Abstract: Synthetic aperture radar （SAR） images often exhibit characteristic artifacts， among which azimuth ambiguities caused by limited pulse repetition frequency （PRF） and non-ideal antenna patterns are particularly prominent. Meanwhile， as the demand for high resolution and wide coverage increases， SAR systems often need to reduce PRF to expand swath width and decrease data volume， further aggravating azimuth ambiguities and severely degrading image quality. Existing methods usually struggled to rapidly suppress azimuth ambiguities， deteriorating image resolution. In recent years，$L_{\mathrm{1}}$-norm regularization techniques have attracted widespread attention owing to their superior reconstruction performance on undersampled echo data； however， conventional $L_{\mathrm{1}}$-norm regularization-based sparse SAR imaging methods still failed to achieve high-quality imaging for low-PRF echo data. To address this issue， this study proposed a sparse SAR unambiguous imaging method based on spectrum truncation. The method modifies the iterative process of solving the $L_{\mathrm{1}}$-norm optimization problem using the iterative shrinkage-thresholding algorithm to achieve ambiguity-free imaging. Specifically， in each iteration， the Doppler spectrum of the current residual was truncated， and matched filtering was applied separately to the original and truncated residuals. Then， the two resulting images were compared pixel by pixel， retaining the smaller value. If the smaller value was obtained from the truncated residual， it was further scaled to enhance ambiguity suppression. Finally， the high-resolution， low-ambiguity residual was used to update the image estimate. Simulation results showed that the proposed method effectively suppressed azimuth ambiguities while retaining the noise and clutter suppression capability of conventional $L_{\mathrm{1}}$-norm regularization sparse SAR imaging methods. Moreover， its computational complexity remained comparable to conventional methods， providing a practical technical reference for high-resolution， ambiguity-free reconstruction over large scenes.