Tao Hong, M.Sc. Thesis Seminar
In the previous research, people tend to optimize the sensing matrix to improve the signal reconstruction accuracy for compressive sensing (CS) system. However, they assume the signal is exactly sparse which is not true in practice. So we try to find a way to design a sensing matrix which is robust to the case when the signal is not exactly sparse. Moreover, we also take the complexity of sensing a signal into account in designing the sensing matrix procedure. A novel model is proposed and an alternating algorithm is derived to solve it. A global sequence convergence analysis is built for the proposed algorithm in this case.
Recently, we introduce a novel speeding-up convergence method called SESOP-MG which merges SEquential Subspace Optimization (SESOP) and Multigrid (MG) for large-scale optimization problems. Utilizing the hierarchical methodology in MG, we obtain additional descent directions from the coarse problem which can be solved easily compared with the original one called fine problem. Adding such additional descent directions to the subspace of SESOP, we observe a faster convergence rate compared with the original MG. The theoretical analysis also demonstrates that our observation is promised.