Abstract: Radar-detected targets commonly exhibit micro-motion characteristics. Separating the echoes from the target body and its micro-motion components is crucial for feature extraction and target identification. This paper proposes an adaptive noise estimation method for separating target body and micro-vibration component echo signals in narrowband radar systems. First, based on the low-rank of the time-frequency representation (TFR) of the main body echo signal and the sparsity of the TFR of the micro-vibration component echo signal, the problem of separating the target main body and micro-vibration component echo signals is modeled as a low-rank sparse decomposition problem. Second, considering that echo signals typically contain noise in practice, a noise variable is introduced into the model. Based on the principle of orthogonal matching, the penalty parameter for the noise variable is adaptively updated. Finally, an alternating iteration framework is employed, utilizing singular value decomposition, soft thresholding functions, and the dual ascent principle to estimate the TFR of the main body echo signal, the micro-motion component echo signal, and the noise power, respectively. Simulation and experimental results validate the effectiveness and robustness of the proposed method.