基于方向滤波器组的无冗余拉普拉斯金字塔框架设计

Non-Redundant Laplacian Pyramid Design Based on Directional Filter Bank

拉普拉斯金字塔(Laplacian Pyramid,LP)是多分辨率分析的有效工具,并且得到了广泛的应用,例如应用在contourlet变换中.然而,拉普拉斯金字塔固有的冗余特性,限制了其在图像压缩等领域的应用.本文提出一种基于方向滤波器组的无冗余拉普拉斯金字塔框架.首先,分析了目前常见的金字塔结构的冗余的来源;然后,回顾了临界抽取理论;进而,结合DFB与无冗余的金字塔结构提出了一种具有多分辨率以及多方向性的实现结构;最后,在图像的非线性近似(NLA)方面的试验表明,该方案在一定程度上优于contourlet变换以及小波变换.

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 Iransform, however the drawback of its implicit oversampling prevents it from being used for im- age 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）.