外文翻譯----一種基于嵌入式零樹小波算法的魯棒圖像壓縮新方法（二）

1、<p>　　A New Method of Robust Image Compression Based on</p><p>　　the Embedded Zerotree Wavelet Algorithm</p><p>　　Charles D. Creusere</p><p>　　III. ROBUST EZW (REZW) ALGORITHM&

2、lt;/p><p>　　The basic idea of the REZW image compression algorithm is to divide the wavelet coefficients up into S groups and then to quantize and code each of them independently so that S different embedded bi

3、tstreams are created. These bitstreams are then interleaved as appropriate (e.g., bits, bytes, packets, etc.) prior to transmission so that the embedded nature of the composite bitstream is maintained. In the remainder o

4、f this paper we assume that individual bits are interleaved. For the REZW approach</p><p>　　What do we gain by using this new algorithm over the conventional one? As has been pointed out in Section II, the E

5、ZW decoder can use all of the bits received before the occurrence of the first error to reconstruct the image. By coding the wavelet coefficients with multiple, independent (and interleaved) bit streams, a single bit err

6、or truncates only one of the streams—the others are still completely received. Consequently, the wavelet coefficients represented by the truncated stream are reconst</p><p>　　IV. STOCHASTIC ANALYSIS</p>

7、;<p>　　To evaluate the effectiveness of this family of robust compression algorithms, we assume that the coded image is transmitted through a binary symmetric, memoryless channel with a probability of bit error gi

8、ven by. We would like to know the number of bits correctly received in each of the S streams. Since this quantity is itself a random variable, we use its mean value to characterize the performance of the different algori

9、thms. Because the channel is memoryless, streams terminate independently o</p><p><b>　　(2)</b></p><p>　　which is a valid probability mass function as one can easily verify by summing

10、 over all k: In (2), is the probability that the first k bits are correct whileis the probability that the (k + 1)th bit is in error. Note that a separate term conditioned on B/S is necessary to take into account the pos

11、sibility that all of the bits in the stream are correctly received. The mean value can now be calculated as</p><p><b>　　(3)</b></p><p>　　On the average, the total number of bits corr

12、ectly received is. If B/S is large relative to1/, then . Generally, the gain actually achieved is not this high, but it is nonetheless significant. In Section V, we use (3) to analyze the impact of transmission errors on

13、 the average quality of the reconstructed image for all possible values of S.</p><p>　　作者：Charles D. Creusere</p><p><b>　　國籍: 美國</b></p><p>　　出處：圖像處理 電機及電子學工程師聯(lián)合會 1997年第

14、10期1436-1442頁</p><p>　　ISSN1057-7149</p><p>　　一種基于嵌入式零樹小波算法的魯棒圖像壓縮新方法（二）</p><p>　　Charles D. Creusere</p><p>　　三、魯棒嵌入式零樹小波（REZW）算法</p><p>　　該REZW圖像壓縮算法的基本思

15、想是將小波系數(shù)分成S組然后每組逐個獨立的進行量化和編碼，于是便創(chuàng)建了S組不同的內嵌比特流。然后在傳輸之前將這些碼流適當交叉（如，位，字節(jié)，包等），使混合比特流的內嵌性質得以維持。在本文的其余部分，我們假設個別位交錯。為了使REZW算法有效，每個小波系數(shù)組必須是同樣大小并且均一地跨越圖像。類似的方法已被建議使用來并行EZW算法，若非這種使用分組代替系數(shù)的算法，處理器之間的數(shù)據(jù)傳輸也不會最小化。</p><p>　　

16、我們使用這種新算法代替?zhèn)鹘y(tǒng)的算法究竟會有什么增益？正如在第二部分所指出的那樣，EZW解碼器可以利用在第一個錯誤出現(xiàn)前接收到的所有位來重建圖像。通過將小波系數(shù)編碼成多個獨立（交錯）的比特流，一個單一的位錯誤只截斷比特流中的一個，其余的比特流仍可以被完整地接收到。因此，被截斷的比特流的小波系數(shù)的描繪重建為不完整的分辨率而那些其他比特流的描繪都重建為完整地編碼器分辨率。如果每個比特流的一組系數(shù)都跨越整個圖像，那么在解碼器中的逆小波變換必須均勻

17、地混合不同的分辨率，這樣產(chǎn)生的圖象在空間上才會擁有符合標準的質量。</p><p><b>　　四、隨機分析</b></p><p>　　為了評估這一系列魯棒壓縮算法的效率，我們假設利用一種二元對稱、無記憶并且伴隨著可能由引起的比特錯誤的信道來傳輸編碼圖像。我們希望知道S組比特流中每組準確地接收到的比特數(shù)。由于這個數(shù)值本身是一個隨機變量，我們使用其均值來描述不同算法的

18、性能。由于信道的無記憶性，比特流彼此獨立地終止，但其終結點的平均值總是相同的指定值。假設圖像被壓縮為總數(shù)為B的比特并且將其分成S組，那么每個數(shù)據(jù)流中數(shù)值B/S個比特的接收概率k可以通過公式</p><p>　?。?）準確得到。這是一個有效的概率函數(shù)，可以通過對所有k值求和來驗證其有效性。在公式（2）中，表示前k個比特傳輸正確的概率，而表示第k+1個比特傳輸錯誤的概率。請注意，考慮到比特流中的所有位都是正確接收的

19、可能性，提出一個單獨的基于B/S術語是必要的。平均值現(xiàn)在可以通過公式 </p><p><b>　?。?）</b></p><p>　　來計算。一般來說，正確收到的比特總數(shù)是。如果B/S是遠遠大于1/，則。一般來說，實際所能達到的增益并沒有那么高，但是這也是十分重要的。在第五節(jié)中，我們使用公式（3）分析所有可能的S值下，平均傳輸誤差對重建圖像質量的影響。<