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首页> 外文期刊>IEEE Transactions on Information Theory >Denoising and Filtering Under the Probability of Excess Loss Criterion
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Denoising and Filtering Under the Probability of Excess Loss Criterion

机译：超额损失准则下的去噪和滤波

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Subclasses of finite alphabet denoising and filtering (causal denoising) schemes are compared. Performance is measured by the normalized cumulative loss (a.k.a. distortion), as measured by a single-letter loss function. We aim to minimize the probability that the normalized cumulative loss exceeds a given threshold. We call this quantity the probability of excess loss. Specifically, we consider a scheme to be optimal if it attains the maximal exponential decay rate of the probability of excess loss. This provides another way of comparing schemes that complements and contrasts previous work which considered the expected value of the normalized cumulative loss. In particular, the question of whether the optimal denoiser is symbol-by-symbol for an independent and identically distributed (i.i.d.) source and a discrete memoryless channel (DMC) is investigated. For Hamming loss, the optimal denoiser is proven to be symbol-by-symbol. Perhaps somewhat counterintuitively, for a general single letter loss function, the optimal scheme need not be symbol-by-symbol. The optimal denoiser requires unbounded delay and unbounded look-ahead while symbol-by-symbol schemes mandate zero delay and look-ahead. It is natural to wonder about the effect of limited delay and limited look-ahead. Consequently, finite sliding-window denoisers and finite block denoisers are defined. They are shown to perform no better than symbol-by-symbol denoisers. Finally, the effect of causality is investigated. While it is difficult to characterize the performance of filters with unbounded memory explicitly, it is shown that finite memory filters perform no better than symbol-by-symbol filters
机译：比较了有限字母降噪和滤波（因果降噪）方案的子类。性能是通过归一化的累积损耗（也称为失真）来衡量的，如通过单字母损耗函数来衡量的。我们的目标是使归一化累积损失超过给定阈值的可能性最小。我们称此数量为超额损失的可能性。具体来说，我们认为，如果方案达到过度损失概率的最大指数衰减率，则该方案是最佳方案。这提供了比较方案的另一种方式，该方案补充和对比了以前的工作，而以前的工作考虑了归一化累计损失的期望值。特别地，研究了对于独立且相同分布的（i.i.d.）源和离散的无记忆信道（DMC），最佳降噪器是否逐符号的问题。对于汉明损失，最优去噪器被证明是逐个符号的。也许有点违反直觉，对于一般的单个字母丢失函数，最佳方案不必是逐个符号的。最佳去噪器需要无限制的延迟和无限制的前瞻，而逐个符号方案要求零延迟和前瞻。很自然地想知道有限的延迟和有限的超前效果。因此，定义了有限的滑动窗口降噪器和有限的块降噪器。它们的性能不比逐个符号的去噪器好。最后，研究了因果关系的影响。虽然很难明确地描述具有无界内存的过滤器的性能，但事实表明有限内存过滤器的性能并不比逐个符号过滤器好

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