影像壓縮是多媒體通訊的必要步驟，影像壓縮的主要目的是減少影像儲存空間的需求與加快在網路上傳輸的速度。這篇論文主要提出兩個影像壓縮的演算法：第一個演算法是針對離散小波轉換後的影像做編碼，此演算法是利用dictator來消除在相同階層子頻帶的相關性，與分區塊且利用繼承樹來進行預測的演算法很類似，不同點在於排序過程。第二個演算法則是針對離散餘弦轉換後的影像作壓縮。此演算法是將離散餘弦轉換後的係數重排成十個頻域後，對DCT係數作三階樹狀結構編碼。在這兩個演算法的實驗數據中，第一個演算法比現行壓縮標準JPEG2000以及分區塊且利用繼承樹來進行預測的演算法的壓縮品質要好，適用在醫學影像及自然影像的壓縮。而第二個演算法的壓縮品質比現行壓縮標準JPEG好大約 3~4 dB。但由於用此方法壓縮後的影像有輕微方塊效應，所以此方法只適用在自然影像上。

Image compression is essential in multimedia system. The primary objective of image compression is to find a bit-rate-reduction method for saving storage space and achieving fast transmission on the Internet. This thesis proposes two novel algorithms for image compression. First algorithm proposes a dictator to eliminate the correlation in the same level subband for the wavelet-based image encoding. This algorithm is similar to the SPIHT but different in sorting pass. Second algorithm modified the first algorithm for block-based DCT image. This algorithm represents the DCT coefficients into three-scale tree structure with ten-subband coefficients. In our experiments, the first proposed algorithm for DWT coefficients reduces more redundancy than SPIHT algorithm and JPEG2000 at the same bit-rate and is suitable for both medical images and natural images. The second proposed algorithm for DCT coefficients outperforms JPEG standard about 3 to 4 dB but this algorithm is not suitable for medical image compression because it causes tiny blocking effect.

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