以小波轉換為基礎的影像壓縮方法，已經變成了最普遍的靜態影像壓縮技術。利用小波轉換後的係數進行影像壓縮的相關方法目前是一個相當活躍的研究領域。在許多以小波為基礎的靜態影像壓縮技術中，較為有名的有EZW(Embedded Zerotree Wavelet)、SPIHT(Set Partitioning in Hierarchical Trees)、以及EBCOT(Embedded Block Coding With Optimized Truncation)。在本論文中，我們提出了稱為CEIDT(Concurrent Encoding In Descendant Trees)的方法，此方法是以SPIHT為基礎，而且PSNR比SPIHT好，大約提昇了0.1dB到0.9dB。我們提出的方法與複雜度極高的EBCOT相較之下，要來的簡單的多。

本論文的第二部分是針對以小波轉換為基礎的彩色影像壓縮方法，大部分彩色影像壓縮的演算法都式架構在YUV Domain上。然而，輸出的設備是用RGB或CMYK，因此失真的衡量標準，應該是在RGB或CMYK的色域上。本論文提出了新的位元YUV分配方法，可以提昇RGB的PSNR。例如：以Lena彩色影像，使用新的位元分配方法，PSNR比傳統的方法提高了1dB左右。此外，效能的提昇程度，也與影像本身有關。我們所提出的新方法，可以很簡單的就能應用在CMYK格式上。

本論文中也附上關於這兩部分的實驗數據，用以說明本論文提出的新方法的效能。

Wavelet based approaches have become the most popular techniques in still image compression in the last few years. The associate encoding methods of the wavelet coefficients to compress the image as much as possible are an active research area. Among them, techniques called EZW (Embedded Zerotree Wavelet), SPIHT (Set Partitioning in Hierarchical Trees), and EBCOT (Embedded Block Coding With Optimized Truncation) are the most famous ones. In this thesis, we propose a method called CEIDT (Concurrent Encoding In Descendant Trees) rooted from SPIHT to further improve the compression ratio. PSNR improvement ranges from 0.1 To 0.9 dB. The performance of the proposed method is comparable to the highly complicate EBCOT but with a much simpler coding procedure.

The second part of the thesis is to deal with the bit allocation problem when compressing a color image with DWT/CEIDT method. Most color image compression algorithm is performed in YUV domain. However, most output devices use RGB or CYMK. Therefore, the distortion measure should be performed in RGB or CMYK format. A novel bit allocation in YUV domain to provide better PSNR performance in RGB domain is proposed. When encoding “Lena” with the proposed bit allocation method, PSNR increases more than 1 dB compared to conventional approaches, all using the above DWT/CEIDT technique. The improvement depends on images. The proposed method can be easily applied to CMYK format, too.

Computer simulations of both parts of the thesis are provided to demonstrate the performances of the proposed algorithms.

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