Whenever inspected by humans, reconstructed signals should not be distinguished from real ones. Typically, such a high perceptual quality comes at the price of high reconstruction error, and vice versa. We study this distortion-perception (DP) tradeoff over finite-alphabet channels, for the Wasserstein-$1$ distance induced by a general metric as the perception index, and an arbitrary distortion matrix. Under this setting, we show that computing the DP function and the optimal reconstructions is equivalent to solving a set of linear programming problems. We provide a structural characterization of the DP tradeoff, where the DP function is piecewise linear in the perception index. We further derive a closed-form expression for the case of binary sources.

翻译：当人类观察者检查时，重建信号不应与真实信号区分开来。通常，这种高感知质量是以高重建误差为代价的，反之亦然。我们研究了有限字母表信道上的失真-感知（DP）权衡问题，其中感知指标采用由一般度量诱导的Wasserstein-$1$距离，并考虑任意失真矩阵。在此设定下，我们证明计算DP函数与最优重建等价于求解一组线性规划问题。我们提供了DP权衡的结构性表征，即DP函数关于感知指标是分段线性的。进一步，我们推导了二元信源情形下的闭式表达式。