离散信源的熵表示.ppt

8 Image Compression 8.1 Fundamentals 8.2 Image Compression Models 8.3 Elements of Information Theory 8.4 Error-Free Compression 8.5 Lossy Compression 8.6 Image Compression Standards 8.1 Fundamentals 图像信息占据大量的存储容量,所用传输信道也较宽. 一幅512×512像素，8b/像素的灰度图像占据256KB的磁盘空间； 一幅512×512像素，每分量8b/像素的彩色图像则占据3×256＝768KB的磁盘空间； 如果以每秒24帧传送此彩色图像，则一秒钟的数据量就有24×768＝18.5MB，那么一张680MB容量的CD－ROM仅能存储30多秒的原始数据。 对图像数据的压缩必不可少。 8.1 Fundamentals The term data compression refers to the process of reducing the amount of data required to represent a given quantity of information. A clear distinction must be made between data and information. 8.1 Fundamentals 8.1 Fundamentals 8.1 Fundamentals An 8-level image has the gray-level distribution shown in Table 8.1. If code 1 in table is used, the average number of bits required to code the image is Lavg = 3. If code 2 is used, Lavg = 2.7 8.1 Fundamentals 8.2 Image Compression Models图像压缩模型 1)．香农信息保持编码定理 香农信息论已证明,信源熵是进行无失真编码的理论极限.低于此极限的无失真编码方法是不存在的,这是熵编码的理论基础.而且可以证明,考虑像素间的相关性,使用高阶熵一定可以获得更高的压缩比. 3)．变长最佳编码定理 在变长编码中,对出现概率大的信息符号赋予短码字,而对于出现概率小的信息符号赋予长码字.如果码字长度严格按照所对应符号出现概率大小逆序排列,则编码结果平均码字长度一定小于任何其他排列形式. 1．Huffman coding 一幅20×20的图像共有5个灰度级：s1,s2,s3,s4,和 s5，它们的概率依次为0.4,0.175,0.15,0.15和 0.125。 例8.7 Huffman编码过程示意图 8.4 Error-Free Compression 编码结果 图像熵 信源符号 出现概率 码字 码长 s1 0.4 0 1 S2 0.175 111 3 S3 0.15 110 3 S4 0.15 101 3 S5 0.125 100 3 编码后均码长 8.4 Error-Free Compression 2. Arithmetic coding 8.4 Error-Free Compression 3. Run-length coding 行程编码 4. Lossless Predictive Coding 无损预测编码 8.5.1 Lossy Predictive Coding 8.5.2 Transform Coding 8.5 Lossy Compression Most of the standard discussed are sanctioned by the International Standardization Organization (ISO) and the Consultative Committee of the International Telephone and Telegraph (CCITT) binary and continuous-tone (monochrome and color) image compression still-frame and video(i.e., sequential-frame) applications 8.6 Image Compress