Construction of High-Order Balanced Multiwavelets Using Groebner Basis

To construct balanced multiwavelets which can avoid prefiltering in image processing,through a study of performance of balance in balanced multiwavelets,combing its symmetry and orthogonality,a high-order multivariable polynomial system is formed,where the coefficients of balanced multiwavelets are variables.By the application of Groebner basis algorithm in computational algebra,a group of coefficients of the 1～3 order balanced multiwavelets filter bank are obtained,and its oscillograms plotted.The oscillograms show that the higher the order of balanced wavelets,the smoother its waveform becomes,but the difficulty in computation is obviously increased.