SPIHT 是一個結合離散小波轉換的高效率影像壓縮技術，而經小波轉換後的影像具有將能量往前(低頻) 集中的效果，且由於此影像壓縮技術可以選擇在任一位元處終止，所以SPIHT 適用於漸進傳輸。儘管SPIHT 有著極佳的壓縮表現，但仍存在一個重要的問題：就是在解碼時對資料序列中任一位元的錯誤有著極為敏感的特性，使得有可能導致解出與原影像毫無關聯、令人無法理解的結果。因此，引發我們想要去解決：如何在具有雜訊且確定會產生錯誤的通道中，傳輸經SPIHT 壓縮的影像，並能夠在接收端盡可能地重建這種對位元錯誤極其敏感的壓縮影像。為便於進一步的討論，我們將場景設定成傳送端單向傳送資料，而且不會收到來自接收端的任何回應。而在我們提出的解決方法中，首先會將經SPIHT 壓縮過的影像資料，分成長度相同的兩類資料封包，其中一類稱為CP，另一類叫做RP。為了使其具備錯誤控制能力，會在每個資料封包加入CRC，讓接收端能夠透過當下取得封包的校驗和(check sum)，來判定是否已正確地完成接收，且只有被正確接收的才採用。而具有上述性質的雜訊通道，我們將其稱做接收可移除通道(erasure channel)。為了進行非均等錯誤保護，因此封包會因為其重要性較高而給予較多次的重複傳送，這稱為重送分配(DA)。同時我們也引用魚骨圖來簡化對傳送方法的理解與分析及加速計算，並能在封包傳送前做適當的效能估測。在論文中我們提出了兩種重送分配方法，第一種是透過窮舉所有合理組合的方式，並在過程中透過計算出各個組合所對應的期待SNR 值，找出近乎最佳的分配結果。不過這個方法需要耗費非常大的計算成本。第二種是漸進式重複分配(PDA)，事實上此方法本身就具有漸進的風格與策略，其計算的複雜度與成本均大幅地降低。此外，後者所獲致的解碼影像也有著相當好的效果。實驗結果顯示我們提出的方法，有效地增進接收影像解碼後的效果。同時透過把將要傳送的資料分成CP 與RP 後，可以讓我們在傳送端進行更聰明地的重送分配，也因此能夠使接收端獲得更高品質的解碼影像。

Based on the embedded zero tree (EZT) coding with discrete wavelet transform (DWT), SPIHT (set partitioning in hierarchical trees) is a highly efficient image compression technique that can be stopped at any bit, and thus allows for progressive transmission. However, one problem exist- ing in SPIHT is that its decoding could be extremely sensitive to bit errors in the code sequence. In this dissertation, we address the issue of trans- mitting SPIHT-encoded images via noisy channels, wherein errors are inevitable. The communication scenario assumed in this dissertation is that the transmitter cannot get any acknowledgement from the receiver. In our scheme, the original SPIHT code sequence is first segmented into packets. Each packet is classified as either a CP (critical packet) or an RP (refinement packet). For error control, cyclic redundancy check (CRC) is incorporated into each packet. By checking the CRC check sum, the receiver is able to tell whether a packet is correctly received or not. In this way, the noisy channel can be effectively modeled as an erasure channel. For unequal error protection (UEP), each of those packets is repeatedly transmitted for a few times, as determined by a process called diversity allocation (DA). For simplifying the analysis of our scheme, a fish-bone diagram is introduced to help formulation and estimation be- fore transmission. Two DA algorithms are proposed. The first algorithm produces a nearly optimal decoded image (as measured in the expected signal-to-noise ratio). However, its computation cost is extremely high. The second algorithm works in a progressive fashion, called progressive diversity allocation (PDA), and is naturally compatible with progressive transmission. Its computation complexity is extremely low. Nonetheless, its decoded image is nearly as good. Experimental results show that the proposed scheme significantly improves the decoded images. They also show that making distinction between CP and RP results in wiser diversity allocation to packets and thus produces higher quality in the decoded images.

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