矢量量化技术及其在图像信号处理中的应用研究
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摘要
矢量量化，基于其优良的率失真特性，已经广泛的应用在信号和图像处理领域，例如模式识别、语音和图像压缩编码。决定矢量量化器性能的关键技术是矢量量化的码书设计和矢量量化的编码算法。在获得高质量码书和完成编码方面，实现复杂度都将随着矢量维数的增加面快速增长，这成为了矢量量化技术在信号处理领域特别是实时信号处理领域应用的一个严重的障碍，也成为了近几十年来研究最多的方面。随着各种新的非线性信号处理方法在码书设计中的使用，以及大量快速搜索方法的出现，矢量量化技术也在快速的发展着。
本论文以矢量量化应用最多的领域，即图像信号处理领域为研究对象，在有效利用图像信号的特性的基础上，对于矢量量化码书形成算法和快速编码算法作了创新性和探索性研究。主要内容为：
1．分析和研究了现有的几种初始码书算法的问题，在理论上提出了一种基于训练矢量的统计特征量的分类平均初始码书算法。实现对于较平滑图像信号矢量量化的码书质量的有效提高。
2．详细研究了几种典型的矢量量化码书形成算法，探讨了这些算法在形成码书的过程中，可能存在的不足。在矢量量化的码书形成算法中，首次提出适度性原则，保证码子是胞腔内绝大多数训练矢量的代表，去掉或减少小部分非典型训练矢量对码子的影响，使代表更加具有广泛性，形成附加的优化条件：子区域误差近似相等。实现对于频率敏感竞争学习(FSCL)算法，频率敏感自组织特征映射(FSOFM)算法的改进。并探讨了这两种改进算法在小波变换域的一种实现方案，最后给出了一种结合小波变换和非线性插补矢量量化(NLIVQ)的编码方案。适度性原则的引入，在提高码书质量的同时，也减少了形成码书所需要的计算量，进而降低了码书设计的复杂度。
3．详细研究了几种典型的，和全搜索等价的，基于不等式排查的快速编码算法。对这些算法的编码效率进行了分析，具体地针对基于各种低维特征量(均值，方差，范数)的排查不等式的排查效率，进行了比较。提出了基于子矢量范数的排查不等式，基于均值和子矢量范数的排查不等式，以及基于均值和子矢量方差的排查不等式等三种改进算法。通过这些基于低维特征量的排查不等式和部分失真排除方法的有效结合，实现了更高效的快速编码算法。
4．利用基于等误差自组织特征映射(EDSOFM)算法形成的码书，在基于图像内容的检索的领域，构造了基于矢量量化编码索引直方图的彩色图像描述子。利用基于子矢量范数排查不等式构造的快速搜索算法，实现了对于彩色图像检索库的快速检索。
Vector quantization (VQ) is an efficient coding technique to quantize signal vectors due to its excellent rate-distortion performance. It has been widely used in signal and image processing, such as pattern recognition, speech, and image coding. The codebook designing method and encoding method play an important role in VQ and decide VQ performance. To obtain the better codebook and perform encoding, the heavy computations, which are called as the computing complexities of VQ, are required. The computing complexities of VQ increase with the increase of the dimension of vector. It becomes a serious barrier of VQ applied to the signal processing, especially in the real-time signal processing. How to reduce its computing complexities has become an important investigating field for decades of years. By using many nonlinear signal-processing methods to codebook design and a lot of fast searching methods to encoding, many VQ methods have been developed.
In this thesis, the VQ in the field of image processing, as a field in which VQ is widely used, is investigated. By using the feature of image efficiently, we make some novel researches on the codebook design and fast encoding. The main results are as follows:
1. Some existing initial codebook algorithms are investigated. A new initial codebook algorithm is proposed. In the proposed method, training vectors are sorted according to the norm or sum of training vectors. Then, the ordered vectors are partitioned into N groups where N is the size of codebook. The initial codewords are obtained from calculating the centroid of each group. It can be efficiently applied to smooth images.
2. Some existing codebook designs are investigated in detail. Their shortages are carefully analyzed. The moderate principle is firstly proposed- Using this principle, the influence of nontypical training vectors on codeword is reduced or eliminated. Then each codeword becomes a representation of most typical training vectors in its cell. Using this principle, an additive condition for VQ optimization, which makes the sub-distortion of each cell close to each other, can be got. The improvements to existing algorithms, such as the frequency sensitive self-organizing feature maps (FSOFM) algorithm, and the frequency sensitive competitive learning (FSCL) algorithm, can be obtained. The realization of the two improved methods in wavelet domain is researched. Another improved method, which combined wavelet transform with the optimal Nonlinear Interpolative Vector Quantization (NLIVQ), is also researched. In a word, the moderate principle can be used to improve codebook and reduce computations.
3. Some existing fast searching algorithms, which are based on the inequalities elimination and can achieve the same quality of encoded images as the full searching algorithm (FSA), are investigated in detail. By comparing the eliminating efficiency of each low dimensional feature of a vector (the sum, the variance, and the norm), three eliminating methods, which are the method based on subvector norm, the method based on vector sum and subvector norm, and the method based on subvector sum and variance, are proposed. Combined these eliminating inequalities with the partial distance elimination (PDE) method, the search efficiency can be further improved.
4. By using the codebook based on equidistortion SOFM algorithm, the descriptors of color image in the content-based, image retrieval (CBIR) system are constructed by the index histogram of VQ-compressed index sequence. By using the fast searching method based on the eliminating inequality of subvector norm, a fast searching method in color image retrieval database is presented.
本论文以矢量量化应用最多的领域，即图像信号处理领域为研究对象，在有效利用图像信号的特性的基础上，对于矢量量化码书形成算法和快速编码算法作了创新性和探索性研究。主要内容为：
1．分析和研究了现有的几种初始码书算法的问题，在理论上提出了一种基于训练矢量的统计特征量的分类平均初始码书算法。实现对于较平滑图像信号矢量量化的码书质量的有效提高。
2．详细研究了几种典型的矢量量化码书形成算法，探讨了这些算法在形成码书的过程中，可能存在的不足。在矢量量化的码书形成算法中，首次提出适度性原则，保证码子是胞腔内绝大多数训练矢量的代表，去掉或减少小部分非典型训练矢量对码子的影响，使代表更加具有广泛性，形成附加的优化条件：子区域误差近似相等。实现对于频率敏感竞争学习(FSCL)算法，频率敏感自组织特征映射(FSOFM)算法的改进。并探讨了这两种改进算法在小波变换域的一种实现方案，最后给出了一种结合小波变换和非线性插补矢量量化(NLIVQ)的编码方案。适度性原则的引入，在提高码书质量的同时，也减少了形成码书所需要的计算量，进而降低了码书设计的复杂度。
3．详细研究了几种典型的，和全搜索等价的，基于不等式排查的快速编码算法。对这些算法的编码效率进行了分析，具体地针对基于各种低维特征量(均值，方差，范数)的排查不等式的排查效率，进行了比较。提出了基于子矢量范数的排查不等式，基于均值和子矢量范数的排查不等式，以及基于均值和子矢量方差的排查不等式等三种改进算法。通过这些基于低维特征量的排查不等式和部分失真排除方法的有效结合，实现了更高效的快速编码算法。
4．利用基于等误差自组织特征映射(EDSOFM)算法形成的码书，在基于图像内容的检索的领域，构造了基于矢量量化编码索引直方图的彩色图像描述子。利用基于子矢量范数排查不等式构造的快速搜索算法，实现了对于彩色图像检索库的快速检索。
Vector quantization (VQ) is an efficient coding technique to quantize signal vectors due to its excellent rate-distortion performance. It has been widely used in signal and image processing, such as pattern recognition, speech, and image coding. The codebook designing method and encoding method play an important role in VQ and decide VQ performance. To obtain the better codebook and perform encoding, the heavy computations, which are called as the computing complexities of VQ, are required. The computing complexities of VQ increase with the increase of the dimension of vector. It becomes a serious barrier of VQ applied to the signal processing, especially in the real-time signal processing. How to reduce its computing complexities has become an important investigating field for decades of years. By using many nonlinear signal-processing methods to codebook design and a lot of fast searching methods to encoding, many VQ methods have been developed.
In this thesis, the VQ in the field of image processing, as a field in which VQ is widely used, is investigated. By using the feature of image efficiently, we make some novel researches on the codebook design and fast encoding. The main results are as follows:
1. Some existing initial codebook algorithms are investigated. A new initial codebook algorithm is proposed. In the proposed method, training vectors are sorted according to the norm or sum of training vectors. Then, the ordered vectors are partitioned into N groups where N is the size of codebook. The initial codewords are obtained from calculating the centroid of each group. It can be efficiently applied to smooth images.
2. Some existing codebook designs are investigated in detail. Their shortages are carefully analyzed. The moderate principle is firstly proposed- Using this principle, the influence of nontypical training vectors on codeword is reduced or eliminated. Then each codeword becomes a representation of most typical training vectors in its cell. Using this principle, an additive condition for VQ optimization, which makes the sub-distortion of each cell close to each other, can be got. The improvements to existing algorithms, such as the frequency sensitive self-organizing feature maps (FSOFM) algorithm, and the frequency sensitive competitive learning (FSCL) algorithm, can be obtained. The realization of the two improved methods in wavelet domain is researched. Another improved method, which combined wavelet transform with the optimal Nonlinear Interpolative Vector Quantization (NLIVQ), is also researched. In a word, the moderate principle can be used to improve codebook and reduce computations.
3. Some existing fast searching algorithms, which are based on the inequalities elimination and can achieve the same quality of encoded images as the full searching algorithm (FSA), are investigated in detail. By comparing the eliminating efficiency of each low dimensional feature of a vector (the sum, the variance, and the norm), three eliminating methods, which are the method based on subvector norm, the method based on vector sum and subvector norm, and the method based on subvector sum and variance, are proposed. Combined these eliminating inequalities with the partial distance elimination (PDE) method, the search efficiency can be further improved.
4. By using the codebook based on equidistortion SOFM algorithm, the descriptors of color image in the content-based, image retrieval (CBIR) system are constructed by the index histogram of VQ-compressed index sequence. By using the fast searching method based on the eliminating inequality of subvector norm, a fast searching method in color image retrieval database is presented.
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