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(jī)及電子學(xué)工程師聯(lián)合會(huì) 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(gè)獨(dú)立的進(jìn)行量化和編碼，于是便創(chuàng)建了S組不同的內(nèi)嵌比特流。然后在傳輸之前將這些碼流適當(dāng)交叉（如，位，字節(jié)，包等），使混合比特流的內(nèi)嵌性質(zhì)得以維持。在本文的其余部分，我們假設(shè)個(gè)別位交錯(cuò)。為了使REZW算法有效，每個(gè)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(huì)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(huì)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(gè)錯(cuò)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(gè)獨(dú)立（交錯(cuò)）的比特流，一個(gè)單一的位錯(cuò)誤只截?cái)啾忍亓髦械囊粋€(gè)，其余的比特流仍可以被完整地接收到。因此，被截?cái)嗟谋忍亓鞯男〔ㄏ禂?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(gè)比特流的一組系數(shù)都跨越整個(gè)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(huì)擁有符合標(biāo)準(zhǔn)的質(zhì)量。</p><p><b>　　四、隨機(jī)分析</b></p><p>　　為了評(píng)估這一系列魯棒壓縮算法的效率，我們假設(shè)利用一種二元對(duì)稱、無記憶并且伴隨著可能由引起的比特錯(cuò)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(zhǔn)確地接收到的比特?cái)?shù)。由于這個(gè)數(shù)值本身是一個(gè)隨機(jī)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(dú)立地終止，但其終結(jié)點(diǎn)的平均值總是相同的指定值。假設(shè)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(gè)數(shù)據(jù)流中數(shù)值B/S個(gè)比特的接收概率k可以通過公式</p><p>　?。?）準(zhǔn)確得到。這是一個(gè)有效的概率函數(shù)，可以通過對(duì)所有k值求和來驗(yàn)證其有效性。在公式（2）中，表示前k個(gè)比特傳輸正確的概率，而表示第k+1個(gè)比特傳輸錯(cuò)誤的概率。請(qǐng)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(gè)單獨(dú)的基于B/S術(shù)語是必要的。平均值現(xiàn)在可以通過公式 </p><p><b>　　（3）</b></p><p>　　來計(jì)算。一般來說，正確收到的比特總數(shù)是。如果B/S是遠(yuǎn)遠(yuǎn)大于1/，則。一般來說，實(shí)際所能達(dá)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(duì)重建圖像質(zhì)量的影響。<