臺灣博碩士論文加值系統

內插法在數位影像處理上被廣泛應用，如：多項式內插法、離散傅立葉轉換後補零。多項式內插法是藉由提升運算量來提升精準度。在頻譜上的內插法為離散傅立葉轉換後補零的方式; 容易因為邊界效應而使數值預估失準。
離散餘弦轉化法第二型(DCT-II)常用於數位影像處理及訊號處理，而目前文獻顯示DCT-II也可以應用於影像大小調整，但是還是有些缺陷，因為在放大倍率為偶數倍時，原始數值會發生變化。而原始影像的數據是最重要的，因此現在使用的方法在偶數倍率時並不適用。
因為現在DCT-II的方法有此缺陷，所以本實驗室團隊對DCT-II插值法進行討論與修正後，可以保證在偶數倍率時，原始數值不會發生變化，而本篇則嘗試使用修正後DCT-II插值法進行影像大小調整，並減少運算複雜度及改善一些缺陷，跟先前的方法相比，本論文使用的方法在放大倍率不論是奇數與偶數倍率時，均可以保證最重要的原始數值不會發生變化，並且可以消除由子區塊運算所造成的塊狀邊界，並可以得到相對較少的處理運算時間，獲得較好的畫質。

The interpolation is be widely used by digital image process, e.g. Polynomial Interpolation, DFT with zero-padding, etc. The polynomial interpolation increase accuracy at the cost of increasing computation complexity. In frequency domain, the DFT with zero-padding induces inaccurate estimates for edge of image.
Discrete Cosine Transform Type-II (DCT-II) is popularly used in digital image process and signal process. Now, some successful literatures use the DCT-II with zero-padding to resize image, but it has an important defect. When the magnification factor is even, the original data would change. The original image data is the important reference, and therefore the current method is not applicable when the magnification is even.
As current DCT-II interpolation method has this flaw, so our team revised the procedure of DCT-II interpolation a. It can guarantee the original value will not change when the magnification factor is even. This thesis tries to use the proposed DCT-II interpolation for resizing image with reduction of the computation complexity to improves well known defect. Compared with previous methods, the method used in this thesis can ensure that the most important original data value will not change no matter the magnification factor is odd or even, In addition artificial block edge can be removed by operation of sub-block. The proposed approach can achieve lower the operation time of the processing, and obtain better image quality.

謝誌 i
摘要 iii
Abstract v
目次 vii
圖次 ix
表次 xi
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究方法與目的 2
1.3 論文架構 2
第二章 常見內插法介紹 4
2.1 前言 4
2.2 多項式(POLYNOMIAL)內插法 4
2.3 離散傅立葉轉換內插法 7
第三章 DCT內插法介紹 9
3.1 DCT介紹 9
3.2 DCT TYPE-I介紹 9
3.3 DCT TYPE-II介紹 11
3.4 DCT TYPE-I內插法介紹 12
3.5 修正後DCT TYPE-II內插法介紹 14
第四章 影像放大 18
4.1 整體影像放大 18
4.2 減少運算時間 20
第五章 改善相關問題 24
5.1 消除塊狀邊界 24
5.2 改善水波紋 29
5.3 PSNR畫質比較 33
第六章 結論與建議 35
6.1 結論 35
6.2 後續研究與建議 35
參考文獻 37

[1]B. Yang, Z. Cao, and K. B. Letaief, “Analysis of low-complexity windowed DFT-based MMSE channel estimator for OFDM systems”, IEEE Trans. Commun., vol.49, pp.1977-1987, Nov.2001.
[2]J. Mukherjee and S. K. Mitra, “Image Resizing in the Compressed Domain Using Subband DCT”, IEEE Trans. Circuits Syst. Video Technol., vol.12, no.7, pp.620-627, July 2002
[3]A. Acharya and S. Meher, “An Efficient, Adaptive Unsharp Masking Based Interpolation for Video Intra Frame Up-sampling”, Asia Pacific Conference on Postgraduate Research in Microelectronics & Electronics, pp.100-105, 2012.
[4]C. Salazar and T. D. Tran, “A Complexity Scalable Universal DCT Domain Image Resizing Algorithm”, IEEE Trans. Circuits Syst. Video Technol., vol. 17, no. 4, pp.495-499, April 2007.
[5]C. Y. Hsu and S. M. Chen, “Discrete Interpolation Using the Discrete Cosine Transform with the Mapping of the Boundary Conditions”, IEEE Signal Process. Lett., vol. 02, no. 10, pp.185-187, October 1995.
[6]林泓任, 離散餘弦及正弦轉換法之本質探討及其應用在內插法上的研究, 大同大學通訊工程研究所碩士論文, 2013.
[7]彭俊程, 應用離散正弦轉換實現影像內插, 大同大學通訊工程研究所碩士論文, 2013.
[8]Z. Wang, G. A. Jullien, and W. C. Miller, “Interpolation using the discrete sine transform with increased accuracy”, Eletron. Lett., vol.29, no.22, pp.1918-1920, Oct.1993.
[9]R. Dugad and N. Ahuja, “A fast scheme for image size change in the compressed domain”, IEEE Trans. Circuits Syst. Video Technol., vol. 11, no. 4, pp.461-474, April 2001.
[10]A. Acharya and S. Meher, “No reference, fuzzy weighted unsharp masking based DCT interpolation for better 2-D up-sampling”, IEEE International Conference on Fuzzy System, pp.1-8, July 2013.
[11]G. Vanhoy, H. Volos, C.E.C. Bastidas and T. Bose, “A Spatial Interpolation Method for Radio Frequency Maps Based on the Discrete Cosine Transform”, IEEE MILCOM, pp.1045-1050, Nov. 2013.