Research On Network Sparse Signal Processing Based On Distributed Recursive Least Square Algorithm

With the development of the network theory and network technology, the signal and information processing over network has become the hotspot in signal processing community. Distributed estimation is an important technique for in-network signal processing. It relies only on local data exchange and cooperation between immediate neighbors to achieve good estimation performance whilst reduce complexity and resource consumption, as well as increase scalability and robustness, as opposed to the centralized estimation.The traditional distributed estimation lacks the mechanism to utilize the inherent structure of the signals to improve the estimation. However, it is found that many nature or man-made signals present high level of sparsity, which contains only a few large coefficients among many negligible ones. This thesis focuses on the sparse signal estimation over network. We address the problem of in-network distributed estimation for sparse signals and extend the distributed recursive least-squares (RLS) algorithm to the sparse estimation issue. Moreover, it is noticed that the sparsity of many signals is often time-varying in many applications. Therefore, we also develop the distributed RLS for the sparse time-varying signals. The main works of this thesis are as follows:1. Brief introduction of signal processing over network and sparse estimation problem. Firstly, the basic ideas of the in-network processing and the sparse signal estimation is introduced; then, the two structures used for the in-network processing is discussed, including the centralized processing and distributed processing; finally, the distributed RLS algorithm, which is the core of our following work, is introduced.2. Development of the distributed sparse estimation based on the distributed RLS algorithm. The developed algorithm relies on the expectation-maximization (EM) algorithm and the sparse regularization to iteratively update the local estimation and therefore to achieve the global optimal estimation. The key to the proposed algorithm is to design the thresholding operators to constraint the sparsity of the local estimation according to the sparse regularization. To improve the estimation of the l1-norm and l0-norm regularizations, we propose the lp-norm(0<p<1) regularization and the continuous power function approximation-based regularization. The proposed sparse regularizations improve the sparsity-promoting ability of the l1-norm and avoid the instability of the l0-norm due to its non-convexity. The effectiveness of the proposed algorithms is proved in simulation experiments.3. Study of the distributed estimation for time-varying sparse signal. To utilize a prior information of the time-varying sparse signal in the distributed RLS estimation, we propose the weighted l1norm regularization, which updates the weights according to the sparse structure of the local estimation. Combined with the weighted l1-norm regularization, the developed distributed sparse RLS algorithm can track the variations of the signal’s sparsity. Simulation results demonstrate that the proposed weighted l1-norm regularization-based sparse RLS algorithm can effectively estimate the time-varying sparse signals.