## Denoising of structured random processes. (arXiv:1901.05937v1 [cs.IT])

Denoising stationary process $(X_i)_{i \in Z}$ corrupted by additive white
Gaussian noise is a classic and fundamental problem in information theory and
statistical signal processing. Despite considerable progress in designing
efficient denoising algorithms, for general analog sources,
theoretically-founded computationally-efficient methods are yet to be found.
For instance in denoising $X^n$ corrupted by noise $Z^n$ as $Y^n=X^n+Z^n$,
given the full distribution of $X^n$, a minimum mean square error (MMSE)
denoiser needs to compute $E[X^n|Y^n]$. However, for general sources, computing
$E[X^n|Y^n]$ is computationally very challenging, if not infeasible. In this
paper, starting by a Bayesian setup, where the source distribution is fully
known, a novel denoising method, namely, quantized maximum a posteriori (Q-MAP)
denoiser, is proposed and its asymptotic performance in the high signal to
noise ratio regime is analyzed. Both for memoryless sources, and for structured
first-order Markov s查看全文