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

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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.