利用Box样条构造完全重构模型的研究

Research of Constructing a Perfect Reconstruction Model Using Box Spline

针对图象处理中的图象重构问题 ,结合多频带 DFT滤波器库和双变量 Box样条构造了一个完全重构模型 .在介绍了 DFT滤波器库后 ,给出了形成完全重构模型的条件 .通过双变量 Box样条及其在图象处理中极为有用的几条性质的分析 .提出了一类双变量 Box样条 ,使用该样条即可构造分解 /重构模型 .实验证明 ,该模型能满足完全重构条件 ,并可有效分解合成图象 .最后 。

This paper presents a method to combine so\|called multiband DFT filter bank with bivariate Box splines to construct a perfect reconstruction model for image processing. Based on the theory of B\|splines, which are useful tool in many fields, Box Spline is said to be an extension, with the aim at describing multi\|variate functions. In this paper, firstly, it introduces the DFT filter bank, and presents the condition to form a perfect reconstruct model. Then it describes bivariate Box splines and its some properties in little more details. It especially presents a particular class of bivariate Box splines, and use it to construct a decomposition/reconstruction model, which may be candidates for some kinds of task in image processing. This model is proved to be satisfied by the perfect reconstruction condition, and thus can be quite useful theoretically. At last, some experimental results are given to demonstrate the use fulness of this model.