Laplacian pyramid(LP) is an effective tool to form a multi-resolution system and is widely used since its proposal such as the structure of contourlet transform

however the drawback of its implicit oversampling prevents it from being used for image compression and etc.In this paper

a non-redundant and multi-directional pyramid structure is proposed.We illustrate the source of the redundancy of the pyramid structure first

and then make a review about the maximal decimation theory and give the solution of solving the redundancy of LP.Then we suggest a pyramid based non-redundancy structure and combine this with the DFB to form a new system to achieve the multi-resolution and multi-directional features.The results of our experimental work show its superiority over contourlets and wavelets in the nonlinear approximation (NLA).