AI 中文总结
受在线预测算法启发提出无需信道知识的通用去噪方案，分析其性能与贝叶斯包络的差距上界，刻画其趋近贝叶斯包络的一致性条件，通过泊松信号去噪的数值评估验证方案有效性。
AI 中文摘要
受在线预测经典算法的启发，我们提出一种新型去噪方案，该方案对于生成无噪信号的源和生成带噪信号的信道的概率分布族均具有通用性。新方案不依赖精确信道知识或有限信号字母表的假设。我们的分析给出了其性能与贝叶斯包络差距的上界。对于信号为独立同分布序列且分布族可数的特殊情况，我们刻画了序列长度趋于无穷时，该方案趋近贝叶斯包络的一致性条件。我们还证明，当该一致性条件不满足时，通用去噪方案一般无法趋近贝叶斯包络，这与在线预测情形一致；此外，我们表明，所谓的插件方法（依赖于对潜在分布参数的最大似然估计）一般也无法趋近贝叶斯包络。我们还给出了该方案对泊松信号去噪的数值评估。
英文摘要
Inspired by a classical algorithm for online prediction, we propose a novel denoising scheme which is universal for families of probability distributions both in terms of the source that generates the noiseless signal and in terms of the channel that generates the noisy signal. The new denoising scheme does not rely on assumptions of exact channel knowledge or finite signal alphabets. Our analysis provides an upper bound for the performance gap compared with the Bayes envelope. For the special case in which the signal is an i.i.d. sequence and the family is countable, we characterize the consistency condition under which our scheme approaches the Bayes envelope as the length of the sequence tends to infinity. We also show that in general, approaching the Bayes envelope is not possible for a universal denoising scheme when this consistency condition is not satisfied. Furthermore, we show that, as in the online prediction case, the so-called plug-in approach (which relies on a maximum likelihood estimation of the underlying distribution parameter) does not approach the Bayes envelope in general. We also include numerical evaluations of our scheme for denoising of a Poisson signal.
