1 research outputs found
Denoising of structured random processes
Denoising stationary process 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 corrupted by noise as ,
given the full distribution of , a minimum mean square error (MMSE)
denoiser needs to compute . However, for general sources, computing
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 sources, it is shown that, asymptotically, as
converges to zero, achieved
by Q-MAP denoiser converges to the information dimension of the source. For the
studied memoryless sources, this limit is known to be optimal. A key advantage
of the Q-MAP denoiser is that, unlike an MMSE denoiser, it highlights the key
properties of the source distribution that are to be used in its denoising.
This property dramatically reduces the computational complexity of
approximating the solution of the Q-MAP denoiser. Additionally, it naturally
leads to a learning-based denoiser. Using ImageNet database for training,
initial simulation results exploring the performance of such a learning-based
denoiser in image denoising are presented