A new two-dimensional signal decomposition scheme using the extreme-lifting scheme

We discuss the signal decomposition method using the extreme-lifting scheme and two two-dimensional decomposition schemes: separable one-dimensional scheme and two-dimensional scheme with quincunx sampling. The structure of the relation~between E_x and E_y is symmetrical of these two schemes. Both these two schemes have shortcomings. In order to overcome the shortcomings of the previous two schemes, we also give an unsymmetrical scheme of the extreme-lifting scheme that can be directly used to decompose a two-dimension image. This method can get a better decomposition result than the previous two schemes with little calculation cost