The ultrasound attenuation coefficient estimation (ACE) technique has diagnostic potential for quantifying liver fat content. We previously proposed a reference frequency method (RFM) for estimating the attenuation coefficient that does not require the use of a well-calibrated phantom. This method, however, may be vulnerable to severe reverberation clutters introduced by the body wall. The reverberation clutters are assumed to be static as sonographers press the transducer against the scanning area because the majority of the reverberation signals originate from the abdominal wall. In addition, it is assumed that the tissue signals consist of motion because the subject is freely breathing. The goal of this study is to estimate and suppress static reverberation clutters in received signals so that a robust ACE with large reverberation clutters can be achieved. To estimate and suppress severe reverberation clutters, we proposed using robust principal component analysis (RPCA) in conjunction with wavelet-based sparsity promotion. The benefit of wavelet-based sparsity promotion is that it projects tissue signals into the wavelet domain in order to fitful the sparsity condition in the RPCA. The proposed method was validated on two calibrated tissue-mimicking phantoms (0.95 dB/cm/MHz and 0.68 dB/cm/MHz), where tissue signals were mixed with reverberation clutters. The proposed method produced better attenuation coefficient estimation (0.93 dB/cm/MHz and 0.67 dB/cm/MHz) than without the proposed method (0.81 dB/cm/MHz and 0.5 dB/cm/MHz).