Gauss Mixture Quantization for Image Compression and Segmentation

该研究涉及统计信号处理和信息理论的技术，因为它们适用于具有多个目标的通信系统。这样的系统出现在诸如因特网的多媒体通信网络中。将数据流分解为不同类型对于在大量可用源中找到用户所需的信息至关重要，并且它还可以提供用于显示、渲染、打印或播放利用其特定结构的接收信号的方法。信号处理和编码理论提供了强大的信息源数学模型和算法，通过这些信息源可以进行通信和处理。通常，系统被设计为独立的、不相关的组件的集合。这可能导致整体性能远远低于最佳性能。此外，它可以阻碍理论上的理解，可实现的performance.We的基本限制处理的同时设计的数学模型，帐户在一次为信息源，数据压缩，信号处理和适用于从接收到的数据中提取信息。我们的重点是图像通信和处理。因为，这些技术大量借鉴了语音编码和识别中已证明成功的方法，所以它们对于两种信号类型（单独或一起）都是自然的。它基于矢量量化、高斯混合模型、最小鉴别信息（相对熵）和通用编码的新组合。矢量量化提供了一个理论框架和实现方法。高斯混合模型是描述信息源的一种灵活的模型。它们可以通过关于失真的最小判别信息度量的聚类来拟合到真实的数据。主要目标是开发和应用高斯模型的率失真极端属性的条件版本，以便设计用于压缩、分类、建模及其组合的鲁棒算法。关于建模、压缩和分类/回归之间的关系，有许多悬而未决的问题。我们的目标是提供尽可能多的答案，这样做有助于理解建模，信号处理和编码的相互作用。我们描述了优化和可实现的强大的代码压缩和分类的各种信息源，特别是多模态图像。我们的一部分努力是致力于纯数学方面的树结构回归，这是有关鞅理论和微分积分。

The research is concerned with techniques from statistical signal processing and information theory as they apply to communication systems with multiple goals. Such systems arise in multimedia communications networks like the Internet. The decomposition of data streams into different types is critical to finding information desired by a user among vast available sources, and it can also provide methods for displaying, rendering, printing, or playing the received signal that take advantage of its particular structure. Signal processing and coding theory have provided powerful mathematical models of information sources and algorithms by which these sources can be communicated and processed. Typically systems are designed as a collection of separate, unrelated, components. This can result in much less than optimal overall performance. Furthermore, it can hamper theoretical understanding of the fundamental limits on achievable performance.We treat the simultaneous design of mathematical models that account at once for information sources, data compression, and signal processing and apply to extracting information from the received data. Our emphasis is on image communication and processing. Because, the techniques draw heavily from demonstrably successful methods in speech coding and recognition they are natural for both signal types, individually or together.The research involves a unified approach to data compression, statistical classification and regression, and density estimation. It is based on a novel combination of vector quantization, Gauss mixture models, measures of minimum discrimination information (relative entropy), and universal coding. Vector quantization provides both a theoretical framework and a method for implementation. Gauss mixture models are a flexible class by which to describe information sources. They can be fit to real data by clustering with respect to a minimum discrimination information measure of distortion. A primary objective is the development and application of conditional versions of rate-distortion extremal properties of Gaussian models in order to design robust algorithms for compression, classification, modeling, and combinations thereof. There are many open questions about relations among modeling, compression, and classification/regression. Our goal is to provide answers to as many of them as possible and in so doing to contribute to understanding the interplay of modeling, signal processing, and coding. We describe optimized and implementable robust codes for compression and classification for a variety of information sources, especially for multimodal imagery. Part of our efforts are devoted to purely mathematical aspects of tree-structured regression, which is related to martingale theory and to the differentiation of integrals.