由於多媒體技術快速的進步，使用者對於各式各樣資訊的需求越來越大，導致傳輸頻寬及儲存空間不足！雖然網路通訊以及資料儲存設備技術也有顯著的進步，然而隨著資訊化普及，使用者的需求一直都遠大於網路及儲存空間所能提供之服務。因此資料在傳輸或儲存前要先經過壓縮，才能在有限的頻寬之下取得服務的品質保證。
在各類傳輸媒體之中，以視訊及影像所需資料量最大，因此對於此二種媒體壓縮之演算法一直都是學者專家及工業界研究的主題。離散小波轉換（DWT）是一個壓縮效率極佳的工具，它能夠使得空間域的能量集中在頻率域的低頻部分，因此它已被採用於視訊，影像，音訊…等壓縮裡。本論文裡主要是對DWT在醫學及一般自然影像壓縮上做深入研究，論文中包含我們新發展之演算法，它們可以提昇壓縮倍率並且維持一定的重建品質。
在論文第一個主題是探討DWT轉換完之後的係數處理。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。
論文中第二主題針對離散小波轉換後的影像後處理做一探討，我們提出利用四分數分割及一組形態運算子來去除小波影像的水波效應。此新方法具有快速處理之特性，同時也能達到相當高的壓縮比，在同樣壓縮率下可以比新的靜態影像壓縮標準JPEG 2000有較佳的訊號雜訊比。
在論文最後一個主題裡，提出一個使用頻率重組、分類、方塊相似性與去除水波效應濾波器四個部份來編碼的新醫學影像編碼器。在同樣壓縮率下, 可以比新的靜態影像壓縮標準JPEG 2000及著名的SPIHT有較佳的訊號雜訊比。

Due to the progress of multimedia technologies, the demands of various types of information from users become huge so as to lead to the shortage of transmission bandwidth and storage space. The technologies of network and storage devices have been improving as well; however, the users’ desires always exceed the provided services currently. Therefore, data must be compressed before transmission or storage to achieve the needed quality under the circumstance of limited bandwidth.
Among all kinds of media, video and image data occupy immense volume. Thus, the compression technologies of them have been intensively exploited in effective compression tool, which compacts the spatial energy into few coefficients in frequency domain. DWT has been employed in the compressions of image, video and speech etc. In this dissertation, new algorithms based on DWT are developed to raise the compression performance of nature and medical images.
The first part is to explore the processing of DWT coefficients. 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.
The second part in this dissertation concentrates on the post-processing image quality for wavelet-based image coding. Here, an algorithm presents quad-tree decomposition and a set of morphological filters for reducing the ringing artifacts of images. It has the advantage of fast implementation and enhances reconstructed image quality compared to JPEG2000 at the same bit rate in terms of both PSNR and the perceptual results.
Finally, an algorithm uses spectrum reorganization, classification, block similarity, and de-ringing filter to encode medical images. It can enhance the quality of the reconstructed image in both the PSNR and perceptual results compared to JPEG2000 and SPIHT given the same bit rate.

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