<p>This paper proposes an adaptive noise reduction method via a hierarchical structure. In every level of the structure, the original residue is decomposed into two components which are the updated residue and the noise, respectively. Here, the two components are obtained through solving an optimization problem such that the sum of the difference energies is minimized subject to the length specification on the variable vector. In particular, the two components are guaranteed to be orthogonal to each other when the length of the variable vector is one. The optimization problem is a nonconvex QCQP problem which can be relaxed to a convex SDP problem. It can be proved that the solution of the SDP problem is also the solution of the QCQP problem under a certain condition. As the hierarchical decomposition proceeds, it is found that the SNRs of the denoised signals first increase then decrease with respect to the decomposition levels. In order to estimate the optimal level, an adaptive strategy based on the maximum of the sum of the denoised signal energy and the noise energy is proposed to stop the algorithm. Simulation results show the superior performance yielded by our proposed method over some existing approaches.</p>