Construction and Application of Multi- dimensional Wavelets Using Gröbner Basis

The problem of Construction and Application of Multi-dimensional Wavelets is studied. Using the concept of Gröbner basis and the algorithms of syzygy module in computing algebra, we design the symmetry-orthogonality multi-band multi-dimensional filter banks. Moreover, the expression of multi-scale function is achieved, which is used to construct multi- dimensional wavelets by multidimensional filter banks. Finally a orthogonal 2D wavelets which is Constructed in the paper is used to a remote sensing image coding. Experimental results show that it is much better coding performance.