Social media platforms make tremendous amounts of data available. Often times, 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, 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, one may assume such a distorted image to be 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).

1 aNoetzel, Janis1 aWinter, Andreas uhttps://grupsderecerca.uab.cat/giq/node/85601507nas a2200169 4500008003700000020002400037245009600061210006900157260006000226300001600286520090900302100001801211700002101229700001901250700002001269856004801289 0 d a{978-1-5386-4781-3}00a{Fully Quantum Arbitrarily Varying Channels: Random Coding Capacity and Capacity Dichotomy}0 aFully Quantum Arbitrarily Varying Channels Random Coding Capacit b{IEEE; IEEE Informat Theory Soc; NSF; Huawei; Qualcomm} a{2012-2016}3 a{We consider a model of communication via a fully quantum jammer channel with quantum jammer, quantum sender and quantum receiver, which we dub quantum arbitrarily varying channel (QAVC). Restricting to finite dimensional user and jammer systems, we show, using permutation symmetry and a de Finetti reduction, how the random coding capacity (classical and quantum) of the QAVC is reduced to the capacity of a naturally associated compound channel, which is obtained by restricting the jammer to i.i.d. input states. Furthermore, we demonstrate that the shared randomness required is at most logarithmic in the block length, via a quantum version of the ``elimination of of correlation{''} using a random matrix tail bound. This implies a dichotomy theorem: either the classical capacity of the QAVC is zero, and then also the quantum capacity is zero, or each capacity equals its random coding variant.}1 aBoche, Holger1 aDeppe, Christian1 aNoetzel, Janis1 aWinter, Andreas uhttps://grupsderecerca.uab.cat/giq/node/924