Mukherjee Debargha, Mitra Sanjit K
Dept. of Electr. and Comput. Eng., Univ. of California, Santa Barbara, CA 93106, USA.
IEEE Trans Image Process. 2002;11(12):1337-48. doi: 10.1109/TIP.2002.806235.
Lattice Vector quantization (LVQ) solves the complexity problem of LBG based vector quantizers, yielding very general codebooks. However, a single stage LVQ, when applied to high resolution quantization of a vector, may result in very large and unwieldy indices, making it unsuitable for applications requiring successive refinement. The goal of this work is to develop a unified framework for progressive uniform quantization of vectors without having to sacrifice the mean- squared-error advantage of lattice quantization. A successive refinement uniform vector quantization methodology is developed, where the codebooks in successive stages are all lattice codebooks, each in the shape of the Voronoi regions of the lattice at the previous stage. Such Voronoi shaped geometric lattice codebooks are named Voronoi lattice VQs (VLVQ). Measures of efficiency of successive refinement are developed based on the entropy of the indices transmitted by the VLVQs. Additionally, a constructive method for asymptotically optimal uniform quantization is developed using tree-structured subset VLVQs in conjunction with entropy coding. The methodology developed here essentially yields the optimal vector counterpart of scalar "bitplane-wise" refinement. Unfortunately it is not as trivial to implement as in the scalar case. Furthermore, the benefits of asymptotic optimality in tree-structured subset VLVQs remain elusive in practical nonasymptotic situations. Nevertheless, because scalar bitplane- wise refinement is extensively used in modern wavelet image coders, we have applied the VLVQ techniques to successively refine vectors of wavelet coefficients in the vector set-partitioning (VSPIHT) framework. The results are compared against SPIHT and the previous successive approximation wavelet vector quantization (SA-W-VQ) results of Sampson, da Silva and Ghanbari.
格向量量化（LVQ）解决了基于LBG的向量量化器的复杂性问题，产生了非常通用的码本。然而，单级LVQ在应用于向量的高分辨率量化时，可能会导致非常大且难以处理的索引，使其不适用于需要连续细化的应用。这项工作的目标是开发一个统一的框架，用于向量的渐进均匀量化，而不必牺牲格量化的均方误差优势。开发了一种连续细化均匀向量量化方法，其中连续阶段的码本都是格码本，每个码本的形状都是前一阶段格的Voronoi区域。这种Voronoi形状的几何格码本被称为Voronoi格VQ（VLVQ）。基于VLVQ传输的索引的熵，开发了连续细化效率的度量。此外，结合熵编码，使用树结构子集VLVQ开发了一种渐近最优均匀量化的构造方法。这里开发的方法本质上产生了标量“逐比特平面”细化的最优向量对应方法。不幸的是，它不像标量情况那样容易实现。此外，在实际的非渐近情况下，树结构子集VLVQ中渐近最优性的好处仍然难以捉摸。尽管如此，由于标量逐比特平面细化在现代小波图像编码器中被广泛使用，我们已将VLVQ技术应用于在向量集划分（VSPIHT）框架中连续细化小波系数向量。将结果与SPIHT以及Sampson、da Silva和Ghanbari之前的逐次逼近小波向量量化（SA-W-VQ）结果进行了比较。
