Beckman Inst. for Adv. Sci. and Technol., Illinois Univ., Urbana, IL.
IEEE Trans Image Process. 1997;6(4):507-22. doi: 10.1109/83.563317.
The transform coding of images is analyzed from a common standpoint in order to generate a framework for the design of optimal transforms. It is argued that all transform coders are alike in the way they manipulate the data structure formed by transform coefficients. A general energy compaction measure is proposed to generate optimized transforms with desirable characteristics particularly suited to the simple transform coding operation of scalar quantization and entropy coding. It is shown that the optimal linear decoder (inverse transform) must be an optimal linear estimator, independent of the structure of the transform generating the coefficients. A formulation that sequentially optimizes the transforms is presented, and design equations and algorithms for its computation provided. The properties of the resulting transform systems are investigated. In particular, it is shown that the resulting basis are nonorthogonal and complete, producing energy compaction optimized, decorrelated transform coefficients. Quantization issues related to nonorthogonal expansion coefficients are addressed with a simple, efficient algorithm. Two implementations are discussed, and image coding examples are given. It is shown that the proposed design framework results in systems with superior energy compaction properties and excellent coding results.
为了生成最优变换的设计框架，从一个通用的观点分析了图像的变换编码。本文认为，所有的变换编码器在处理由变换系数形成的数据结构时都是相似的。提出了一种通用的能量压缩度量方法，以生成具有理想特性的优化变换，特别适合于标量量化和熵编码的简单变换编码操作。结果表明，最优的线性解码器（逆变换）必须是最优的线性估计器，与生成系数的变换结构无关。本文提出了一种顺序优化变换的公式，并提供了其计算的设计方程和算法。研究了所得变换系统的特性。特别地，结果表明，所得到的基是不正交和完备的，产生了优化的能量压缩、去相关的变换系数。用一个简单有效的算法解决了与非正交展开系数相关的量化问题。讨论了两种实现，并给出了图像编码的例子。结果表明，所提出的设计框架可得到具有优越的能量压缩特性和优异的编码效果的系统。
