ε不敏感失真测度的率失真界
Rate-Distortion Bounds for an Epsilon-Insensitive Distortion Measure
摘要：
率失真函数的直接评估很少实现时，它是严格大于其香农下限。在本文中，我们考虑率失真函数的失真测量定义的ε不敏感的损失函数。我们首先提出了适用于任何源分布有限微分熵的香农下界。然后，重点对拉普拉斯和高斯源，我们证明了这些源的率失真函数严格大于其香农下界，并获得解析评估的率失真函数的上界。小失真限制和数值评估的界限表明，香农下限提供了一个很好的近似率失真函数的ε不敏感的失真措施。
英文摘要：
Direct evaluation of the rate-distortion function has rarely been achieved when it is strictly greater than its Shannon lower bound. In this paper, we consider the rate-distortion function for the distortion measure defined by an epsilon-insensitive loss function. We first present the Shannon lower bound applicable to any source distribution with finite differential entropy. Then, focusing on the Laplacian and Gaussian sources, we prove that the rate-distortion functions of these sources are strictly greater than their Shannon lower bounds and obtain analytically evaluable upper bounds for the rate-distortion functions. Small distortion limit and numerical evaluation of the bounds suggest that the Shannon lower bound provides a good approximation to the rate-distortion function for the epsilon-insensitive distortion measure.
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