  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.
