Abstract
Signal degradation is ubiquitous and computational restoration of degraded signal has been investigated for many years. Recently, it is reported that the capability of signal restoration is fundamentally limited by the perception-distortion tradeoff, i.e. the distortion and the perceptual difference between the restored signal and the ideal `original' signal cannot be made both minimal simultaneously. Distortion corresponds to signal fidelity and perceptual difference corresponds to perceptual naturalness, both of which are important metrics in practice. Besides, there is another dimension worthy of consideration, namely the semantic quality or the utility for recognition purpose, of the restored signal. In this paper, we extend the previous perception-distortion tradeoff to the case of classification-distortion-perception (CDP) tradeoff, where we introduced the classification error rate of the restored signal in addition to distortion and perceptual difference. Two versions of the CDP tradeoff are considered, one using a predefined classifier and the other dealing with the optimal classifier for the restored signal. For both versions, we can rigorously prove the existence of the CDP tradeoff, i.e. the distortion, perceptual difference, and classification error rate cannot be made all minimal simultaneously. Our findings can be useful especially for computer vision researches where some low-level vision tasks (signal restoration) serve for high-level vision tasks (visual understanding).
Abstract (translated)
信号退化是一种普遍存在的现象，对退化信号的计算恢复进行了多年的研究。近年来，据报道，信号恢复能力基本上受到感知失真权衡的限制，即恢复信号与理想“原始”信号之间的失真和感知差异不能同时最小化。失真对应于信号的保真度，知觉差异对应于知觉的自然性，两者都是实践中的重要指标。此外，还有另一个值得考虑的维度，即恢复信号的语义质量或识别用途。本文将以前的感知失真权衡扩展到分类失真感知（CDP）权衡的情况，在此基础上引入了恢复信号的分类误差率以及失真和感知差异。我们考虑了CDP权衡的两个版本，一个使用预先定义的分类器，另一个处理恢复信号的最佳分类器。对于这两个版本，我们都可以严格证明CDP权衡的存在，即失真、感知差异和分类错误率不能同时最小化。我们的研究结果特别适用于计算机视觉研究，其中一些低水平视觉任务（信号恢复）用于高水平视觉任务（视觉理解）。
URL
https://arxiv.org/abs/1904.08816
