此篇論文提出客觀的嶄新影像放大評估法，係基於基準函數的峰值訊噪比方法，以基準函數所生成的虛擬圖形作為實驗資料，排除傳統實驗中縮小方法差異之影響，客觀驗證放大影像之品質；同時也提出以離散餘弦轉換達到超大尺度之影像放大，並獲得快速且高品質影像的成果。影像放大法以矩陣相乘實作離散餘弦轉換而加速運算時間，在超大尺度放大時相對快速，同時，解決傳統離散餘弦轉換放大時影像偏移與方塊效應的問題，並藉由處理整張影像考慮全域之細節達到超越其它影像放大法而有更佳品質的放大影像。提出的影像放大法可以藉由調整轉換矩陣的維度大小而簡易地完成指定像素尺寸之放大。最後，實驗結果證實此離散餘弦轉換放大法有效地達到快速且高品質之影像放大。

An objective novel evaluation approach, implemented by the benchmark function-based peak signal-to-noise ratio (PSNR), for evaluating the performance of image enlargement is proposed in this thesis. Also, a fast large-scale image enlargement method via the improved discrete cosine transform (DCT) is proposed to improve the quality and speed of image zooming. The proposed image enlargement algorithm based on DCT saves computation time by multiplication of the DCT matrix. Comparing to the traditional DCT approach, the improved approach overcomes the image shifting and blocky effects. In comparisons to other interpolation methods, DCT enlargement outperforms them in edge details because it considers the global frequency information of the whole image. The DCT enlargement is easy to implement the arbitrary pixel-size-based zooming of an image by employing the different size of transform matrix. Illustrative examples show the effectiveness of the proposed approach.

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