信道不确定性下的离散去噪算法
Algorithms for Discrete Denoising Under Channel Uncertainty
摘要：
去噪算法的目标是从其噪声破坏的观测值中重建信号。完美的重建很少是可能的，性能是在给定的保真度标准下测量的。在最近的工作中，作者解决了去噪未知的离散信号损坏的离散无记忆信道时，而不是完全已知的，只知道躺在一些不确定性的可能的渠道。一个序列的去噪器推导出这种情况下，并证明是渐近最优的最坏情况下的标准认为最相关的设置。在目前的工作中，我们解决的实施和复杂性，这个去噪参数化的标量通道，建立其实用性。我们表明，对称信道，问题可以映射到一个凸优化问题，可以有效地解决。我们还提出了实证结果表明，这些计划在实践中做得很好的潜力。我们的计划的一个关键组成部分是一个估计的不确定性集合中的信道的子集是可行的，在这个意义上能够引起噪声损坏的信号统计的一些信道输入分布。我们建立了这个估计的效率，算法和实验。我们还提出了一个修改最近开发的离散通用去噪器（DUDE），假设一个信道的基础上说，估计，并表明，在实践中，所得到的计划执行良好。具体来说，我们专注于二进制字母表的情况下，二进制对称通道，但也讨论了扩展的算法一般有限字母表和一般通道参数化的标量。
英文摘要：
The goal of a denoising algorithm is to reconstruct a signal from its noise-corrupted observations. Perfect reconstruction is seldom possible and performance is measured under a given fidelity criterion. In a recent work, the authors addressed the problem of denoising unknown discrete signals corrupted by a discrete memoryless channel when the channel, rather than being completely known, is only known to lie in some uncertainty set of possible channels. A sequence of denoisers was derived for this case and shown to be asymptotically optimal with respect to a worst-case criterion argued most relevant to this setting. In the present work we address the implementation and complexity of this denoiser for channels parametrized by a scalar, establishing its practicality. We show that for symmetric channels, the problem can be mapped into a convex optimization problem, which can be solved efficiently. We also present empirical results suggesting the potential of these schemes to do well in practice. A key component of our schemes is an estimator of the subset of channels in the uncertainty set that are feasible in the sense of being able to give rise to the noise-corrupted signal statistics for some channel input distribution. We establish the efficiency of this estimator, both algorithmically and experimentally. We also present a modification of the recently developed discrete universal denoiser (DUDE) that assumes a channel based on the said estimator, and show that, in practice, the resulting scheme performs well. For concreteness, we focus on the binary alphabet case and binary symmetric channels, but also discuss the extensions of the algorithms to general finite alphabets and to general channels parameterized by a scalar.
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