Experimental Self-Mixing (SM) or optical feedback interferometric signals are usually affected by additive white Gaussian noise (AWGN) and impulsive noise. Depending on SM sensing setup , these noises can significantly reduce the signal to noise ratio (SNR) of SM signals which in turn affects the measurement performance of signal processing algorithms employed for metric information retrieval. In this paper, adaptive line enhancement (ALE) technique is proposed to remove AWGN and impulsive noise from SM signals. Specifically, a recursive least squares (RLS) based ALE algorithm has been designed and the results have been compared with established methods such as high-order digital low-pass filtering and discrete wavelet transform. The comparison indicates better precision in case of use of RLS-ALE even when significant variations occur in the operating optical feedback regime and remote target velocity as well as in presence of speckle. The proposed algorithm can also estimate the SNR of SM signals belonging to weak-, moderate-, and strong-optical feedback regime with SNR ranging from 0 dB to 40 dB, with a mean absolute error of 1.35 dB and a 1.09 dB precision. Statistical analysis of noise recovered from different experimental SM signals attests the Gaussian-and impulsive-nature of noise. Thus, the proposed method also enables a simple and reliable quantitative analysis and comparison of different laser diode based SM laser sensors operating under variable optical conditions.