Spectral Entropy and Adaptive, Lossy Source Coding

语音、静止图像、高质量音频和视频的有效数字表示，称为有损源压缩，今天具有大量的商业应用。这些应用包括数字蜂窝电话、MP3播放器、DVD、HDTV、视频会议、互联网电话和静止图像的传输/存储。在这些应用中，最好的源压缩方法本质上是自适应的，并且基于一种称为非线性近似的技术。然而，这些压缩方法主要是基于实验设计的，没有任何指导理论。本研究探讨一种新的方法，自适应有损源压缩的基础上的数学量称为频谱熵。这种新的信源压缩方法，称为SpEnt（谱熵）方法，提供了一个基本的声音的自适应信源压缩方法，迄今为止一直缺少。本研究开发了基于SpEnt的有损压缩方法，用于语音、视频和静止图像，这些方法应该在许多商业产品中得到应用。在样本函数自适应编码器中，不仅在每个块或帧中发送的参数的数量可能从块到块（从帧到帧）变化，而且对于给定数量的发送参数，在每个块中发送的参数可能变化。对于具有固定基函数集合的此类编码器，通常说发送对应于最佳n个基函数的系数，而不是前n个，并且这在谐波分析中被称为非线性近似。坎贝尔得出的数量，他称之为系数率的随机过程在1960年，他表明，系数率取决于谱熵（熵的功率谱密度的原始过程）。没有证明任何编码定理，也没有说明系数率对源压缩的可能影响。最近的工作由PI和他的学生产生了两个新的推导坎贝尔的系数率。一个推导允许相对于称为过程的有效带宽的量来解释系数速率。另一个推导揭示了一种新的方法来源压缩的基础上系数率，适应于每个实现的源。更具体地，通过研究项的乘积的级数展开中的主导项，示出了在特定系数的N个样本的序列中，应当被编码的系数样本的数量与系数方差成比例。因此，特定系数是否正被编码逐块地改变，并且因此，基于谱熵的有损压缩显然福尔斯落入非线性近似方法的类别中。受这些结果的启发，本研究制定了一种新的方法来有损源压缩，称为频谱熵（SpEnt）的方法，并开发SpEnt为基础的编码器的宽带语音（50 Hz至7 kHz），视频，电话带宽的语音和静态图像的有损压缩。此外，这项工作探讨的作用，频谱熵和坎贝尔的系数率作为基本量的自适应编码的源实现的序列。

The efficient digital representation of voice, still images, high quality audio, and video, called lossy source compression, has a host of commercial applications today. These applications include digital cellular telephones, MP3 players, DVDs, HDTV, videoconferencing, Internet telephony, and the transmission/storage of still images. The best approaches to source compression in these applications are adaptive in nature and are based upon a technique called nonlinear approximation. However, these compression methods have been designed primarily based on experiments without any guiding theory. This research investigates a new approach to adaptive lossy source compression based upon a mathematical quantity called the spectral entropy. This new approach to source compression, denoted as the SpEnt (spectral entropy) method, offers a fundamentally sound approach to adaptive source compression that has been missing heretofore. This work develops SpEnt-based lossy compression methods for speech, video, and still images that should find applications in many commercial products.The most successful methods for lossy source compression today are sample-function adaptive coders (also called input-by-input adaptive or realization-adaptive). In sample function adaptive coders, not only might the number of parameters transmitted in each block or frame vary from block-to-block (frame-to-frame), but for a given number of transmitted parameters, which parameters are transmitted in each block may vary. For such coders with a fixed set of basis functions, it is usually said that the coefficients corresponding to the best n basis functions are sent, rather than the first n, and this is called nonlinear approximation in harmonic analysis. Campbell derived the quantity that he called the coefficient rate of a random process in 1960, and he showed that the coefficient rate depends on the spectral entropy (the entropy of the power spectral density of the original process). No coding theorems were proved and no possible implications of coefficient rate for source compression were stated. Recent work by the PI and his students produced two new derivations of Campbell's coefficient rate. One derivation allows coefficient rate to be interpreted with respect to a quantity called the effective bandwidth of the process. The other derivation reveals a new approach to source compression based upon coefficient rate that adapts to each realization of the source. More specifically, by studying the dominant terms in the series expansion of the product of terms, it was shown that in a sequence of N samples of a particular coefficient, the number of coefficient samples that should be coded is proportional to the coefficient variances. Thus, whether a particular coefficient is being coded or not is changing from block-to-block, and thus, lossy compression based upon the spectral entropy clearly falls in the class of nonlinear approximation methods. Motivated by these results, this research formulates a new approach to lossy source compression, called the spectral entropy (SpEnt) method, and develops SpEnt based coders for lossy compression of wideband speech (50 Hz to 7 kHz), video, telephone bandwidth speech, and still images. Further, this work examines the role of spectral entropy and Campbell's coefficient rate as fundamental quantities in adaptive coding of a sequence of source realizations.