We consider the problem of reconstructing a discrete-time signal (sequence)
with continuous-valued components corrupted by a known memoryless channel. When
performance is measured using a per-symbol loss function satisfying mild
regularity conditions, we develop a sequence of denoisers that, although
independent of the distribution of the underlying `clean' sequence, is
universally optimal in the limit of large sequence length. This sequence of
denoisers is universal in the sense of performing as well as any sliding window
denoising scheme which may be optimized for the underlying clean signal. Our
results are initially developed in a ``semi-stochastic'' setting, where the
noiseless signal is an unknown individual sequence, and the only source of
randomness is due to the channel noise. It is subsequently shown that in the
fully stochastic setting, where the noiseless sequence is a stationary
stochastic process, our schemes universally attain optimum performance. The
proposed schemes draw from nonparametric density estimation techniques and are
practically implementable. We demonstrate efficacy of the proposed schemes in
denoising gray-scale images in the conventional additive white Gaussian noise
setting, with additional promising results for less conventional noise
distributions.

本文研究了利用非参数密度估计技术重构有连续值分量且被已知的无记忆信道损坏的离散时间信号的问题，并提出了一系列去噪器，可以在具备温和正则条件的情况下，在大信号长度极限下实现通用最优性。