Autoregressive backprojection (ARBP) approximates the procedure of forming syntheticaperture radar (SAR) sequential images as an autoregressive (AR) process, avoiding redundant computation between adjacent images. Azimuth apodization for ARBP entails designing the aforementioned AR process, including AR order selection and AR model parameter estimation. However, the conventional azimuth apodization method for ARBP provides only empirical means to conduct such a procedure. Moreover, it cannot address the ringing effect from the infinite impulse response of the AR model, and consequently, other unwanted azimuth pulses will degrade the SAR images. This study discusses azimuth apodization for ARBP and proposes a scheme that includes methods for AR model order selection and parameter estimation. Firstly, matrix rank-k approximation is adopted for AR model order selection. Then, a revised azimuth apodization procedure for parameter estimation is discussed. It introduces a penalty factor to render the ringing effect and model estimation error controllable. Moreover, experiments based on an open data set validate the proposed ARBP azimuth apodization scheme. In this way, the proposed azimuth apodization obtains a balance between computational complexity and imaging quality for ARBP.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.