It is well known that for Earth observations, the spaceborne synthetic aperture radar (SAR) systems at L‐band can be seriously affected by the ionosphere. Fortunately, the destructive ionospheric information, total electron content (TEC), can be retrieved and removed by model inversion from SAR echoes and becomes a subject of interest for ionospheric research. Considering the system noise and channel phase imbalance, this paper focuses on accurate TEC retrieval from the Faraday rotation angle, which is embedded in Advanced Land Observing Satellite phased array L‐band synthetic aperture radar (PALSAR) full‐pol data. For the consideration of denoising, averaging filtering is widely used in existing studies to remove the system noise. In order to further reduce the noise effects, a fast total variation (FTV) denoising method is applied in this paper. By using the PALSAR full‐pol data sets, a series of simulation results show that the FTV denoising is effective for noise suppression and markedly reduce the standard deviation. For the error of channel phase imbalance, a new Faraday estimator based on the covariance matrix of circular basis is proposed. Compared with previous estimators, theoretical analysis and simulation results show that this new estimator can give the best performance for sensors that are dominated by channel phase imbalance errors. Thus, the proposed estimator can be a candidate method for TEC retrieval when phase imbalance is the domain error.