Comparison of basis selection methods

We describe and evaluate three forward sequential basis selection methods: basic matching pursuit (BMP), order recursive matching pursuit (ORMP) and modified matching pursuit (MMP), and a parallel basis selection method: the focal underdetermined system solver (FOCUSS) algorithm. Computer simulations show that the ORMP method is superior to the BMP method in terms of its ability to select a compact basis set. However, it is computationally more complex. The MMP algorithm is developed which is of intermediate computational complexity and has a performance comparable to the ORMP method. All the sequential selection methods are shown to have difficulty in environments where the basis set contains highly correlated vectors. The drawback can be traced to the sequential nature of these methods suggesting the need for a parallel basis selection method like FOCUSS. Simulations demonstrate that the FOCUSS algorithm does indeed perform well in such correlated environments. However, a drawback of FOCUSS is that it is computationally more intense then the sequential selection methods.