Design and Real-Time Implementation of 2-D Orthogonal Transforms with Trend Vanishing Moments for High-Functioning Image Representation

本课题提出了二维趋势消失矩正交变换，并对其进行了理论分析、设计、实现和应用研究。首先，定义了二维信号变换的一个性质--趋势消失矩（TVM），阐明了它与趋势面湮灭性质的关系。提出了基于TVMs的二维信号变换的具体设计和实现方法，实现了TVMs的定向设计和实时实现。最后通过图像复原的应用验证了所提方法的有效性。还调查了对过采样情况的扩展。

In this project, 2-D orthogonal transforms with trend vanishing moments were proposed, and then the theoretical analysis, design, implementation and applications were studied. First of all, a property of 2-D signal transforms, trend vanishing moment (TVM), was defined and the relation to the annihilation property for trend surfaces was clarified. Then, the concrete design and implementation methods were proposed for 2-D signal transforms with TVMs and the directional design and real-time implementation were realized. In addition, the significance of the proposed methods was verified through the application to image restoration. The extension to the oversampled case was also investigated.