31 research outputs found
Information Theoretic Principles of Universal Discrete Denoising
Today, the internet makes tremendous amounts of data widely available. Often,
the same information is behind multiple different available data sets. This
lends growing importance to latent variable models that try to learn the hidden
information from the available imperfect versions. For example, social media
platforms can contain an abundance of pictures of the same person or object,
yet all of which are taken from different perspectives. In a simplified
scenario, one may consider pictures taken from the same perspective, which are
distorted by noise. This latter application allows for a rigorous mathematical
treatment, which is the content of this contribution. We apply a recently
developed method of dependent component analysis to image denoising when
multiple distorted copies of one and the same image are available, each being
corrupted by a different and unknown noise process. In a simplified scenario,
we assume that the distorted image is corrupted by noise that acts
independently on each pixel. We answer completely the question of how to
perform optimal denoising, when at least three distorted copies are available:
First we define optimality of an algorithm in the presented scenario, and then
we describe an aymptotically optimal universal discrete denoising algorithm
(UDDA). In the case of binary data and binary symmetric noise, we develop a
simplified variant of the algorithm, dubbed BUDDA, which we prove to attain
universal denoising uniformly.Comment: 10 pages, 6 figure
Scaling of Entanglement-Assisted Communication in Amplified Fiber Links
Quantum communication technology offers several advanced strategies. However,
their practical use is often times still not well understood. In this work we
outline the theoretical communication capacity scaling in amplified fiber
links. We present a scenario in which the assistance via pre-shared
entanglement offers an arbitrary capacity, given enough bandwidth and spatial
modes are provided by the fiber. The future capacity advantage over
conventional classical techniques as well as non-assisted quantum techniques is
potentially infinite. We discuss this theoretical observation in connection to
current trends in fiber development