditioned LSQR (SP-LSQR) decomposition algorithm is proposed to perform the inversion imaging of SAIRs so as to improve the convergence speed. The simulation results show that compared with the Tikhonov and band-limited regularizations, the SP-LSQR method can not only reduce the reconstruction error, but also be more robust to interference noise. In addition, the SP-LSQR method effectively improves the computational efficiency without reducing the accuracy of the inversion results, compared with the LSQR method.