隨著薄膜液晶顯示器技術的提升，解析度也越來越高。超解析演算法可將原本低解析度的影像放大，以滿足高解析度顯示器的視覺品質需求。這篇論文主要以快速碎形影像放大演算法概念提出改良。這篇論文所提出的演算法包含兩個步驟。首先，採用Lanczos影像放大演算法對輸入的低解析度影像做運算來得到一個初始的高解析度影像。由於初始的高解析度影像在有紋理細節的區域會損失一些較細部的資訊，所以有必要再增加額外的參考資訊來對初始的高解析度影像做適當的補償。第二，對初始的高解析度影像作縮小取樣，並且以原輸入低解析度影像相減得到殘餘訊息。再將此殘餘的影像與原輸入的低解析度影像建立迴歸模型，透過碎形精煉放大作為細節補償原本失去的細節。因為碎形精煉主要透過相鄰兩點的資訊與自身點做運算，所以在有紋理、邊緣的區域均能有較強的放大表現。實驗結果顯示，使用適應性碎形精煉補償的超解析演算法能提供較好的影像視覺品質，且有良好的峰值信噪比及較快的執行速度。

With the improvement in technology of thin-film-transistor liquid-crystal display(TFT-LCD), the display resolution becomes higher and higher. Super resolution algorithms are used to enlarge the original low resolution (LR) image to meet the visual quality of the high resolution (HR) display. In this thesis, an improved fast fractal super
resolution is proposed. The proposed method consists of two steps. First, the Lanczos method is used for LR images to get the primitive HR images. Since the primitive HR image may lose some information in the detail area, it needs to add other information to compensate the primitive HR images. Second, down-sampling the primitive HR image is performed, then the residual image between the down-sampled primitive HR image and input LR image is obtained. After that a regression model is built to correlate the relationship between the residual LR image and the input LR image. And the processing with fractal refinement compensates the primitive HR image. Since fractal refinement utilizes its self-similarity for encoding, it can obtain good performance in texture and edge areas. From the experiment results, it is shown that the proposed fractal refinement compensation achieves good performance.

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